Space Travel Under Constant 1g Acceleration

The basic principle behind every high-thrust interplanetary space probe is to accelerate briefly and then coast, following an elliptical, parabolic, or mildly hyperbolic solar trajectory to your destination, using gravity assists whenever possible. But this is very slow.

Imagine, for a moment, that we have a spacecraft that is capable of a constant 1g (“one gee” = 9.8 m/s2) acceleration. Your spacecraft accelerates for the first half of the journey, and then decelerates for the second half of the journey to allow an extended visit at your destination. A constant 1g acceleration would afford human occupants the comfort of an earthlike gravitational environment where you would not be weightless except during very brief periods during the mission. Granted such a rocket ship would require a tremendous source of power, far beyond what today’s chemical rockets can deliver, but the day will come—perhaps even in our lifetimes—when probes and people will routinely travel the solar system in just a few days. Journeys to the stars, however, will be much more difficult.

The key to tomorrow’s space propulsion systems will be fusion and, later, matter-antimatter annihilation. The fusion of hydrogen into helium provides energy E = 0.008 mc2. This may not seem like much energy, but when today’s technological hurdles are overcome, fusion reactors will produce far more energy in a manner far safer than today’s fission reactors. Matter-antimatter annihilation, on the other hand, completely converts mass into energy in the amount given by Einstein’s famous equation E = mc2. You cannot get any more energy than this out of any conceivable on-board power or propulsion system. Of course, no system is perfect, so there will be some losses that will reduce the efficiency of even the best fusion or matter-antimatter propulsion system by a few percent.

How long would it take to travel from Earth to the Moon or any of the planets in our solar system under constant 1g acceleration for the first half of the journey and constant 1g deceleration during the second half of the journey? Using the equations below, you can calculate this easily.

Keep in mind that under a constant 1g acceleration, your velocity quickly becomes so great that you can assume a straight-line trajectory from point a to point b anywhere in our solar system.

Maximum velocity is reached at the halfway point (when you stop accelerating and begin decelerating) and is given by

The energy per unit mass needed for the trip (one way) is then given by

How much fuel will you need for the journey?

hydrogen fusion into helium gives: Efusion = 0.008 mfuel c2

matter-antimatter annihilation gives: Eanti = mfuel c2

This assumes 100% of the fuel goes into propelling the spacecraft, but of course there will be energy losses and operational energy requirements which will require a greater amount of fuel than this. Moreover, we are here calculating the amount of fuel you’ll need for each kg of payload. We would need to use calculus to determine how much additional energy will be needed to accelerate the ever changing amount of fuel as well. The journey may well be analogous to the traveler not being able to carry enough water to survive crossing the desert on foot.

Now, let’s use the equations above for a journey to the nearest stars. There are currently 58 known stars within 15 light years. The nearest is the triple star system Alpha Centauri A & B and Proxima Centauri (4.3 ly), and the farthest is LHS 292 (14.9 ly).

I predict that interstellar travel will remain impractical until we figure out a way to harness the vacuum energy of spacetime itself. If we could extract energy from the medium through which we travel, we wouldn’t need to carry fuel onboard the spacecraft.

We already do something analogous to this when we perform a gravity assist maneuver. As the illustration below shows, the spacecraft “borrows” energy by infinitesimally slowing down the much more massive Jupiter in its orbit around the Sun and transferring that energy to the tiny spacecraft so that it speeds up and changes direction. When the spacecraft leaves the gravitational sphere of influence of Jupiter, it is traveling just as fast as it did when it entered it, but now the spacecraft is farther from the Sun and moving faster than it would have otherwise.

Of course, our spacecraft will be “in the middle of nowhere” traveling through interstellar space, but what if space itself has energy we can borrow?

13 thoughts on “Space Travel Under Constant 1g Acceleration”

1. Chris says:

I seem to remember reading something of Doctor Robert Forward where his conclusion was that you could power a 100 ton colony ship to the Alpha Centauri system in 10 years with 4 tons of antimatter. Not accounting for losses if I remember right nor for operating the ship’s systems which would only be a small portion of fuel in comparison to the drive system. It would also leave a portion to travel around the system to the planet of choice. I also believe that his article specified that the 100 tons was everything that arrived at the A.C. system. That would mean starting out with about 9 tons of total fuel and consumables might add to that depending on the percentage recycled. That last is just my guess and I don’t remember how many colonists were included. But they would have been included in the 100 tons.

1. Thanks, Chris. I found this paper by Robert Forward published in October 1987: Advanced Space Propulsion Study: Antiproton and Beamed Power Propulsion, and I’m sure there are others. I’m encouraged that many ideas are actively being considered for advanced space propulsion systems. Visiting the Alpha Centauri system first with a robotic mission and later with humans seems the best goal for our first interstellar missions.

1. Shawn Stockle says:

Hi David, I would like to calculate how many kilotones of energy would be required to propel a 10 ton ship at a constant 1g acceleration rate for 3.6 years. I have a feeling you know how to do the math. Every kilogram of uranium contains the same energy as about 17 kilotones of TNT. A rough guess of mine would be about a half a pound of uranium would be enough to get to the Centauri system.

1. Hi Shawn, Unless something is horribly wrong with my calculations, I have bad news. The energy needed per kg of payload to reach the Alpha Centauri system at 1g acceleration for the first half of the journey and 1g deceleration for the second half of the journey is 4.0702 × 1017 J/kg. So traveling there with a 10 metric ton ship would require 4.0702 × 1021 joules of energy.

If a metric ton of TNT releases 4.184 terajoules (4.184 × 1012 J), then dividing this into 4.0702 × 1021 gives us 9.728 × 108 metric tons of TNT.

