Space Travel Calculator

One small step for man, one giant leap for humanity, how fast can we travel in space is interstellar travel possible, can humans travel at the speed of light – relativistic space travel, space travel calculator – relativistic rocket equation, intergalactic travel – fuel problem, how do i calculate the travel time to other planets.

Ever since the dawn of civilization, the idea of space travel has fascinated humans! Haven't we all looked up into the night sky and dreamed about space?

With the successful return of the first all-civilian crew of SpaceX's Inspiration4 mission after orbiting the Earth for three days, the dream of space travel looks more and more realistic now.

While traveling deep into space is still something out of science fiction movies like Star Trek and Star Wars, the tremendous progress made by private space companies so far seems very promising. Someday, space travel (or even interstellar travel) might be accessible to everyone!

It's never too early to start planning for a trip of a lifetime (or several lifetimes). You can also plan your own space trip and celebrate World Space Week in your own special way!

This space travel calculator is a comprehensive tool that allows you to estimate many essential parameters in theoretical interstellar space travel . Have you ever wondered how fast we can travel in space, how much time it will take to get to the nearest star or galaxy, or how much fuel it requires? In the following article, using a relativistic rocket equation, we'll try to answer questions like "Is interstellar travel possible?" , and "Can humans travel at the speed of light?"

Explore the world of light-speed travel of (hopefully) future spaceships with our relativistic space travel calculator!

If you're interested in astrophysics, check out our other calculators. Find out the speed required to leave the surface of any planet with the escape velocity calculator or estimate the parameters of the orbital motion of planets using the orbital velocity calculator .

Although human beings have been dreaming about space travel forever, the first landmark in the history of space travel is Russia's launch of Sputnik 2 into space in November 1957. The spacecraft carried the first earthling, the Russian dog Laika , into space.

Four years later, on 12 April 1961, Soviet cosmonaut Yuri A. Gagarin became the first human in space when his spacecraft, the Vostok 1, completed one orbit of Earth.

The first American astronaut to enter space was Alan Shepard (May 1961). During the Apollo 11 mission in July 1969, Neil Armstrong and Buzz Aldrin became the first men to land on the moon. Between 1969 and 1972, a total of 12 astronauts walked the moon, marking one of the most outstanding achievements for NASA.

Buzz Aldrin climbs down the Eagle's ladder to the surface.

In recent decades, space travel technology has seen some incredible advancements. Especially with the advent of private space companies like SpaceX, Virgin Galactic, and Blue Origin, the dream of space tourism is looking more and more realistic for everyone!

However, when it comes to including women, we are yet to make great strides. So far, 566 people have traveled to space. Only 65 of them were women .

Although the first woman in space, a Soviet astronaut Valentina Tereshkova , who orbited Earth 48 times, went into orbit in June 1963. It was only in October 2019 that the first all-female spacewalk was completed by NASA astronauts Jessica Meir and Christina Koch.

Women's access to space is still far from equal, but there are signs of progress, like NASA planning to land the first woman and first person of color on the moon by 2024 with its Artemis missions. World Space Week is also celebrating the achievements and contributions of women in space this year!

In the following sections, we will explore the feasibility of space travel and its associated challenges.

Interstellar space is a rather empty place. Its temperature is not much more than the coldest possible temperature, i.e., an absolute zero. It equals about 3 kelvins – minus 270 °C or minus 455 °F. You can't find air there, and therefore there is no drag or friction. On the one hand, humans can't survive in such a hostile place without expensive equipment like a spacesuit or a spaceship, but on the other hand, we can make use of space conditions and its emptiness.

The main advantage of future spaceships is that, since they are moving through a vacuum, they can theoretically accelerate to infinite speeds! However, this is only possible in the classical world of relatively low speeds, where Newtonian physics can be applied. Even if it's true, let's imagine, just for a moment, that we live in a world where any speed is allowed. How long will it take to visit the Andromeda Galaxy, the nearest galaxy to the Milky Way?

Space travel.

We will begin our intergalactic travel with a constant acceleration of 1 g (9.81 m/s² or 32.17 ft/s²) because it ensures that the crew experiences the same comfortable gravitational field as the one on Earth. By using this space travel calculator in Newton's universe mode, you can find out that you need about 2200 years to arrive at the nearest galaxy! And, if you want to stop there, you need an additional 1000 years . Nobody lives for 3000 years! Is intergalactic travel impossible for us, then? Luckily, we have good news. We live in a world of relativistic effects, where unusual phenomena readily occur.

In the previous example, where we traveled to Andromeda Galaxy, the maximum velocity was almost 3000 times greater than the speed of light c = 299,792,458 m/s , or about c = 3 × 10 8 m/s using scientific notation.

However, as velocity increases, relativistic effects start to play an essential role. According to special relativity proposed by Albert Einstein, nothing can exceed the speed of light. How can it help us with interstellar space travel? Doesn't it mean we will travel at a much lower speed? Yes, it does, but there are also a few new relativistic phenomena, including time dilation and length contraction, to name a few. The former is crucial in relativistic space travel.

Time dilation is a difference of time measured by two observers, one being in motion and the second at rest (relative to each other). It is something we are not used to on Earth. Clocks in a moving spaceship tick slower than the same clocks on Earth ! Time passing in a moving spaceship T T T and equivalent time observed on Earth t t t are related by the following formula:

where γ \gamma γ is the Lorentz factor that comprises the speed of the spaceship v v v and the speed of light c c c :

where β = v / c \beta = v/c β = v / c .

For example, if γ = 10 \gamma = 10 γ = 10 ( v = 0.995 c v = 0.995c v = 0.995 c ), then every second passing on Earth corresponds to ten seconds passing in the spaceship. Inside the spacecraft, events take place 90 percent slower; the difference can be even greater for higher velocities. Note that both observers can be in motion, too. In that case, to calculate the relative relativistic velocity, you can use our velocity addition calculator .

Let's go back to our example again, but this time we're in Einstein's universe of relativistic effects trying to reach Andromeda. The time needed to get there, measured by the crew of the spaceship, equals only 15 years ! Well, this is still a long time, but it is more achievable in a practical sense. If you would like to stop at the destination, you should start decelerating halfway through. In this situation, the time passed in the spaceship will be extended by about 13 additional years .

Unfortunately, this is only a one-way journey. You can, of course, go back to Earth, but nothing will be the same. During your interstellar space travel to the Andromeda Galaxy, about 2,500,000 years have passed on Earth. It would be a completely different planet, and nobody could foresee the fate of our civilization.

A similar problem was considered in the first Planet of the Apes movie, where astronauts crash-landed back on Earth. While these astronauts had only aged by 18 months, 2000 years had passed on Earth (sorry for the spoilers, but the film is over 50 years old at this point, you should have seen it by now). How about you? Would you be able to leave everything you know and love about our galaxy forever and begin a life of space exploration?

Now that you know whether interstellar travel is possible and how fast we can travel in space, it's time for some formulas. In this section, you can find the "classical" and relativistic rocket equations that are included in the relativistic space travel calculator.

There could be four combinations since we want to estimate how long it takes to arrive at the destination point at full speed as well as arrive at the destination point and stop. Every set contains distance, time passing on Earth and in the spaceship (only relativity approach), expected maximum velocity and corresponding kinetic energy (if you turn on the advanced mode ), and the required fuel mass (see Intergalactic travel – fuel problem section for more information). The notation is:

  • a a a — Spaceship acceleration (by default 1   g 1\rm\, g 1 g ). We assume it is positive a > 0 a > 0 a > 0 (at least until halfway) and constant.
  • m m m — Spaceship mass. It is required to calculate kinetic energy (and fuel).
  • d d d — Distance to the destination. Note that you can select it from the list or type in any other distance to the desired object.
  • T T T — Time that passed in a spaceship, or, in other words, how much the crew has aged.
  • t t t — Time that passed in a resting frame of reference, e.g., on Earth.
  • v v v — Maximum velocity reached by the spaceship.
  • K E \rm KE KE — Maximum kinetic energy reached by the spaceship.

The relativistic space travel calculator is dedicated to very long journeys, interstellar or even intergalactic, in which we can neglect the influence of the gravitational field, e.g., from Earth. We didn't include in the destination list our closest celestial bodies, like the Moon or Mars, because it would be pointless. For them, we need different equations that also take into consideration gravitational force.

Newton's universe – arrive at the destination at full speed

It's the simplest case because here, T T T equals t t t for any speed. To calculate the distance covered at constant acceleration during a certain time, you can use the following classical formula:

Since acceleration is constant, and we assume that the initial velocity equals zero, you can estimate the maximum velocity using this equation:

and the corresponding kinetic energy:

Newton's universe – arrive at destination and stop

In this situation, we accelerate to the halfway point, reach maximum velocity, and then decelerate to stop at the destination point. Distance covered during the same time is, as you may expect, smaller than before:

Acceleration remains positive until we're halfway there (then it is negative – deceleration), so the maximum velocity is:

and the kinetic energy equation is the same as the previous one.

Einstein's universe – arrive at the destination at full speed

The relativistic rocket equation has to consider the effects of light-speed travel. These are not only speed limitations and time dilation but also how every length becomes shorter for a moving observer, which is a phenomenon of special relativity called length contraction. If l l l is the proper length observed in the rest frame and L L L is the length observed by a crew in a spaceship, then:

What does it mean? If a spaceship moves with the velocity of v = 0.995 c v = 0.995c v = 0.995 c , then γ = 10 \gamma = 10 γ = 10 , and the length observed by a moving object is ten times smaller than the real length. For example, the distance to the Andromeda Galaxy equals about 2,520,000 light years with Earth as the frame of reference. For a spaceship moving with v = 0.995 c v = 0.995c v = 0.995 c , it will be "only" 252,200 light years away. That's a 90 percent decrease or a 164 percent difference!

