# Acceleration in space

Scenario: I have a generation ship moving between two star systems. Given that such a ship needs to have a completely self sufficient life cycle system to make it viable, ejecting mass continuously does not seem to me to be a very viable option for acceleration.

With this given scenario what other methods can be used to achieve acceleration and deceleration in interstellar space? I would like answers to be bound by the known laws of physics in our universe.

• Hello, Rudhra, welcome to Worldbuilding. Please provide more information about type of space travel in your story. Newton's three laws of motion cover the basic science of moving spaceships and accelerating them. Spaceships are accelerated when reaction mass is expelled from the vehicle. This can be chemicals, ionized matter or plasma, even detonating nuclear bombs can be used to propel spaceships. We could quote Newton's laws, but that won't help your story. Help us help you, and the answers will come. Sep 18 '16 at 9:26
• Hi, Thanks for your suggestion. nzaman's answer has already helped provide me with more clarity. I will add further details as per your suggestion. Sep 18 '16 at 9:28
• Excellent! That puts meat on the bone. It's not easy to ask questions, we all need to work at it. Sep 18 '16 at 9:49
• This really isn't a hard-science question. Hard science "answers should be based on current, undisputed science". Interstellar travel has never been accomplished and exactly zero currently operational propulsion methods are viable candidates for getting real people across interstellar space using anything resembling current technology. Recommend removing the hard-science tag, and possibly replacing it with the reality-check tag. Sep 18 '16 at 23:09
• @MichaelS: The engineering has never been accomplished but the science is feasible. Especially considering that this is a generation ship (we actually have one real-life example of a generation ship, though not interstellar: the planet Earth). Sep 19 '16 at 6:54

The best way to conserve mass is to use external energy to accelerate the ship.

Robert L Forward had designed a multi stage lightsail which allowed ships to accelerate, and then, by detaching portions of the sail and using them to reflect laser energy back to the starship, decelerate at the target star. The disadvantage is laser driven lightsails are still quite massive, and the amount of laser energy needed to drive the starship is measured in Terrawatts. Building the laser launcher alone is a huge undertaking (usually described as being done by building a ring of solar power satellites and lasers in polar orbit around Mercury), gigantic focusing lenses over a thousand kilometres in diameter in the outer solar system, and then the starship itself.

Since a generation ship is bound to be larger than an exploration starship like the one Froward was proposing, you will need to scale things up considerably. (Realistically, if you can accelerate a ship to the sorts of speeds Forward is considering, then it isn't really a generation ship, but since it may take centuries to build colonies in the new star system, a generation ship sized construct is probably needed as a base to live and work out of until fresh colony space is created. NextBigFuture published an interesting speculation about "Tabby's Star" which suggested an orbiting mirror the size of the Moons orbit around the Earth could power monster lightsails.

If a lightsail ins't your thing, then maybe a gigantic mass driver could be used to accelerate the starship. Deceleration can be handled by various means including a rocket, magsail or deploying a lightsail to use the target star's energy. Once again. we are talking about a monstrous device. Marshal Savage conceptualized something like this in his book "The Millenial Project", describing a system which stretched across the solar system. One reason to make it so big is to keep acceleration down to a reasonable limit (3g is about the best an unprotected human can withstand, trained pilots with G suits can withstand up to 9g, for sustained acceleration beyond that limit people might have to be immersed in fluid and have all their internal spaces packed with oxygenated fluorocarbons).

Once again, using high initial accelerations allows the ship to cross the interstellar distance in decades rather than centuries, so the advantage to a large ship is as a shelter and workspace on arrival; generations of colonists might need to stay aboard the ship until a colony planet is terraformed.

• I guess i can conceptualize a Dyson swarm or ring powering the laser and going ahead with the light sails concept. Maybe throw in a gravitational slingshot maneuver to enter the laser's path for better initial velocity? Sep 18 '16 at 11:55
• @Rudhra It's generally recommended to not accept an answer for a day or two. Our community is a very international one, and allowing at least a day before accepting an answer gives the community a chance to both post additional (perhaps better) answers, as well as for community voting on answers. Questions with accepted answers also tend to receive less attention from other members of the community.
– user
Sep 18 '16 at 12:08
• @Rudhra Let me say thank you on behalf of myself and other international members of this community. Sep 18 '16 at 13:34
• Variants like a magnetic sail.
• Bussard Ramjets.
• Accept that you will need fuel or reaction mass for acceleration/deceleration, and plan for it. Take a very efficient fuel like antimatter, and/or accept a long flight.

Whatever you do, a solution will have a minuscule payload and an astronomical pricetag.

• I'm surprised why this is flagged for lack of citations. Is Wikipedia no longer reliable enough?
– o.m.
Sep 19 '16 at 6:15
• I'm afraid that none of these actually work. Light sails require a light source interstellar space is without stars. Magnetic sails don't work beyond the heliopause (the edge of the solar system). Ramjets have massive drag.
– Aron
Sep 19 '16 at 11:14
• @Aron, I wrote that all those drives will be inefficient. I guess that applies to all hard-science solutions.
– o.m.
Sep 19 '16 at 11:52
• @om there is nothing to do with efficiency. They don't work. Zero thrust. But given that you put zero reaction mass into them, any thrust would have made then efficient. The only one that 'works' is the ram jet. But that is limited to only the exhaust velocity of the ion engine it feeds, which is best case only a few thousand m/s against the interstellar medium.
– Aron
Sep 19 '16 at 12:17
• @Aron, of course a lightsail works in interstellar space. It produces very little thrust.
– o.m.
Sep 19 '16 at 12:37

A rocket does accelerate in space. Momentum of hot gas out the back = forward momentum. Change the burn rate and you change the momentum (i.e., accelerate). Also, the mass of the rocket changes as fuel is being burnt, so at a constant burn rate, the rocket accelerates naturally.

