# Accelerating, then decelerating, without expending energy or propellant in space?

If I understand it correctly, moving in the absence of forces like gravity and without friction doesn't require energy, only accelerating and decelerating does. So you could move a spaceship a very long distance with very low energy requirement if you just move it very slowly. Now spending more energy to achieve the same end result just in less time sounds a bit strange to me so I was wondering if there is some theoretical way around that.

For example, on the earth, there are bikes with brakes that wind up springs. After you brake, there is elastic energy in the spring and when you release the spring, it gets converted back to kinetic energy. Brake again and you moved fast and the bike is theoretically (no friction) in the same state as before, just in a different place and because it both accelerated and decelerated, I assume the earth didn't move, even minimally. So theoretically, the bike could do this infinitely.

Now, is something like this theoretically possible in space? For example, could the spaceship collect the propellant in a really long elastic bag which then snaps back and decelerates it again?

P.S.: I'm not a physicist so apologies if I didn't use some concepts correctly. I know energy cannot really be lost, what I mean with "expended" is that the spaceship has less of it.

• That would be the Holy Grail of space travel. Unfortunately, any system like you mention can only travel as far as the connecting link (elastic bag, wire, rail, etc) is long before you are back to the basic "expel propellant in one direction to go in the opposite direction" scenario, except with an extremely difficult to control vehicle. Mar 3, 2017 at 10:40
• Well you can do it... if you consider you — the person — and your propellant as part of "yourself". Then you actually do not spend any energy when travelling in space. It is just that "yourself" does not actually go anywhere either. The collective center of mass of "yourself" remains right where it is, even if you — the person — have moved. For all practical intents and purposes however, yeah, that propellant is spent. Hence: no, you cannot start and stop in empty space without expending propellant. Mar 3, 2017 at 12:54
• This may also be of use to research. nasa.gov/mission_pages/tdm/solarsail/index.html
Mar 3, 2017 at 15:31
• Now spending more energy to achieve the same end result just in less time sounds a bit strange to me. For takeoff from the gravity well (or to get to orbit), you need to attain approximately escape velocity, which is huge. For interplanetary travel, you are presumably trying to get there before your whole crew dies. Mar 3, 2017 at 18:49
• "So you could move a spaceship a very long distance with very low energy requirement if you just move it very slowly." Actually, you can move that ship an unlimited distance at any velocity you want without expending any additional energy at all. This is Newton's First Law. You are right, however, about acceleration requiring energy for most cases. Mar 4, 2017 at 20:44

No, it's not possible.

Your bike example is not a good analog. When you accelerate the bike one way, you actually also accelerate the Earth itself the other way. You stay in touch with the Earth, and that's why you can collect some of that momentum later and get energy back from it. But the center of mass of you + Earth stays in one place and does not move at all.

In space, this would work to some extent. But again, the centre of mass of your starship and propellant would stay in one place. This means that either you would need an interstellar / interplanetary long elastic bag, or you wouldn't move really far.

There were many attempts to solve what you are writing about. It's called Reactionless Drive (for not expending propellant, at least). Go read the linked article if you want, but long story short: Maybe it is possible, but the best we have is some speculations.

For not expending energy, we don't even have sound speculations. Escaping gravity well and changing velocity to match it with target is going to cost energy no matter what, as far as physics is understood nowadays. And to see why can't we get energy back from braking, see this question on Physic SE - there are details of physics involved.

• Of course there are simplifications in my answer, but OP is not physicist so I did my best to be reasonably accurate, but my priority was on being easy to understand. Mar 3, 2017 at 10:48
• Thanks for the easily understandable explanation and the link! I didn't know that this concept is already explored, now I have search term to know more about it. Mar 3, 2017 at 11:32
• @KonradHöffner Thank you for accepting my answer, but don't do it this fast. What if someone will have better explanation? Or creative way around these issues? By accepting, you're saying you don't need any more answers, so it's usually a good idea to wait a day or two. And I don't mind if you will un-accept my answer, only to accept this or better answer in few days :) Mar 3, 2017 at 13:19
• @SethWhite You can get energy back from elastic pulled. Some will get wasted to heat, but (at least in theory) a lot of it would be recoverable. Mar 3, 2017 at 15:28
• But see my answer, below. I think you missed the idea of tge OP which is to regenerate travel energy, not have a reactionless drive. Mar 5, 2017 at 18:54

Not only it is possible but it is used often. Unfortunately, gravitational assist has some restrictions.

Gravitational assist means that you aim towards a massive body (for local travel a planet, for interestellar travel it could be a sun) and use it to change your speed. The gravitational pull of the body will make your ship go faster as you approach the planet and slower as you get away from it.

The trick is that, if you want to accelerate in velocity in a particular direction, you approach a planet that moves in that direction. While in relation to this planet the maneuver is neutral (if you do not apply thrust you move at the same speed with relation to the planet at the beginning and at the end), part of the energy of the movement of the body is passed to your ship, that gets accelerated.

Of course, the restrictions are considerable:

• There must be a planet that moves in the general direction that you want to accelerate towards.

• You must get to the planet.

• The time between flybies around stellar bodies may be considerable.

An example of storing energy along the lines you ask, similar to the regenerative brakes, was described by Robert L. Forward as an application of space tethers.

Imagine you have a long teather, spinning like a propeller. A cargo pod docks at the center, then moves to the fast-spinning rim, whereit is released. This throws the pod, reducing the energy stored in the flywheel. At the other end of the voyage, a similar teather catches a fast moving pod, gentely as its velocity is the same as the moving tip. Then it is shifted to the center where it is released.