Now you probably understand why special relativity allows us to intergalactic travel. Below you can find the relativistic rocket equation for the case in which you want to arrive at the destination point at full speed (without stopping). You can find its derivation in the book by Messrs Misner, Thorne ( Co-Winner of the 2017 Nobel Prize in Physics ) and Wheller titled Gravitation , section §6.2. Hyperbolic motion. More accessible formulas are in the mathematical physicist John Baez's article The Relativistic Rocket :

  • Time passed on Earth:
  • Time passed in the spaceship:
  • Maximum velocity:
  • Relativistic kinetic energy remains the same:

The symbols sh ⁡ \sh sh , ch ⁡ \ch ch , and th ⁡ \th th are, respectively, sine, cosine, and tangent hyperbolic functions, which are analogs of the ordinary trigonometric functions. In turn, sh ⁡ − 1 \sh^{-1} sh − 1 and ch ⁡ − 1 \ch^{-1} ch − 1 are the inverse hyperbolic functions that can be expressed with natural logarithms and square roots, according to the article Inverse hyperbolic functions on Wikipedia.

Einstein's universe – arrive at destination point and stop

Most websites with relativistic rocket equations consider only arriving at the desired place at full speed. If you want to stop there, you should start decelerating at the halfway point. Below, you can find a set of equations estimating interstellar space travel parameters in the situation when you want to stop at the destination point :

So, after all of these considerations, can humans travel at the speed of light, or at least at a speed close to it? Jet-rocket engines need a lot of fuel per unit of weight of the rocket. You can use our rocket equation calculator to see how much fuel you need to obtain a certain velocity (e.g., with an effective exhaust velocity of 4500 m/s).

Hopefully, future spaceships will be able to produce energy from matter-antimatter annihilation. This process releases energy from two particles that have mass (e.g., electron and positron) into photons. These photons may then be shot out at the back of the spaceship and accelerate the spaceship due to the conservation of momentum. If you want to know how much energy is contained in matter, check out our E = mc² calculator , which is about the famous Albert Einstein equation.

Now that you know the maximum amount of energy you can acquire from matter, it's time to estimate how much of it you need for intergalactic travel. Appropriate formulas are derived from the conservation of momentum and energy principles. For the relativistic case:

where e x e^x e x is an exponential function, and for classical case:

Remember that it assumes 100% efficiency! One of the promising future spaceships' power sources is the fusion of hydrogen into helium, which provides energy of 0.008 mc² . As you can see, in this reaction, efficiency equals only 0.8%.

Let's check whether the fuel mass amount is reasonable for sending a mass of 1 kg to the nearest galaxy. With a space travel calculator, you can find out that, even with 100% efficiency, you would need 5,200 tons of fuel to send only 1 kilogram of your spaceship . That's a lot!

So can humans travel at the speed of light? Right now, it seems impossible, but technology is still developing. For example, a photonic laser thruster is a good candidate since it doesn't require any matter to work, only photons. Infinity and beyond is actually within our reach!

To calculate the time it takes to travel to a specific star or galaxy using the space travel calculator, follow these steps:

  • Choose the acceleration : the default mode is 1 g (gravitational field similar to Earth's).
  • Enter the spaceship mass , excluding fuel.
  • Select the destination : pick the star, planet, galaxy you want to travel to from the dropdown menu.
  • The distance between the Earth and your chosen stars will automatically appear. You can also input the distance in light-years directly.
  • Define the aim : select whether you aim to " Arrive at destination and stop " or “ Arrive at destination at full speed ”.
  • Pick the calculation mode : opt for either " Einstein's universe " mode for relativistic effects or " Newton's universe " for simpler calculations.
  • Time passed in spaceship : estimated time experienced by the crew during the journey. (" Einstein's universe " mode)
  • Time passed on Earth : estimated time elapsed on Earth during the trip. (" Einstein's universe " mode)
  • Time passed : depends on frame of reference, e.g., on Earth. (" Newton's universe " mode)
  • Required fuel mass : estimated fuel quantity needed for the journey.
  • Maximum velocity : maximum speed achieved by the spaceship.

How long does it take to get to space?

It takes about 8.5 minutes for a space shuttle or spacecraft to reach Earth's orbit, i.e., the limit of space where the Earth's atmosphere ends. This dividing line between the Earth's atmosphere and space is called the Kármán line . It happens so quickly because the shuttle goes from zero to around 17,500 miles per hour in those 8.5 minutes .

How fast does the space station travel?

The International Space Station travels at an average speed of 28,000 km/h or 17,500 mph . In a single day, the ISS can make several complete revolutions as it circumnavigates the globe in just 90 minutes . Placed in orbit at an altitude of 350 km , the station is visible to the naked eye, looking like a dot crossing the sky due to its very bright solar panels.

How do I reach the speed of light?

To reach the speed of light, you would have to overcome several obstacles, including:

Mass limit : traveling at the speed of light would mean traveling at 299,792,458 meters per second. But, thanks to Einstein's theory of relativity, we know that an object with non-zero mass cannot reach this speed.

Energy : accelerating to the speed of light would require infinite energy.

Effects of relativity : from the outside, time would slow down, and you would shrink.

Why can't sound travel in space?

Sound can’t travel in space because it is a mechanical wave that requires a medium to propagate — this medium can be solid, liquid, or gas. In space, there is no matter, or at least not enough for sound to propagate. The density of matter in space is of the order 1 particle per cubic centimeter . While on Earth , it's much denser at around 10 20 particles per cubic centimeter .

BMR - Harris-Benedict equation

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1) electromagnetic fields, 2) magnetic explosions, 3) wave-particle interactions.

One hundred years ago today, on May 29, 1919, measurements of a solar eclipse offered verification for Einstein’s theory of general relativity. Even before that, Einstein had developed the theory of special relativity, which revolutionized the way we understand light. To this day, it provides guidance on understanding how particles move through space — a key area of research to keep spacecraft and astronauts safe from radiation.

The theory of special relativity showed that particles of light, photons, travel through a vacuum at a constant pace of 670,616,629 miles per hour — a speed that’s immensely difficult to achieve and impossible to surpass in that environment. Yet all across space, from black holes to our near-Earth environment, particles are, in fact, being accelerated to incredible speeds, some even reaching 99.9% the speed of light.

One of NASA’s jobs is to better understand how these particles are accelerated. Studying these superfast, or relativistic, particles can ultimately help protect missions exploring the solar system, traveling to the Moon, and they can teach us more about our galactic neighborhood: A well-aimed near-light-speed particle can trip onboard electronics and too many at once could have negative radiation effects on space-faring astronauts as they travel to the Moon — or beyond.

Here are three ways that acceleration happens.

Most of the processes that accelerate particles to relativistic speeds work with electromagnetic fields — the same force that keeps magnets on your fridge. The two components, electric and magnetic fields, like two sides of the same coin, work together to whisk particles at relativistic speeds throughout the universe.

In essence, electromagnetic fields accelerate charged particles because the particles feel a force in an electromagnetic field that pushes them along, similar to how gravity pulls at objects with mass. In the right conditions, electromagnetic fields can accelerate particles at near-light-speed.

On Earth, electric fields are often specifically harnessed on smaller scales to speed up particles in laboratories. Particle accelerators, like the Large Hadron Collider and Fermilab, use pulsed electromagnetic fields to accelerate charged particles up to 99.99999896% the speed of light. At these speeds, the particles can be smashed together to produce collisions with immense amounts of energy. This allows scientists to look for elementary particles and understand what the universe was like in the very first fractions of a second after the Big Bang. 

Download related video from NASA Goddard’s Scientific Visualization Studio

Magnetic fields are everywhere in space, encircling Earth and spanning the solar system. They even guide charged particles moving through space, which spiral around the fields.

When these magnetic fields run into each other, they can become tangled. When the tension between the crossed lines becomes too great, the lines explosively snap and realign in a process known as magnetic reconnection. The rapid change in a region’s magnetic field creates electric fields, which causes all the attendant charged particles to be flung away at high speeds. Scientists suspect magnetic reconnection is one way that particles — for example, the solar wind, which is the constant stream of charged particles from the Sun — is accelerated to relativistic speeds.

Those speedy particles also create a variety of side-effects near planets.  Magnetic reconnection occurs close to us at points where the Sun’s magnetic field pushes against Earth’s magnetosphere — its protective magnetic environment. When magnetic reconnection occurs on the side of Earth facing away from the Sun, the particles can be hurled into Earth’s upper atmosphere where they spark the auroras. Magnetic reconnection is also thought to be responsible around other planets like Jupiter and Saturn, though in slightly different ways.

NASA’s Magnetospheric Multiscale spacecraft were designed and built to focus on understanding all aspects of magnetic reconnection. Using four identical spacecraft, the mission flies around Earth to catch magnetic reconnection in action. The results of the analyzed data can help scientists understand particle acceleration at relativistic speeds around Earth and across the universe.

Particles can be accelerated by interactions with electromagnetic waves, called wave-particle interactions. When electromagnetic waves collide, their fields can become compressed. Charged particles bouncing back and forth between the waves can gain energy similar to a ball bouncing between two merging walls.

These types of interactions are constantly occurring in near-Earth space and are responsible for accelerating particles to speeds that can damage electronics on spacecraft and satellites in space. NASA missions, like the Van Allen Probes , help scientists understand wave-particle interactions.