• Yes and no. A constant burn rate, given a single engine or a single set of engines, should imply an approximately constant thrust. The combination of constant thrust and decreasing mass gives an increasing acceleration (growing rate of change of velocity). To achieve constant acceleration, resulting in increasing velocity over time, the engines would need to be throttled down to compensate for the reduced mass of the spacecraft as propellant is expended. To achieve roughly constant velocity reduce the engine thrust to zero by turning off the flow of fuel and propellant, and enter freefall.
– user
Sep 18 '16 at 12:05

Momentum of a closed system is always conserved unless there is external force.

Consider the mass of the rocket together with its fuel at $t_0$ be $M_0\,.$ Let the gas be ejected at $\dot m\,.$ Therefore, mass of the rocket along with its remnant of fuel after an infinitesimal increment $\mathrm dt$ is given as $$M(t_0+ \mathrm dt) = M_0 - \dot m~\mathrm dt\,.$$

Linear-momentum at time $t$ is $(M_0-\dot m~\mathrm(t-t_0) )\mathbf v\,.$

Applying the conservation of Linear momentum, we get \begin{align}(M-\dot m~\mathrm dt)\mathbf v_\textrm{rocket w.r.t. ground} + (\dot m~\mathrm dt)\mathbf v_\textrm{gas w.r.t. ground} &= \mathbf 0\\ \implies(M-\mathrm dM)(\mathbf v+ \mathrm d\mathbf v) + \mathrm dM(\mathbf v+ \mathrm d\mathbf v-\mathrm v_\textrm{gas w.r.t. rocket}) & = \mathbf 0\\ \implies \mathrm d\mathbf v &= \frac{\mathrm dM~\mathbf u}{M-\mathrm dM}\\ \implies \dot{\mathbf v } &= \frac{\dot m\mathbf u}{M_0-\dot m t} \,,\end{align} where $\mathbf u$ is the velocity of the gas with respect to the rocket; in the derivation, product of infinitesimal quantities have been neglected.

• Well, since OP is editing; this is the answer to v1 of his post.
– user16451
Sep 18 '16 at 9:35
• Hi, my initial question seems to have been perfectly answered here. I have edited the question to show the actual intent behind the question. Sorry for the trouble. Still new here. Sep 18 '16 at 9:41

You can accelerate prior to the interstellar portion of the mission. This could be done with booster rockets like many real-world missions, or it could be done with a space tug (which is really just a variation of a booster rocket). You could also get fancy and use some kind of rail-gun setup, with magnets or lasers or whatever mounted to orbiting stations in the departure solar system and each station adds a bit more momentum to the ship.

Whatever method you use, the ship would just drift through space until it reaches its destination. If it's the first ship to arrive, it's probably1 going to have to use one or more rockets to enter planetary orbit and eventually land. Otherwise you don't need to use any major thrust on the way, though, as Michael Kjörling points out, you'd likely want some thrust to make course corrections along the way2. If it's not the first ship to arrive, previous ships could have the same kind of fancy setups to slow the ship down, but those will take a lot of resources to build, and won't likely exist until many ships have arrived and settled into the new star system.

That said, your ship can't have a completely closed setup. EM energy will leak out into space, plus entropy says every time your life cycle loops around, you don't have quite as much extra energy. So you need a power source that will keep the ship warm, feed the plants, etc. for the duration of your trip, although a decent-sized batch of nuclear fuel should suffice depending on the size of the ship and crew.

The other consideration is that you'll get there faster if you keep accelerating to the halfway point. This means you need much more fuel to accelerate, then even more fuel to decelerate, and even more fuel to get all that fuel out of the solar system, and even more fuel to get all of that off the origin planet's surface. It will be a lot more expensive, but less time in transit means less opportunity for failure, and fewer generations living in the ship.

1 I think you could technically use a giant lightsail to airbrake once you get to the other end, but my gut feeling is there's not enough acceleration there to slow you down from the very high speeds you'd want to traverse interstellar space at. However, the wikipedia article mentions a hypothetical way to propel a spacecraft to the inner Oort cloud (about 0.8 ly from Earth) in 30 years, so similar technology might be used to reach Proxima Centauri (about 4.2 ly from Earth) in a reasonable timeframe using no rockets.

2 Tiny errors in velocity at the beginning of the trip could cause you to miss the other star system entirely if not accounted for. As seen in Brendan's answer to another question, even the moon flights made a couple small course corrections along the way, and that's about 100 million times closer than the nearest star system.

• Thanks for reminding me of Entropy. Will take that into consideration. Sep 18 '16 at 11:49
• I would highly recommend having some delta-v budget for mid-course corrections (as opposed to "you don't need to use any thrust on the way"). Even interplanetary, let alone interstellar, space is really quite empty, but with anything resembling current technology, we might be able to aim for a star system but we'll certainly need to to late course corrections as we approach it in order to aim for the intended planet. And of course, you need the delta-v to land somehow. Lithobraking might work in Le Voyage dans la Lune, but hardly here.
– user
Sep 18 '16 at 12:12