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Starts With A Bang

How Far Could A Human Travel In A Constantly-Accelerating Rocket Ship?

Imagine you had perfect technology and unlimited fuel. How far could you go?

Human spaceflight has brought us beyond Earth, but we could potentially venture even farther.

The very first launch from NASA’s Cape Kennedy space center was of the Apollo 4 rocket. Although it accelerated no faster than a sportscar, the key to its success was that the acceleration was sustained for so long. The Saturn V rockets would later take humanity to the Moon. Although we’ve never ventured farther than Apollo took us all those decades ago, our potential to explore the Universe goes far beyond what we’ve already accomplished. (NASA)

Imagine that we could constantly accelerate at the same rate as Earth’s gravitational pull, 9.8 m/s², indefinitely.

A multistage rocket that lost and jettisoned mass as it moved faster and faster would be required to reach speeds approaching the speed of light, like the Super Haas rocket shown here. You must either posses a super-efficient type of fuel or gather more fuel along your journey to achieve relativistic speeds. In theory, a ship with constant acceleration could take us farther into the Universe than anything else we’ve hitherto envisioned. (DRAGOS MURESAN, UNDER C.C.A.-S.A.-3.0)

While you’d initially speed up, you’ll rapidly approach the speed of light.

A “light clock” will appear to run different for observers moving at different relative speeds, but this is due to the constancy of the speed of light. Einstein’s law of special relativity governs how these time and distance transformations take place between different observers.(JOHN D. NORTON, VIA PITT.EDU/~JDNORTON/TEACHING/HPS_0410/CHAPTERS/SPECIAL_RELATIVITY_CLOCKS_RODS)

Owing to Einstein’s Special Relativity, time will dilate and lengths will contract.

One revolutionary aspect of relativistic motion, put forth by Einstein but previously built up by Lorentz, Fitzgerald, and others, is that rapidly moving objects appear to contract in space and dilate in time. The faster you move relative to someone at rest, the greater your lengths appear to be contracted, while the more time appears to dilate for the outside world. (CURT RENSHAW)

As you continue to accelerate, the distances and travel times to faraway destinations will plummet.

One of the most efficient uses of human life for interstellar or intergalactic travel involves accelerating at a constant rate, turning around, and then decelerating at a constant rate, ensuring you reach your destination at non-relativistic speeds while minimizing your overall travel time from your perspective. (WIKIMEDIA COMMONS USER P. FRAUNDORF)

At the halfway mark, simply reverse your thrust to accelerate in the opposite direction for the remaining journey.

A logarithmic view of our Solar System, extending out all the way to the next-nearest stars, shows the extent of the asteroid belt, the Kuiper belt, and our Oort cloud. It would take a long journey of many months, even approaching a full year, of constant acceleration followed by deceleration to reach even the innermost edge of the Oort cloud. (NASA)

Reaching the inner Oort Cloud, at the Solar System’s boundary, takes approximately one year.

The stars Alpha Centauri (upper left) including A and B, are part of the same trinary star system as Proxima Centauri (circled). These are the three nearest stars to Earth, and they’re located between 4.2 and 4.4 light-years away. From the point of view of a relativistic traveler, fewer than 4 years would pass on a journey to any of these stars. (WIKIMEDIA COMMONS USER SKATEBIKER)

But it’s only a little longer — 4 years — to arrive at the Alpha Centauri system, 4.3 light-years away.

A relativistic journey toward the constellation of Orion. As you move closer to the speed of light, not only does space appear distorted, but your distance to the stars appears contracted, and less time passes for you as you travel. StarStrider, a relativistic 3D planetarium program by FMJ-Software, was used to produce the Orion illustrations. You don’t have to break the speed of light to travel 1,000+ light-years in less than 1,000 years, but that’s only from your point of view. (ALEXIS BRANDEKER)

Journeying to the Orion Nebula, located more than 1,000 light-years distant, requires just 15 years.

The Milky way’s central region in visible light, with the location of the galactic center marked by E. Siegel. Billions of stars can be found there, but even though it’s 25,000 light-years away, we could get there by accelerating and decelerating at a constant 9.8 m/s² in just 2 decades, from the point of view of a human on the journey. (JAIME FERNÁNDEZ OF CASTILLOSDESORIA.COM)

Only 20 years of traveling brings you to the Milky Way’s center, 25,000 light-years away.

The Andromeda Galaxy resides in our local group, and is nearly twice as large in diameter as our Milky Way. It is located 2.5 million light-years away, but if we constantly accelerated towards it at 9.8 m/s², turning around to decelerate halfway along the journey, we’d reach it after traveling for just 30 years from our frame of reference. (ADAM EVANS / FLICKR)

Arrival at the Andromeda galaxy, 2.5 million light-years distant, is achievable after just 30 years.

The size of our visible Universe (yellow), along with the amount we can reach (magenta). If we accelerated at 9.8 m/s² for approximately 22.5 years and then turned around and decelerated for another 22.5 years, we could reach any galaxy within the magenta circle, even in a Universe with dark energy. (E. SIEGEL, BASED ON WORK BY WIKIMEDIA COMMONS USERS AZCOLVIN 429 AND FRÉDÉRIC MICHEL)

In fact, you could reach any galaxy presently within 15 billion light-years after merely 45 years of travel.

Different stills from a simulation of the merger of the Milky Way and Andromeda galaxies. While someone on a relativistic journey might age only years or decades, someone remaining at rest will experience time without dilation; in 4-to-7 billion years, the Milky Way and Andromeda will merge, while the Sun will become a red giant and die. Anyone returning after a long, one-way journey will find their home significantly aged and irrevocably changed. (NASA, ESA, Z. LEVAY, R. VAN DER MAREL, T. HALLAS, AND A. MELLINGER)

Distant journeys are irrevocably one-way, as billions of years pass back on Earth.

Mostly Mute Monday tells a scientific story about the Universe in visuals, images, and no more than 200 words. Talk less; smile more.

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.


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