Wave-particle interactions are also thought to be responsible for accelerating some cosmic rays that originate outside our solar system. After a supernova explosion, a hot, dense shell of compressed gas called a blast wave is ejected away from the stellar core. Filled with magnetic fields and charged particles, wave-particle interactions in these bubbles can launch high-energy cosmic rays at 99.6% the speed of light. Wave-particle interactions may also be partially responsible for accelerating the solar wind and cosmic rays from the Sun.

Download this and related videos in HD formats from NASA Goddard’s Scientific Visualization Studio

By Mara Johnson-Groh NASA’s Goddard Space Flight Center , Greenbelt, Md.

Space Travel Calculator

Traveling in space: an introduction, before einstein: non-relativistic space travel, how to calculate the travel time: speed of light as ultimate speed limit, travel in a relativistic spaceship: calculations for time and speed, fuel calculator for space travel: astronomical pit-stop.

Humans are barely a spacefaring civilization, as we only entered our spatial neighborhood: our space travel calculator will answer the question "what if..."

  • What if I board a ship that travels in space at constant acceleration?
  • What if I can ignore the speed of light in calculating the travel time in space?
  • What if Einstein was right (he is) and space travel is relativistic?

And much more.

Traveling in space is a whole different kettle of fish. No air means no friction, the ideal rocket equation rules undisputed, and usually, your destination is not exactly behind the corner.

Spaceflight is hard: humanity ventured as far as the Moon (slightly beyond if you consider the orbits around it) and did so only six times between 1969 and 1972. Since then, we have only ventured into Earth's orbit. However, the push for exploration didn't make vane; we are limited by technology and physics!

In this tool, we will consider what would happen to a spaceship that travels in space at constant acceleration . The good news is that since there is no friction up there, we don't have to burn fuel to maintain a constant speed. If our engine is on, we are accelerating (in fact, most of the time spent in space by a craft consists of coasting , engines off, and patiently waiting to reach the time for a correction in the trajectory).

Input the spacecraft mass, your destination (trust us on the directions), and what you want to do precisely: a fly-by or a full stop (in this case, we will calculate your space travel in two parts, the latter at a constant deceleration that would bring you at destination with zero speed, à la Expanse ).

🙋 Feel free to input a destination of your choice by inserting any distance in the proper variable's field.

The last choice before the departure: is your universe following the rules of Newton or Einstein? We'll see the differences in a second. Board the spaceship Calculator , buckle up and wait for the countdown.

🔎 To explain our space travel calculator, we will assume a constant 1 g 1g 1 g acceleration (the most comfortable for a human) and an empty spacecraft mass of 1.000  t 1.000\ \text{t} 1.000   t . The destination we chose for our spaceship calculator is the center of our galaxy , a supermassive black hole 27 , 900 27,900 27 , 900 light years away.

Gravity rules Newton's universe alone. There is no speed limit and no one of the weird relativistic effects we will meet shortly. We calculate your space travel using the equation for motion in a purely classic framework.

If you choose to arrive at your destination at the maximum speed possible, then we input your acceleration in space in the formula:

  • a a a — The acceleration ;
  • t t t — The time of flight ; and
  • v f v_{\text{f}} v f ​ — The final speed .

To calculate the time, we use the distance d d d :

If you plan on visiting Sagittarius A, then you need to decelerate. In this case, the final speed is $$v_{\text{ f}} = 0$$, obviously, and the time of flight changes accordingly:

The time required to travel such a distance is... astronomical . As you can see in our constant acceleration space travel calculator:

  • For a maximum speed flyby, the time is 232.5  y 232.5\ \text{y} 232.5   y ; and
  • To stop at destination, 328.8  y 328.8\ \text{y} 328.8   y .

The maximum velocity in the first case is 240 240 240 times the speed of light. If Einstein could hear this, he would be utterly disappointed. To right this wrong, we will calculate the travel time if the speed of light genuinely represent an impenetrable barrier.

We enter the territory of relativistic effects . Relativistic space travel calculations are a bit more complicated. In layman's terms, the faster you go, the slower time passes for you, and the perceived length for you, the traveler, also reduces. These two effects, described by the theory of special relativity, are coded in two equations:

γ \gamma γ is the Lorentz factor :

Where β \beta β is the ratio, always smaller than 1 1 1 , between the spacecraft's speed and the light's speed.

To find the time required to reach a given destination in a universe ruled by Einstein's relativity theory, with constant acceleration in space, the formula we've seen before must be changed and split: time is relative, and because of this, the trip will have two durations.

For a maximum speed fly-by from the perspective of a stationary observer:

The duration of the journey as experienced by our astronauts is:

In these equations, d d d is the distance. In this relativistic framework, we calculate it with the formula:

Lastly, we can calculate the maximum velocity in relativistic space travel without deceleration:

In these formulas, we used the hyperbolic functions : visit our hyperbolic functions calculator to learn more about them.

For a visit to Sagittarius A*, the times required for relativistic travel at constant 1 g 1g 1 g acceleration would be:

The difference is noticeable , to say the least. The maximum speed would be 0.4 0.4 0.4 parts per billion smaller than the speed of light: the dilation effects would be extreme.

The formulas would change slightly if we wanted to stop at our destination. From the observer's point of view, the time passed is:

In our example, t = 27 , 902  y t=27,902\ \text{y} t = 27 , 902   y . From the perspective of the travelers, the time is:

Corresponding to 20  y 20\ \text{y} 20   y . The perceived time is much longer than before: almost two times. This is because the astronauts would not "enjoy" a noticeable time dilation during the initial and final parts of the journey.

For distance and maximum velocity, we apply the following formulas:

You can use our space travel calculator also to find the kinetic energy of an object moving at such speeds. You won't be surprised to learn that the kinetic energy of an object moving almost at the speed of light is astronomical .

Rocketry is another word for mastery in fuel economy : you can learn everything about it with our rocket thrust calculator . Imagining an interstellar journey using chemical, ionic, or nuclear rockets is wishful thinking. To even have a shot to the stars, we need to learn how to control the mass to energy conversion . The annihilation reaction between matter and antimatter would have a perfect yield, converting all the mass involved into energy .

Assuming this 100 % 100\% 100% efficiency, we can compute the required mass for our journey both in the classic and relativistic case:

The results of these equations are disheartening: to send our ship to the center of our galaxy and stop there, the required fuel in the relativistic case is almost 830 830 830 billion tons.

Will humans ever reach the star? Will Enterprises and Millenium Falcons cross the darkness between other Suns? With the technology of today, it's unlikely. But things change quickly, and what looks impossible today may be tomorrow's science. Be hopeful and keep dreaming about touching the sky.

Schwarzschild radius

Time dilation.

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Warp drives: Physicists give chances of faster-than -light space travel a boost

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The closest star to Earth is Proxima Centauri. It is about 4.25 light-years away, or about 25 trillion miles (40 trillion km). The fastest ever spacecraft, the now- in-space Parker Solar Probe will reach a top speed of 450,000 mph. It would take just 20 seconds to go from Los Angeles to New York City at that speed, but it would take the solar probe about 6,633 years to reach Earth’s nearest neighboring solar system.

If humanity ever wants to travel easily between stars, people will need to go faster than light. But so far, faster-than-light travel is possible only in science fiction.

In Issac Asimov’s Foundation series , humanity can travel from planet to planet, star to star or across the universe using jump drives. As a kid, I read as many of those stories as I could get my hands on. I am now a theoretical physicist and study nanotechnology, but I am still fascinated by the ways humanity could one day travel in space.

Some characters – like the astronauts in the movies “Interstellar” and “Thor” – use wormholes to travel between solar systems in seconds. Another approach – familiar to “Star Trek” fans – is warp drive technology. Warp drives are theoretically possible if still far-fetched technology. Two recent papers made headlines in March when researchers claimed to have overcome one of the many challenges that stand between the theory of warp drives and reality.

But how do these theoretical warp drives really work? And will humans be making the jump to warp speed anytime soon?

A circle on a flat blue plane with the surface dipping down in front and rising up behind.

Compression and expansion

Physicists’ current understanding of spacetime comes from Albert Einstein’s theory of General Relativity . General Relativity states that space and time are fused and that nothing can travel faster than the speed of light. General relativity also describes how mass and energy warp spacetime – hefty objects like stars and black holes curve spacetime around them. This curvature is what you feel as gravity and why many spacefaring heroes worry about “getting stuck in” or “falling into” a gravity well. Early science fiction writers John Campbell and Asimov saw this warping as a way to skirt the speed limit.

What if a starship could compress space in front of it while expanding spacetime behind it? “Star Trek” took this idea and named it the warp drive.

In 1994, Miguel Alcubierre, a Mexican theoretical physicist, showed that compressing spacetime in front of the spaceship while expanding it behind was mathematically possible within the laws of General Relativity . So, what does that mean? Imagine the distance between two points is 10 meters (33 feet). If you are standing at point A and can travel one meter per second, it would take 10 seconds to get to point B. However, let’s say you could somehow compress the space between you and point B so that the interval is now just one meter. Then, moving through spacetime at your maximum speed of one meter per second, you would be able to reach point B in about one second. In theory, this approach does not contradict the laws of relativity since you are not moving faster than light in the space around you. Alcubierre showed that the warp drive from “Star Trek” was in fact theoretically possible.

Proxima Centauri here we come, right? Unfortunately, Alcubierre’s method of compressing spacetime had one problem: it requires negative energy or negative mass.

A 2–dimensional diagram showing how matter warps spacetime

A negative energy problem

Alcubierre’s warp drive would work by creating a bubble of flat spacetime around the spaceship and curving spacetime around that bubble to reduce distances. The warp drive would require either negative mass – a theorized type of matter – or a ring of negative energy density to work. Physicists have never observed negative mass, so that leaves negative energy as the only option.