If every kg of uranium releases the energy equivalent of 17 metric kilotons of TNT, then dividing 9.728 × 108 by 17,000 we get 57,220 kg of uranium needed. This is so much more than the mass of the ship that I would need to use calculus to account for the change in ship + fuel mass as a function of time. But this is so much uranium that I don’t think it would be feasible for interstellar travel. But for travel within our solar system, it would probably work fine.

The problem, of course, is relativity. As we reach relativistic velocities, the faster we go, the more energy it takes just to go a little faster. On this journey, we would reach 0.95c at the halfway point to the Alpha Centauri system.

Do my calculations make sense? I used the equations shown in the article above.

1. Shawn Stockle says:

Hi David, thanks for doing the math, 1 kg of uranium has 17 kilotones not metric tonnes on TNT energy. I think relativistic changes to the ship would all be from the vantage point of an outside/stationary observer. I think no matter how fast the ship goes a cup of tea would weigh exactly the same. There is nothing special about any velocity, we are all traveling at the speed of light. There does seem to be a difference of opinion on this subject. In the future I plan to research everything Einstein had to say on this matter.

2. Ah, thanks for correcting me on that Shawn. Sorry about that. I changed my original comment to reflect that 1 kg of uranium has 17,000 metric tons and not 17 metric tons of TNT energy.

2. Shawn Stockle says:

The key is to make a fission rocket that does not consume hydrogen or xenon (you cant bring 500 tons of that with you). 1kg of uranium has the same energy as 120,000 tons of coal and plutonium has a lot more than that so you would not need a lot of it, so the mass of the ship will not change. A 10 ton ship would need a mere 10 tons of continuous thrust.
A fission rocket should be simpler than a chemical rocket. Both uranium and plutonium are jittery atoms, they are on the verge of fissioning all by themselves (and sometimes they do). There should be a way of getting them to fission in a linear fashion. I made 2 youtube video’s that outline potential ways of doing this “best method for interstellar travel” and “liquid plutonium rocket”.

1. Thanks, Shawn! Wanted to post the two YouTube videos you made here so that others can watch them, too. I found them interesting and thought-provoking. Well worth the time to watch!

Best Method for Interstellar Travel

Liquid Plutonium Rocket

I agree with you that we need an international weapons ban. Globally, we must work toward establishing a global “supergovernment” that enacts and enforces binding international laws that are in the best interest of all the world’s peoples. Individual nations will have to give up some sovereignty in order to effectively address global threats such as nuclear weapons, warfare, human rights violations, pandemics, climate change, pollution, environmental degradation, and loss of biodiversity. Whether the United Nations can be strengthened to serve in this role or a new organization created will need to be explored.

Shawn, I have one question about fission. I thought that the only way to induce fission is through the introduction of neutrons. How do you do it with an electrical current?

1. Shawn Stockle says:

I would bet my left arm that the processes in my video’s would work. The uranium or plutonium atoms will probably have to head towards each other single file however which would be the main technical hurdle. I also want to point out that these would be low output engines compared to chemical rockets. There is many other potential ways of using an electrical current to trigger fission, I plan to make more video’s in the future. The next one will be called “alternating current fission rocket”. Imagine 2 iridium electrodes with a narrow specific gap in between with a specific current that is right above the threshold of jumping from one electrode to the other in a vacuum, precisely so that all it takes is one metallic atom to cause the current to jump from one electrode to the other. The idea being to “pop” a uranium or plutonium atom like a fuse, being the jittery atoms they are I cant image that fission would not occur.
Another idea is “metallic hydrogen fusion rocket”. If you pass an overcurrent to 2 electromagnets they will destroy themselves with the impact. Imagine the same concept but with individual polarized metallic hydrogen atoms. I dont think this will ever be technically possible but it something to think about.

1. Thanks for the explanation, Shawn. I am looking forward to your future videos on this subject. Feel free to post them here.

Dave

1. Shawn Stockle says:

I realize I made a mistake in my above comment. When I said “right above the threshold of jumping from one electrode to the other” I should have said right below the threshold.
It may be possible to use laser energy to get uranium or plutonium to fission in a linear fashion. What would happen if a powerful laser hit a piece of uranium or plutonium sheet? Given the fact that they are jittery, on the verge of fissioning atoms anyway I think fission would be likely. This too could be the basis for a simple fission rocket.
The clock is ticking till the day the human race starts to explore/colonize our galaxy. Whatever machine we make to do that will be made from the periodic table of elements, its our toolkit. In a million years from now its going to be the same toolkit.

3. Gordon Smith says:

Due to the cosmic radiation, human bodies won’t be able survive very long in deep space travel. Perhaps scientists can overcome this problem in the future .
sincerely,
an old guy who went to a one room country grade school in the 50’s

1. Your point about radiation (especially at relativistic speeds) is well taken, Gordon. It is even a concern for the safety of astronauts undertaking interplanetary space travel at much lower speeds, a current topic of investigation (see, for example, https://arxiv.org/abs/1902.10122).

As for interstellar travel at relativistic speeds, the challenges of protecting human lives from radiation and relativistic particle impacts (let alone anything larger) are enormous. Here is a recent paper (and a critical response) addressing the issues involved:

https://arxiv.org/abs/1608.05284

https://arxiv.org/abs/1701.04319

Though I didn’t attend a one room country grade school in the 50s as you did, I was born in the 50s and attended grade school in the 60s. I am thankful that my formative years occurred before computers, smart phones, social media, the internet, etc. Best not to have so many technological distractions getting in the way of normal social development during one’s formative years.