To create negative energy, a warp drive would use a huge amount of mass to create an imbalance between particles and antiparticles. For example, if an electron and an antielectron appear near the warp drive, one of the particles would get trapped by the mass and this results in an imbalance. This imbalance results in negative energy density. Alcubierre’s warp drive would use this negative energy to create the spacetime bubble.

But for a warp drive to generate enough negative energy, you would need a lot of matter. Alcubierre estimated that a warp drive with a 100-meter bubble would require the mass of the entire visible universe .

In 1999, physicist Chris Van Den Broeck showed that expanding the volume inside the bubble but keeping the surface area constant would reduce the energy requirements significantly , to just about the mass of the sun. A significant improvement, but still far beyond all practical possibilities.

A sci-fi future?

Two recent papers – one by Alexey Bobrick and Gianni Martire and another by Erik Lentz – provide solutions that seem to bring warp drives closer to reality.

Bobrick and Martire realized that by modifying spacetime within the bubble in a certain way, they could remove the need to use negative energy. This solution, though, does not produce a warp drive that can go faster than light.

[ Over 100,000 readers rely on The Conversation’s newsletter to understand the world. Sign up today .]

Independently, Lentz also proposed a solution that does not require negative energy. He used a different geometric approach to solve the equations of General Relativity, and by doing so, he found that a warp drive wouldn’t need to use negative energy. Lentz’s solution would allow the bubble to travel faster than the speed of light.

It is essential to point out that these exciting developments are mathematical models. As a physicist, I won’t fully trust models until we have experimental proof. Yet, the science of warp drives is coming into view. As a science fiction fan, I welcome all this innovative thinking. In the words of Captain Picard , things are only impossible until they are not.

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Relativistic Flight Mechanics and Space Travel

  • Richard F. Tinder 0

Washington State University, USA

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Part of the book series: Synthesis Lectures on Engineering, Science, and Technology (SLEST)

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Table of contents (6 chapters)

Front matter, introduction.

Richard F. Tinder

Relativistic Rocket Mechanics

Space travel and the photon rocket, minkowski diagrams, k-calculus, and relativistic effects, other prospective transport systems for relativistic space travel, back matter.

Book Title : Relativistic Flight Mechanics and Space Travel

Authors : Richard F. Tinder

Series Title : Synthesis Lectures on Engineering, Science, and Technology

DOI : https://doi.org/10.1007/978-3-031-79297-7

Publisher : Springer Cham

eBook Packages : Synthesis Collection of Technology (R0) , eBColl Synthesis Collection 1

Copyright Information : Springer Nature Switzerland AG 2007

Softcover ISBN : 978-3-031-79296-0 Published: 31 December 2007

eBook ISBN : 978-3-031-79297-7 Published: 01 June 2022

Series ISSN : 2690-0300

Series E-ISSN : 2690-0327

Edition Number : 1

Number of Pages : XXII, 117

Topics : Engineering Design , Materials Engineering , Professional & Vocational Education

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[Physics FAQ] - [Copyright]

Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for correcting the fuel equation. Original by Philip Gibbs, 1996.

The Relativistic Rocket

The theory of relativity sets a severe limit to our ability to explore the galaxy in space ships.  As an object approaches the speed of light, more and more energy is needed to maintain its acceleration, with the result that to reach the speed of light, an infinite amount of energy would be required.  It seems that the speed of light is an absolute barrier which cannot be reached or surpassed by massive objects (see the FAQ article on faster than light travel ).  Given that our galaxy is about 80,000 light years across, there seems little hope for us to get very far in galactic terms.

Science fiction writers might make use of worm holes or warp drives to overcome this restriction, but it is not clear that such things can ever be made to work in reality.  Another way to get around the problem may be to use the relativistic effects of time dilation and length contraction to cover large distances within a reasonable time span for those aboard a space ship.  When a rocket accelerates at $1\;\text{g}$ (9.81 m/s$^2$), its crew experiences the equivalent of a gravitational field with the same strength as that on Earth.  If this acceleration could be maintained for long enough, the crew would eventually reap the benefits of the relativistic effects that increase the effective rate of travel.

What then, are the appropriate equations for the relativistic rocket?

First of all, we need to be clear what we mean by continuous acceleration at $1\;\text{g}$.  The acceleration of the rocket must be measured at any given instant in a non-accelerating frame of reference travelling at the same instantaneous speed as the rocket (see the FAQ article on accelerating clocks ), because this is the acceleration that its occupants would physically feel—and we want them to accelerate at a comfortable rate that has the effect of mimicking their weight on Earth.  We'll call this acceleration $a$.  The proper time measured by the crew of the rocket (i.e. how much they age) is called $T$, and the time measured in the non-accelerating frame of reference in which they started (e.g. Earth) is $t$.  We assume that the stars are essentially at rest in this Earth frame.  The distance covered by the rocket as measured in this frame of reference is $d$, and the rocket's velocity is $v$.  The time dilation or length-contraction factor at any instant is the gamma factor $\gamma$.

The relativistic equations for a rocket with constant positive acceleration $a > 0$ are the following.  First, define the hyperbolic trigonometric functions sh, ch, and th (also known as sinh, cosh, and tanh): \begin{align} \text{sh } x &= (e^x - e^{-x})/2 \,,\\ \text{ch } x &= (e^x + e^{-x})/2 \,,\\ \text{th } x &= \text{sh } x/\text{ch } x \,. \end{align} Using these, the rocket equations are

These equations are valid in any consistent system of units, such as seconds for time, metres for distance, metres per second for speeds and metres per second squared for accelerations.  In these units $c\simeq 3 \times 10^8$ m/s.  To do some example calculations, it's easier to use units of years for time and light years ("ly") for distance.  Then $c = 1$ ly/yr and $g\simeq 1.03$ ly/yr$^2$.  Here are some typical values of the various parameters for $a = 1$ g. \begin{array}{lllll} \hline T\text{ (years)} & t\text{ (years)} & d\text{ (ly)} & v/c & \gamma\\ \hline 1 & 1.19 & 0.56 & 0.77 & 1.58 \\ 2 & 3.75 & 2.90 & 0.97 & 3.99 \\ 5 & 83.7 & 82.7 & 0.99993 & 86.2 \\ 8 & 1840 & 1839 & 0.9999998 & 1895 \\ 12 & 113,\!243 & 113,\!242 & 0.99999999996 & 116,\!641 \\ \hline \end{array}

In theory, then, you can travel across the galaxy in just 12 years of your own time.  If you want to arrive at your destination and stop, then let's say you turn your rocket around at the halfway point and decelerate at 1 g.  In that case it will take nearly twice as long in terms of proper time $T$ for the longer journeys; the elapsed time $t$ on Earth will be only a little longer, since in both cases the rocket is spending most of its time at a speed near that of light.  We can still use the above equations to work this out, since although the acceleration is now negative, we can "run the film backwards" to reason that they must still apply.  Here's the general formula: $$ T = {2c\over g}\, \text{ch}^{-1}\left({gd\over 2c^2} + 1\right) . $$ Here are some of the times you will age when journeying to a few well known space marks, arriving at low speed: \begin{array}{lll} \hline d\text{ (ly)} & \text{Stopping at:} & T\text{ (years)} \\ \hline 4.3 & \text{Nearest star} & 3.6 \\ 27 & \text{Vega} & 6.6 \\ 30,\!000 & \text{Centre of our galaxy} & 20 \\ 2,\!000,\!000 & \text{Andromeda Galaxy} & 28 \\ n & \text{Anywhere, but see} & 1.94\, \text{ch}^{-1}(n/1.94 + 1) \\[-1ex] & \text{next sentence} & \\ \hline \end{array} For distances greater than about a thousand million light years, the formulae given here are inadequate because the universe is expanding.  General Relativity would have to be used to work out those cases.

If you wish to pass by a distant star and return to Earth, but you don't need to stop there, then a looping route is better than a straight-out-and-back route.  A good course might be to head out at constant acceleration in a direction at about 45° to that of your destination.  At the appropriate point, you start a long arc such that the centrifugal acceleration you experience is also equivalent to Earth's gravity.  After 3/4 of a circle, you decelerate in a straight line until you arrive home.

To experiment with the quantities above, see David Wright's INTO THE FUTURE web page.

What if the universe were newtonian?

As a comparison to the above values of $T$, what if relativity didn't apply: that is, how would $T$ depend on $d$ in a fully newtonian universe, so that the rocket could accelerate at $1\;\text{g}$ forever?  We'll call the elapsed time $T'$ here so as not to confuse it with the $T$ above that we are going to compare it with.  Begin with the usual equation for constant acceleration from a standing start, "$\text{displacement} = 1/2 \times \text{acceleration} \times \text{time}^2$".  Consider that, by symmetry, $T'/2$ is the time to get to the half-way point, so $$ d/2 = 1/2 \,\; a \, (T'/2)^2 \,, $$ which means that $$ T' = 2 \sqrt{d/a\,} \,. $$ With $d = n$ light years and $a = 1\;\text{g} = 1.03$ ly/yr$^2$, this becomes $$ T' = 1.97\sqrt{n\,}\;\text{years}. $$

Here is the above table amended to include comparison values of $T'$: \begin{array}{llll} \hline d\text{ (ly)} & \text{Stopping at:} & T\text{ [relativistic universe] (years)} & T'\text{ [newtonian universe] (years)} \\ \hline 4.3 & \text{Nearest star} & 3.6 & 4.1 \\ 27 & \text{Vega} & 6.6 & 10.2 \\ 30,\!000 & \text{Centre of our galaxy} & 20 & 341 \\ 2,\!000,\!000 & \text{Andromeda Galaxy} & 28 & 2786 \\ n & \text{Anywhere} & 1.94\, \text{ch}^{-1}(n/1.94 + 1) & 1.97 \sqrt{n\,}\\ \hline \end{array} You can see that in our relativistic universe, even though the rocket's speed is limited to the speed of light (unlike in the newtonian universe, which has no speed limit), the very high values attained by the time-dilation factor $\gamma$ on long trips ensure that the relativistic rocket passengers still age far, far less than do the newtonian passengers undergoing the same trip.

Below the rocket, something strange is happening...

But now, back to the relativistic rocket...

In the rocket, you can make measurements of the world around you.  One thing you might do is ask how the distance to an interesting star you are headed towards changes with $T$, the time on your clock.  At blast-off ($t = T = 0$) the rocket is at rest, so this distance initially equals the distance $D$ to the star in the non-accelerating frame.  But once you are moving, however you choose to measure this distance, at each moment it will be reduced by your current distance $d$ travelled in the non-accelerating frame, as well as the whole lot contracted by the current factor of $\gamma$.  Eventually you will pass the star and it will recede behind you.  The distance you measure to it at time $T$ is \begin{equation}\label{D-d-on-gamma} {D - d\over \gamma} = {D + c^2/a\over \text{ch}(aT/c)} - {c^2\over a} \,. \end{equation} A plot of this distance as a function of $T$ shows that, as expected, it starts at $D$, then reduces to zero as you pass the star.  Then it becomes negative as the star moves behind you.  As $T$ goes to infinity, the distance asymptotes to a value of $-c^2/a$.  That means that from your vantage point in the rocket, everything in the universe is falling from "above" to "below" the rocket, but never receding any farther than a distance of $-c^2/a$ as measured by you.  It all piles up just short of this distance, asymptoting to a plane called a horizon .  You see this horizon actually form as the rocket accelerates, because there comes a time when no signal emitted from "below" the horizon can ever reach you.  Everything falls towards that plane, and as each object approaches that plane you see it begin to redden and fade, due to the increasing red shift of its light, because you are accelerating.  Finally it fades out of visibility.  In fact, as anything gets closer to the horizon, its rate of ageing as measured by you slows more and more; time comes to a complete halt on the horizon.  The horizon is a dark plane that appears to be swallowing everything in the universe!  But of course, nothing strange is noticed by the non-accelerating Earth observers.  There is no horizon anywhere for them.

And inside the rocket, something strange is also happening...

Whereas time slows to a stop a certain distance below the rocket, it speeds up above the rocket (that is, in the direction in which it's travelling from Earth's perspective).  This effect could, in principle, be measured inside the rocket too: a clock attached to the rocket's ceiling (i.e. in the rocket's "nose") ages faster than a clock attached to its floor.

For a standard-sized rocket with a survivable acceleration, this difference in how fast things age within its cabin is very small.  Even so, it tells us something fundamental about gravity, via Einstein's equivalence principle .  Einstein postulated that any experiment done in a real gravitational field—provided that experiment has a "small" extent in space and time—will give a result indistinguishable from the same experiment done in the above "uniformly accelerating" rocket.  These space and time extents must be small so that no "tidal" effect due to the inhomogeneous nature of the real gravity field will be apparent.  Analogously, even though Earth is not flat, we can treat it as being flat on a small patch of ground: by this we mean that as we consider smaller and smaller patches of ground, the error we make by treating each patch as flat grows smaller at a faster rate than the size of the patch decreases.  In a similar way, the errors we make by treating the gravity in a sequence of ever-smaller regions of spacetime as equivalent to the interior of a uniformly accelerated rocket in the absence of gravity decrease at a faster rate than do the sizes of those spacetime regions.  So the idea that the rocket's ceiling ages faster than its floor (and that includes the ageing of any bugs sitting on these) transfers to gravity: the ceiling of the room in which you now sit is ageing faster than its floor; and your head is ageing faster than your feet.  This has nothing to do with your centripetal acceleration as Earth turns; it is purely about Earth's gravitational field.

This difference in ageing rates on Earth has been verified experimentally.  It is the content of Einstein's general theory of relativity , and for the weak gravity that exists in Earth's vicinity, we can get quite a good precision by calling in the analogy of the rocket and invoking the equivalence principle.  And general relativity goes on to make itself felt in the GPS satellite system.  Because the satellites that broadcast data to your GPS receiver are ageing quickly compared to clocks on Earth, they must be set to "tick" slightly slowly in the factory by the same factor, before they are sent up to orbit.  That way, once they are in orbit, they will tick at the same rate as clocks on Earth.

The Equivalence Principle

We can use the above equation for the distance $(D - d)/\gamma$ that you measure to your destination star to illustrate the equivalence principle.  As you accelerated from Earth and headed towards that star, it was as if the star began falling towards you with an acceleration of $a$.  After a time measured by you as $T$, the distance you measure to the star is equation \eqref{D-d-on-gamma} above.  Suppose that either your acceleration $a$ is small enough, or the time interval $T$ is small enough, so that the quantity $aT$ is much less than the speed of light $c$; in other words, $aT/c \ll 1$.  Now consider that for any $x$, the hyperbolic cosine can be written as a series $$ \text{ch}\; x = 1 + {x^2\over 2\textit{!}} + {x^4\over 4\textit{!}} + {x^6\over 6\textit{!}} + \dots \,. $$ Set $x = aT/c$ and, because $x$ is small, drop all terms in the expansion of the hyperbolic cosine higher than $x^2$.  Further, remember that for all $|x| < 1$ we can write $$ {1\over 1+x} = 1 - x + x^2 - x^3 + \dots \,, $$ in which case $$ {1\over \text{ch}\;x} \simeq 1 - x^2/2 \quad \text{for } |x| < 1 \,. $$ In that case, we can approximate the distance you measure to the star as \begin{align} {D - d\over \gamma} &= {D + c^2/a \over \text{ch}(aT/c)} - {c^2\over a} \\[1ex] &\simeq \left(D + {c^2\over a}\right) \left[1 - {a^2 T^2\over 2c^2}\right] - {c^2\over a} \\[1ex] &= D + {c^2\over a} - {D a^2 T^2\over 2c^2} - {aT^2\over 2} - {c^2\over a} \\[1ex] &= D - {D a^2 T^2\over 2c^2} - {aT^2\over 2} . \end{align} The second term in the last line divided by the third term equals $Da/c^2$.  When $D$ and $a$ aren't too large (meaning $Da/c^2$ is much less than 1), we can then ignore the second term, to write the distance you measure to the star as $$ \text{distance to star} \simeq D - aT^2/2 \,. $$ Now, what would Newton say?  He'd say that the star had been falling towards you for a time $T$ with acceleration $a$, in which case it must've covered a distance of $aT^2/2$ from its original distance from you of $D$; he'd thus conclude its distance from you is $D - aT^2/2$ exactly.  So you can see that his non-relativistic result agrees with the relativistic one when the combinations of the various parameters are much less than the speed of light.  That's how the equivalence principle works.

How much fuel is needed?

Sadly, there are a few technical difficulties you will have to overcome before you can head off into space.  One of these difficulties is creating your propulsion system and generating fuel.  The most efficient theoretical way to propel the rocket is to use a "photon drive".  This would convert mass to photons or other massless particles which shoot out the back of the rocket.  Perhaps this may even be technically feasible if we ever produce an antimatter-driven "graser" (gamma-ray laser).

Remember that energy is equivalent to mass, so provided mass can be converted to 100% radiation by means of matter–antimatter annihilation, we just want to find the mass $M$ of the fuel required to accelerate the payload $m$.  The answer is most easily worked out by conservation of energy and momentum.

First: conservation of energy

Second: conservation of momentum.

The total momentum before blast-off is zero in the Earth frame: $$ p_\text{initial} = 0 \,. $$ At the trip's end the fuel has all been converted to light with momentum of magnitude $E_L/c$, but in the opposite direction to the rocket.  So the final momentum is $$ p_\text{final} = \gamma\, mv - E_L/c \,. $$ By conservation of momentum these two momentua must be equal, so our second conservation equation is: \begin{equation}\label{old-2} 0 = \gamma\, mv - E_L/c \,. \end{equation} Eliminating $E_L$ from equations \eqref{old-1} and \eqref{old-2} gives $$ (M+m)c^2 - \gamma\, mc^2 = \gamma \,mvc \,, $$ so that the fuel-to-payload ratio is $$ M/m = \gamma (1 + v/c) - 1 \,. $$ This equation is true irrespective of how the ship accelerates to velocity $v$, but if it accelerates at a constant apparent rate $a$, then \begin{align} M/m &= \gamma (1 + v/c) - 1\\[1ex] &= \text{ch}(aT/c)\,[1 + \text{th}(aT/c)] - 1\\[1ex] &= \exp(aT/c) - 1 \,. \end{align}

How much fuel is this?  The next chart shows the amount of fuel needed ($M$) for every kilogramme of payload ($m = 1$ kg). \begin{array}{lll} \hline d\text{ (ly)} & \text{Sailing past} & M \\[-1ex] & \text{without stopping} & \\ \hline 4.3 & \text{Nearest star} & 10\; \text{kg} \\ 27 & \text{Vega} & 57\; \text{kg} \\ 30,\!000 & \text{Centre of our galaxy} & 62\; \text{tonnes} \\ 2,\!000,\!000 & \text{Andromeda Galaxy} & 4100\; \text{tonnes} \\ \hline \end{array} This is a lot of fuel—and remember, we are using a motor that is 100% efficient!

What if we prefer to stop at the destination?  We accelerate to the half-way point at $1\;\text{g}$ and then immediately switch the direction of our rocket so that we now decelerate at $1\;\text{g}$ for the second half of the trip.  The calculations here are just a little more involved since the trip is now in two distinct halves (and the equations at the top assume a positive acceleration only).  Even so, the answer turns out to have exactly the same form: $M/m = \exp(aT/c) - 1$, except that the proper time $T$ is now almost twice as large as for the non-stop case, since the slowing-down rocket is losing the ageing benefits of relativistic speed.  This dramatically increases the amount of fuel needed:

It's useful to think of the problem in terms of relativistic mass, since this is what each rocket motor "feels" as it strives to maintain a $1\;\text{g}$ acceleration or deceleration.  The relativistic mass of each traveller's rocket is continually decreasing throughout their trip (since it's being converted to exhaust energy).  It turns out that at the half-way point, Laurel's total relativistic mass (for fuel plus payload) is about $28m$, and from here until the trip's end, this relativistic mass only decreases by a tiny amount, so that Laurel's rocket needs to do very little work.  So at the halfway point his fuel-to-payload ratio turns out to be about 1.

For Hardy, things are different.  He needs to decrease his relativistic mass to $m$ at the end where he is to stop.  If his rocket's total relativistic mass at the halfway point were the same as Laurel's ($28m$), with a fuel-to-payload ratio of 1, Hardy would need to decrease the relativistic mass all the way down to $m$ at the end, which would require more fuel than Laurel had needed.  But Hardy wouldn't have this much fuel on board—unless he ensures that he takes it with him initially.  This extra fuel that he must carry from the start becomes more payload (a lot more), which needs yet more fuel again to carry that.  So suddenly his fuel requirement has increased enormously.  It turns out that at the half-way point, all this extra fuel gives Hardy's rocket a total relativistic mass of about $442m$, and his fuel-to-payload ratio turns out to be about 29.

Another way of looking at this odd situation is that both travellers know that they must take fuel on board initially to push them at $1\;\text{g}$ for the total trip time.  They don't care about what's happening outside.  In that case, Laurel travels for 28 Earth years but ages just 3.9 years, while Hardy travels for 29 Earth years but ages 6.6 years.  So Hardy has had to sit at his controls and burn his rocket for almost twice as long as Laurel, and that has required more fuel, with even more fuel required because of the fuel-becomes-payload situation that we mentioned above.

This fuel-becomes-payload problem is well known in the space programme: part of the reason the Saturn V moon rocket was so big was that it needed yet more fuel just to carry the fuel that it was already carrying.

Other fuel options

Well, this is probably all just too much fuel to contemplate.  There are a limited number of solutions that don't violate energy–momentum conservation or require hypothetical entities such as tachyons or worm holes.

It may be possible to scoop up hydrogen as the rocket goes through space, using fusion to drive the rocket.  This would have big benefits because the fuel would not have to be carried along from the start.  Another possibility would be to push the rocket away using an Earth-bound graser directed onto the back of the rocket.  There are a few extra technical difficulties but expect NASA to start looking at the possibilities soon :-).

You might also consider using a large rotating black hole as a gravitational catapult, but aside from whether such a thing actually exists, it would have to be very big to avoid the rocket being torn apart by tidal forces or spun at high angular speed.  If there is a black hole at the centre of the Milky Way, as some astronomers think, then perhaps if you can get that far, you can use this effect to shoot you off to the next galaxy.

One major problem you would have to solve is the need for shielding.  As you approach the speed of light you will be heading into an increasingly energetic and intense bombardment of cosmic rays and other particles.  After only a few years of $1\;\text{g}$ acceleration, even the cosmic background radiation is Doppler shifted into a lethal heat bath that's hot enough to melt all known materials.

The Equivalence Principle and a Stone Thrown Upwards

The equivalence principle suggests that provided we don't throw the star "too far" from a region that can be considered to have uniform gravity, we can treat the motion of this stone moving up and coming back down as identical to that of the above star.  So let's use the rocket equations, but now think of the star as a stone and the rocket as a human observer, and alter the equations so that the observer moves "downwards" through the stone at time $t = 0$ (but always accelerating upwards with some $g > 0$), then slows to a stop at a distance $H$ "below" the stone, then moves back up towards the stone.  A plot of the observer's motion in spacetime is still the same hyperbola that the rocket has at the top of this page, so we can mostly use the rocket equations from there; but in this new scenario the hyperbola has been shifted somewhat on the spacetime diagram relative to its origin, so we'll need to tweak the equations to produce that shift.

To do that, first consider the stone to be at a distance $H$ from the uniformly accelerated observer, who is momentarily at rest, then starts to move towards the stone (while always accelerating towards it).  The stone is reached by the observer after a time $t_0 = \sqrt{H^2/c^2 + 2H/g}$.  We'll offset the graph of $d$ versus $t$ so that the observer passes with negative velocity "through" the stone at $t = 0$.  This only requires adding the appropriate constants to $t$ and $d$ in the expression for $d$ at the top of this page.  We'll write the acceleration as $g$ to emphasise that it's a positive number: $$ d = {c^2\over g} \left(\sqrt{1 + {g^2(t-t_0)^2\over c^2}} - 1\right) - H . $$ The "height" $h$ of the stone from the observer should be computed at the observer's proper time by contracting $-d$ by $\gamma$, so $h = -d/\gamma$, where $\gamma$ here is the $\gamma$ at the top of this page evaluated at $t - t_0$.  Setting the observer's proper time to be zero at his initial coincidence with the stone means using a new $T$ given by shifting the $T$ at the top of this page appropriately, giving \begin{align} T &= {c\over g} \text{sh}^{-1}{g(t-t_0)\over c} - {c\over g} \text{sh}^{-1}{-gt_0\over c}\nonumber\\[1ex] &= {c\over g} \text{sh}^{-1}{g(t-t_0)\over c} + {c\over g} \text{sh}^{-1}{gt_0\over c} \label{T-expression}. \end{align} So the height of the stone above the observer at his proper time $T$ is \begin{equation}\label{h-expression} h = {-1\over\gamma}\left[{c^2\over g} \left(\sqrt{1 + {g^2(t-t_0)^2\over c^2}} - 1\right) - H\right] , \end{equation} where $t$ is effectively now just a parameter, with $T$ given in terms of $t$ in \eqref{T-expression}.  You'll need \begin{align} t_0 &= \sqrt{{H^2\over c^2} + {2H\over g}}\;,\\ \gamma &= \sqrt{1 + {g^2(t-t_0)^2\over c^2}}\;.\label{gamma-for-t-t0} \end{align}

You can show that this height $h(T)$ reduces to the newtonian limit by supposing that \eqref{old-1} gravity is weak: $gt_0 /c \ll 1$, and (2) we don't consider times too far outside the scenario: $g(t-t_0)/c \ll 1$.  (For example, $g = 10$ m/s$^2$ while $t_0$ and $t$ equal a few seconds.)  In this limit you'll find that $T \to t$, and $$ \gamma \simeq 1 + {g^2(t-t_0)^2\over 2c^2} . $$ Use the fact that $\text{sh} x \simeq x$ when $x \ll 1$, and you'll recover the newtonian limit $h(t) = \sqrt{2gH}\; t - gt^2/2$.

Now the point here is to plot $h$ versus $T$, and compare it to the usual newtonian expression for the stone's motion in space and time—which is of course a parabola.  The figure shows a plot of $h$ versus $T$ for $g = 1$ light year/year$^2$, $c = 1$ light year/year (of course), and $H = 10$ light years.

relativistic space travel

Why this apparently anomalous acceleration and deceleration?  Remember that the stone is not really accelerating in an inertial frame; instead, the observer is accelerating in an inertial frame.  As the observer accelerates, his standard of simultaneity changes in a non-trivial way (see the FAQ article on Do moving clocks always run slowly? ).  As he moves down past the stone, his "line of simultaneity" coincides with the recent past of the stone's world line and mostly translates through spacetime; then as he slows to a stop, his line of simultaneity begins to rotate in spacetime, sweeping quickly along the stone's world line until it intersects that world line in his future.  Then as he picks up speed, his line of simultaneity mostly stops rotating in spacetime and simply translates again.  The effect of this is that he measures the stone initially to accelerate upwards, then slow for a time, stop, accelerate back down, and then slow down shortly before it hits him.  This motion might be non-intuitive, but most things in relativity are non-intuitive!

We can find the values of the parameters that will make this non-intuitive behaviour appear: just demand that the curve of $h$ versus $T$ be concave up at $T = 0$.  So calculate the second derivative $h''(T)$ and demand it be positive at $T = 0$.  The requirement for this to happen turns out to be $g > (\sqrt{2} - 1) c^2/H$.  This means that if you want to perform such an experiment, either $g$ or $H$ will have to be very large.  But uniform gravitational fields don't seem to exist in the universe, so in either case we might well depart too far from the assumptions of the equivalence principle to see the above behaviour.

This motion of objects is suggestive of current ideas in cosmology.  Cosmology is built on the simplest picture of why galaxies are observed to be rushing away from us: rather than assume they really are rushing away from us, it is perhaps simpler to posit that they are all in a sense "at rest" in a universe whose very fabric (spacetime) is itself expanding, as dictated by Einstein's equations of General Relativity.  In other words, if the galaxies are represented by raisins in a pudding, then we needn't imagine that the raisins are somehow racing outwards through the pudding; instead, they can be "locally at rest" in the pudding, while the entire pudding expands as it bakes.  Recent observations of galactic recession have been interpreted as a sign that the universe's rate of expansion is increasing, but the above description of free fall in which an object thrown up can actually accelerate upwards demonstrates that what might at first be seen as an anomalous acceleration is actually fully in keeping with relativity.  The catch, of course, is that cosmology does not treat galaxies as "objects thrown upward [or outward]".  Even so, perhaps we don't need to invoke new ideas such as dark energy to explain the universe's expansion: the above scenario shows that in certain situations, an object thrown upwards can accelerate up.  Our ideas of simultaneity are not always up to the job of finding these behaviours to be intuitive.

For a derivation of the rocket equations, see "Gravitation" by Misner, Thorne, and Wheeler, Section 6.2.

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December 7, 2023

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Communicating with a relativistic spacecraft gets pretty weird

by Matt Williams, Universe Today

Communicating with a relativistic spacecraft gets pretty weird

Someday, in the not-too-distant future, humans may send robotic probes to explore nearby star systems. These robot explorers will likely take the form of lightsails and wafercraft (a la Breakthrough Starshot) that will rely on directed energy (lasers) to accelerate to relativistic speeds—aka a fraction of the speed of light. With that kind of velocity, lightsails and wafercraft could make the journey across interstellar space in a matter of decades instead of centuries (or longer!) Given time, these missions could serve as pathfinders for more ambitious exploration programs involving astronauts.

Of course, any talk of interstellar travel must consider the massive technical challenges this entails. In a recent paper posted to the arXiv preprint server, a team of engineers and astrophysicists considered the effects that relativistic space travel will have on communications. Their results showed that during the cruise phase of the mission (where a spacecraft is traveling close to the speed of light ), communications become problematic for one-way and two-way transmissions. This will pose significant challenges for crewed missions but will leave robotic missions largely unaffected.

The team consisted of David Messerschmitt, a Professor Emeritus of Electrical Engineering and Computer Science at the University of California at Berkeley; Ian Morrison, a Research Fellow at Curtin University's International Center for Radio Astronomy Research (ICRAR) and the communications and signal processing developer Astro Signal Pty Ltd; Thomas Mozdzen, a research scientist in the School of Earth and Space Exploration at Arizona State University; and Philip Lubin, a professor of physics and the head of the Experimental Cosmology Group at UC Santa Barbara. The preprint of their paper recently appeared online and is being reviewed for publication by Elsevier.

For their study, the team considered both robotic (uncrewed) and crewed mission profiles. The former consists of concepts similar to the Starshot and Directed Energy Propulsion for Interstellar Exploration (DEEP-In)—aka. Starlight—concepts. This latter concept is one that Prof. Lubin and his colleagues at UCSB Experimental Cosmology Group have been developing since 2014 through the NASA Innovative Advanced Concepts (NIAC) program. However, their analysis differed since it considers scenarios where spacecraft are approaching the speed of light—rather than the 10% to 20% called for with the Starlight and Starshot concepts.

For uncrewed missions, remote control operations and data transmission require reliable communications during certain phases. For crewed missions, however, maintaining persistent communications with home is crucial to the long-term well-being of astronauts. Regardless of the mission profile, communications invariably come down to transmissions in the electromagnetic spectrum (radio waves, lasers, etc.) and how they propagate through space. As the team told Universe Today via email:

"The assumption we're making is that communication signals are electromagnetic, hence conveyed via photons. This relates to the propagation speed of a communication signal, which relates to the propagation delay. The timing/latency relationships are independent of the wavelength and hence apply equally to radio, microwave, or optical."

Communicating with a relativistic spacecraft gets pretty weird

Another key consideration is that communications at relativistic speeds must take into account the effects of Special Relativity. In short, a spacecraft traveling at a significant fraction of the speed of light will experience time dilation, where its internal clocks will advance more slowly than mission clocks on Earth. Another consideration is that communications to and from the mission will be subject to Doppler Shift. As Special Relativity teaches us, the speed of light is constant in a vacuum and does not speed up or slow down based on the motion of the observer or source.

But if the space between objects is expanding, the wavelength of the light will be shifted towards the red end of the spectrum (aka redshift). Their analysis found that the situation would be simpler for robotic missions, as communications are only required during the landing phase. However, for crewed missions, persistent communication is desirable for all phases of the mission, including the cruise phase (when the spacecraft will be accelerated to relativistic speed). In this case, said the team, problems emerged:

"The main effects considered are large propagation delays together with the time dilation of clocks traveling at high speed. The analysis is from the point of view of a traveler at relativistic speed rather than an inertial observer (like in an astronomy observatory), which to our knowledge, has not been considered previously in the literature. The results show that round-trip message latencies can be extremely high, rates of streaming media can be significantly slowed, and under certain circumstances, communications become impossible. Relativistic spacecraft and their astronauts must function largely autonomously."

These results have serious implications for the feasibility of interstellar missions. The inability to maintain contact with Earth at certain periods in the mission, the difficulty of transmitting information, and the need for autonomy all present significant challenges. Under these circumstances, future generations may choose to restrict interstellar missions to robotic explorers. Alternatively, they may choose to place crews in hibernation or cryogenic suspension so no communication is needed during the cruise phase.

However, as the team noted, their analysis comes down to quantifying the challenges of maintaining communications with a relativistic mission. This is absolutely necessary before any attempts can be made to plan for interstellar exploration. In addition, there are likely to be several innovations and changes between now and the day that human interstellar missions are being contemplated that could alter the picture. As they summarized:

"[T]he design of any future interstellar missions involving astronauts, especially at greater distances, will be significantly affected by the limits to communications imposed by large distances and spacecraft speeds near the speed of light. While the analytical approach is general, the numerical results are applied to hypothetical future missions where humans travel at close to the speed of light. While such speeds are not feasible with current propulsion technologies, this may change. These speeds may not be necessary for human travel to the nearest stars, but would enable travel to much greater distances within a typical human lifetime."

Journal information: arXiv

Provided by Universe Today

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relativistic space travel

Communicating With a Relativistic Spacecraft Gets Pretty Weird

Someday, in the not-too-distant future, humans may send robotic probes to explore nearby star systems. These robot explorers will likely take the form of lightsails and wafercraft (a la Breakthrough Starshot ) that will rely on directed energy (lasers) to accelerate to relativistic speeds – aka. a fraction of the speed of light. With that kind of velocity, lightsails and wafercraft could make the journey across interstellar space in a matter of decades instead of centuries (or longer!) Given time, these missions could serve as pathfinders for more ambitious exploration programs involving astronauts.

Of course, any talk of interstellar travel must consider the massive technical challenges this entails. In a recent paper , a team of engineers and astrophysicists considered the effects that relativistic space travel will have on communications. Their results showed that during the cruise phase of the mission (where a spacecraft is traveling close to the speed of light), communications become problematic for one-way and two-way transmissions. This will pose significant challenges for crewed missions but will leave robotic missions largely unaffected.

The team consisted of David Messerschmitt , a Professor Emeritus of Electrical Engineering and Computer Science at the University of California at Berkeley; Ian Morrison , a Research Fellow at Curtin University’s International Centre for Radio Astronomy Research (ICRAR) and the communications and signal processing developer Astro Signal Pty Ltd ; Thomas Mozdzen , a research scientist in the School of Earth and Space Exploration at Arizona State University; and Philip Lubin , a professor of physics and the head of the Experimental Cosmology Group at UC Santa Barbara. The preprint of their paper recently appeared online and is being reviewed for publication by Elsevier .

relativistic space travel

For their study, the team considered both robotic (uncrewed) and crewed mission profiles. The former consists of concepts similar to the Starshot and Directed Energy Propulsion for Interstellar Exploration (DEEP-In) – aka. Starlight – concepts. This latter concept is one that Prof. Lubin and his colleagues at UCSB Experimental Cosmology Group have been developing since 2014 through the NASA Innovative Advanced Concepts (NIAC) program. However, their analysis differed since it considers scenarios where spacecraft are approaching the speed of light – rather than the 10% to 20% called for with the Starlight and Starshot concepts.

For uncrewed missions, remote control operations and data transmission require reliable communications during certain phases. For crewed missions, however, maintaining persistent communications with home is crucial to the long-term well-being of astronauts. Regardless of the mission profile, communications invariably come down to transmissions in the electromagnetic spectrum (radio waves, lasers, etc.) and how they propagate through space. As the team told Universe Today via email:

“The assumption we’re making is that communication signals are electromagnetic, hence conveyed via photons. This relates to the propagation speed of a communication signal, which relates to the propagation delay. The timing/latency relationships are independent of the wavelength and hence apply equally to radio, microwave, or optical.”

Another key consideration is that communications at relativistic speeds must take into account the effects of Special Relativity. In short, a spacecraft traveling at a significant fraction of the speed of light will experience time dilation, where its internal clocks will advance more slowly than mission clocks on Earth. Another consideration is that communications to and from the mission will be subject to Doppler Shift. As Special Relativity teaches us, the speed of light is constant in a vacuum and does not speed up or slow down based on the motion of the observer or source.

relativistic space travel

But if the space between objects is expanding, the wavelength of the light will be shifted towards the red end of the spectrum (aka. redshift). Their analysis found that the situation would be simpler for robotic missions, as communications are only required during the landing phase. However, for crewed missions, persistent communication is desirable for all phases of the mission, including the cruise phase (when the spacecraft will be accelerated to relativistic speed). In this case, said the team, problems emerged:

“The main effects considered are large propagation delays together with the time dilation of clocks traveling at high speed. The analysis is from the point of view of a traveler at relativistic speed rather than an inertial observer (like in an astronomy observatory), which to our knowledge, has not been considered previously in the literature. The results show that round-trip message latencies can be extremely high, rates of streaming media can be significantly slowed, and under certain circumstances, communications become impossible. Relativistic spacecraft and their astronauts must function largely autonomously.”

These results have serious implications for the feasibility of interstellar missions. The inability to maintain contact with Earth at certain periods in the mission, the difficulty of transmitting information, and the need for autonomy all present significant challenges. Under these circumstances, future generations may choose to restrict interstellar missions to robotic explorers. Alternatively, they may choose to place crews in hibernation or cryogenic suspension so no communication is needed during the cruise phase.

However, as the team noted, their analysis comes down to quantifying the challenges of maintaining communications with a relativistic mission. This is absolutely necessary before any attempts can be made to plan for interstellar exploration. In addition, there are likely to be several innovations and changes between now and the day that human interstellar missions are being contemplated that could alter the picture. As they summarized:

“[T]he design of any future interstellar missions involving astronauts, especially at greater distances, will be significantly affected by the limits to communications imposed by large distances and spacecraft speeds near the speed of light. While the analytical approach is general, the numerical results are applied to hypothetical future missions where humans travel at close to the speed of light. While such speeds are not feasible with current propulsion technologies, this may change. These speeds may not be necessary for human travel to the nearest stars, but would enable travel to much greater distances within a typical human lifetime.”

Further Reading: arXiv

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Theory of Relativity in Space: Latest science, tests and images

Theory of General Relativity

Albert Einstein's theory of special relativity explains how space and time are linked, but it doesn't include acceleration. By including acceleration, Einstein later developed the theory of general relativity, which explains how massive objects in the cosmos distort the fabric of space-time. The theory explains how this distortion is felt as the force of gravity, as it predicts how much the mass of an object curves space-time. Scientists test relativity by observing objects in space and seeing if their behaviors match up with Einstein's explanations of space-time and gravity, for instance by observing how light bends around massive objects as it travels towards Earth.

Related Topics: The Big Bang Theory , Black Holes , Dark Matter , Gravitational Waves , Multiverse

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High-speed travel.

Every week, the readers of our space newsletter, The Airlock , send in their questions for space reporter Neel V. Patel to answer. This week: time dilation during space travel. 

I heard that time dilation affects high-speed space travel and I am wondering the magnitude of that affect. If we were to launch a round-trip flight to a nearby exoplanet—let's say 10 or 50 light-years away––how would that affect time for humans on the spaceship versus humans on Earth? When the space travelers came back, will they be much younger or older relative to people who stayed on Earth? —Serge

Time dilation is a concept that pops up in lots of sci-fi, including Orson Scott Card’s Ender’s Game , where one character ages only eight years in space while 50 years pass on Earth. This is precisely the scenario outlined in the famous thought experiment the Twin Paradox : an astronaut with an identical twin at mission control makes a journey into space on a high-speed rocket and returns home to find that the twin has aged faster.

Time dilation goes back to Einstein’s theory of special relativity, which teaches us that motion through space actually creates alterations in the flow of time. The faster you move through the three dimensions that define physical space, the more slowly you’re moving through the fourth dimension, time––at least relative to another object. Time is measured differently for the twin who moved through space and the twin who stayed on Earth. The clock in motion will tick more slowly than the clocks we’re watching on Earth. If you’re able to travel near the speed of light, the effects are much more pronounced. 

Unlike the Twin Paradox, time dilation isn’t a thought experiment or a hypothetical concept––it’s real. The 1971 Hafele-Keating experiments proved as much, when two atomic clocks were flown on planes traveling in opposite directions. The relative motion actually had a measurable impact and created a time difference between the two clocks. This has also been confirmed in other physics experiments (e.g., fast-moving muon particles take longer to decay ). 

So in your question, an astronaut returning from a space journey at “relativistic speeds” (where the effects of relativity start to manifest—generally at least one-tenth the speed of light ) would, upon return, be younger than same-age friends and family who stayed on Earth. Exactly how much younger depends on exactly how fast the spacecraft had been moving and accelerating, so it’s not something we can readily answer. But if you’re trying to reach an exoplanet 10 to 50 light-years away and still make it home before you yourself die of old age, you’d have to be moving at close to light speed. 

There’s another wrinkle here worth mentioning: time dilation as a result of gravitational effects. You might have seen Christopher Nolan’s movie Interstellar , where the close proximity of a black hole causes time on another planet to slow down tremendously (one hour on that planet is seven Earth years).

This form of time dilation is also real, and it’s because in Einstein’s theory of general relativity, gravity can bend spacetime, and therefore time itself. The closer the clock is to the source of gravitation, the slower time passes; the farther away the clock is from gravity, the faster time will pass. (We can save the details of that explanation for a future Airlock.)

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Relativity and Space Travel

  • HERBERT DINGLE 1  

Nature volume  180 ,  page 500 ( 1957 ) Cite this article

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I HAVE received several calculations similar to Dr. J. H. Fremlin's. To follow them through in detail is subtle and tedious, but it is unnecessary because it is at once obvious that since all the effects concerned are effects only of the relative motion of Stayathome and Traveller, and the motion of one is the mirror image of that of the other (for every stage of Traveller's motion, whether uniform or accelerated, there is an exactly corresponding stage of Stayathome's motion), there cannot possibly be any difference in the numbers of oscillations received.

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How Humanity Can Travel Incredibly Fast In Space Explored

Posted: February 29, 2024 | Last updated: February 29, 2024

Limitless Space Institute compares the travel time of spacecraft propelled by nuclear power to that of imaginative fusion propulsion. Credit: Limitless Space Institute

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Space perspective’s first flight moves closer to takeoff.

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When Space Perspective's Spaceship Neptune-Excelsior launches next year, this will be the view from ... [+] very comfortable seats.

Carol Scribner and her late husband Larry were among the first to pay $125,000 each for a seat on the upcoming flight into the edge of space offered by the company Space Perspective . For the couple, there was practically nowhere else to go as voracious travelers who had been to 170 countries. Now that flight seems closer to reality: with the completion of the test capsule just announced, the company is aiming to begin commercial flights in 2025.

“We so yearned to travel to space,”Scribner says. “Because of our age and some health problems, the programs available weren't possible for us. When we learned of Space Perspective and that the only requirement would be that you were fit to travel on a commercial airline, we immediately contacted the company. It was a dream of ours and now it was within our grasp.”

The just completed space capsule with the Space Perspective team.

With the capsule now complete, a series of uncrewed test flights will begin soon off the coast of Florida, according to Jane Poynter, Space Perspective’s co-founder and co-CEO, with crewed test flights scheduled for later this year. “Our test capsule is highly instrumented and represents what we will be flying once commercially operational,” she says, “minus the luxurious interior, which we call the Space Lounge, and the restroom, which we call the Space Spa.”

Poynter and her husband Taber MacCallum, co-founder and Chief Technology Officer of the company, both longtime veterans of spaceflight technology development, have been working on this project for over a decade. “Our mission is to take as many people as possible into space because we know that looking down on our beautiful planet from the blackness of space – the quintessential astronaut experience – will radically shift one's perception of our world and humanity's place within it,” she says. “Astronauts often return from missions with a fire inside them to create positive change, and many get involved in environmental and societal causes. Often referred to as the Overview Effect, we call it the Space Perspective.”

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The specially treated, very long vertical windows of the capsule

To develop the space vehicle, they enlisted personnel who had previously worked on spacecraft with NASA, SpaceX, Boeing, Virgin Galactic, Blue Origin and the U.S. Navy. The capsule they developed, Spaceship Neptune-Excelsior, is very different from the other commercial space vehicles: larger than Virgin Galactic’s SpaceShipTwo, Blue Origin’s New Shepard and SpaceX’s Crew Dragon at 16 feet in diameter and 2,000 pressurized cubic feet of interior space allowing it to transport eight people. The windows of the capsule are also larger, vertical- allowing for continuous panoramic views- and designed to protect from harmful sun wavelengths, to control the heat in the cabin and to maintain the veracity of the colors on view above and below.

A rendering of the SpaceBalloon lifting the capsule into the edge of space

The major differences, though, are how far up the spaceship goes and how it gets there: 18 miles up (outer space begins at 62 miles up known as the Kármán line) and propelled gently by the SpaceBalloon they’ve created without the G force stress of rocket propulsion and weightlessness. The acceleration will be a gentle 12 miles an hour and the trip’s duration will be six hours, allowing enough time to engage in cocktails and an upscale dining experience in a leisurely fashion along with WiFi to livestream what the explorers, as the 1,750 ticketholders so far are called, are seeing. Reentry is expected to be just as gradual in a splashdown.

Marine Spaceport Voyager, the launch vessel due to be completed in a few weeks.

This extremely gentle process is the reason that this space experience seemed possible for Carol Scribner and her husband. When he passed away two years ago, though, she gave his seat to her son. But she then met a man very much like her husband who had also been a world traveler and wanted to go to space. Her son gave up his seat to allow her and Gerry, now her fiancé, to go together.

“But it won’t be just us,” she says. This journey is going to be incredibly memorable, not just for me but for the large international family my late husband and I collected together. They'll be hearing the stories and seeing the pictures—I'm a photographer. We're going to bring this world and experience to them. And I know Larry will also be on this trip in some cosmic way…the three of us will experience the world we live in in a way that we haven't seen before.”

Correction: An earlier version of this story stated that the capsule would land on the vessel from which it will launch; it will, instead, be a splashdown.

Laurie Werner

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