Once spun up, cargo pods can be exchanged with no additional cost of energy. The energy needed to propell a pod one way is ballanced by one going the other way, and likewise the change in potential energy is ballanced by two-way cargo of the same mass. I think this regenerative momentum exchange is exactly what you were asking.

The full energy re-use is true enough for the pods, but there is still an ongoing energy need that I don’t think was explained in the tether explainations I’ve seen, but was detailed in a recent short story Stepping Stones by Greg Egan.

The momentum wheels on the terminal ends of the route, as well as any that have unballanced traffic in general, will pick up (linear) momentum in the same direction from both throws and catches. That is, they will repell each other.

There is no law of physics that would prevent cancelling out the excess by sending surplus momentum from one to the other. Say, connect them with a rope! But barring a practical engineering solution, each momentum transfer station will need to deal with it. One way is to be in an false orbit that relies on the excess momentum to work; e.g. the station closest to the sun would be at a slightly farther position so that the constant thrust in the sunward direction gives it the closed orbit. Likewise, the station farthest from the sun would be positioned somewhat closer.

But in general, the momentum transfer stations will need active station keeping, even if only a fraction of the true momentum excess.

Yes, it's possible.

Your elastic bag is Universe itself. And there is a thing called Interstellar medium

You expel the propellant in one place (at the starting point) and collect it at another place(at your destination point).

The main problem, actually two, are the following

• a way of making the collection possible, fast enough.
• recuperating the energy, the efficiency of the process.

Bussard ramjet is one of the concepts which suggest exploiting the situation in favor of interstellar ships. Not everything is easy with it, and it has its own problems, but it is close enough to what you describe, even when it expels and uses energy.

Also as a note, the absence of friction does not mean you need a little energy to move, it depends, gravity forces and gravitational potential is different in different places of the universe, and you have enough kinetic energy to move from gravitational well to a place with higher gravitational potential. Also, those forces do not stay still because planets, stars, and galaxies also are moving.

Sort of, perhaps.

The specific example you gave won't work for the reason Mołot gave, but there is an alternative: move the space that contains your ship.

The Alcubierre drive, the real-world's warp drive (unfortunately still hypothetical), does not directly require reaction mass or consume fuel while it's switched on. Instead, the drive expands space behind your ship while contracting space in front of your ship, so despite ending up somewhere other than where you started, in many important senses you're not actually moving to get there.

The drive has many problems, including but not limited to: The stuff it's made from might not be a thing that exists.

(I'm not qualified to say for sure, but I suspect the fact you're moving the space your in rather than your ship means it doesn't give you more kinetic energy, which in turn means you can't use it to escape a gravity well. I think I have a new question to ask physics.stackexchange.com!)

• But the Alcubierre drive would require insane amounts of energy to instigate. Orders of magnitude greater than the estimated mass of the observable universe. Mar 3, 2017 at 21:12
• Only if you're going faster than light, and even then there are many solutions that can reduce the energy requirements. The Alcubierre drive can be used for slower-than-light, not only superluminal, which also solves the problems with being a time machine, being unable to switch it on or off, being unsteerable, it scooping up ISM and turning it into a shower of gamma rays at your destination if you could stop it, and the interior region being bathed in Hawking radiation because one end is effectively a white hole and the other a black hole. Mar 3, 2017 at 21:19
• the real-world's warp drive (unfortunately still hypothetical) :-s Mar 3, 2017 at 21:48
• @SJuan76 "real-world" in the sense proper physicists get paid to work on making it no-longer hypothetical. :) Mar 3, 2017 at 23:11
• @JDługosz actualy you are quite out of date, the energy requirement has been downsized twice because of redesigning the shape of the Warp Bubble. The current energy requirement is estimated to be the equivalent to the mass of Voyager 1 or a Volkswagen Beetle. You may want to read this link "en.wikipedia.org/wiki/Harold_G._White" Mar 4, 2017 at 0:16

There is a swimming-like motion that expends no propellant that permits changing one's orbital position laterally. But look how slow it is. :(

EDIT: that article sucks. :(

I think this is within the scope of your question.

This is a real project with real funding and a real solution with a now proposed upgraded solution. Using a Sail on a "superfast miniature probes" using a Laser to provide acceleration to relativistic speeds. Approximately 20 years to go 4.22 Light Years. Both solutions use Energy, but the Probe (ship, Proof of Concept for scaling) does not carry propellant or expend energy for propulsion. A good analogy would be a Sailing Ship.

How We Could Visit the Possibly Earth-Like Planet Proxima b

This is not really the story I was looking for but good enough. In the comments you will see a post suggesting using the Solar Wind from the Target Star to slow the device down. Well I am 75% certain it was a group from Cal Tech that did the math and models that suggest a larger Sail will do the job but would add some years to the trip. BUT a benefit is the Sail then could use that Same Solar Wind to Navigate around the Star System looking at it in detail and for a long period of time. The Sail could possible be used as an Energy Source for the on-board electronics.

I've read over these answers and most of them are trying to give you realistic alternatives to what you actually want: an inertia battery. That is, you want a way to store and retrieve velocity sans acceleration.

Now, that's not actually a thing that we know how to build. It may be a physical impossibility in this universe. But if you're going for "semi-believable sci-fi" then you can certainly throw some handwavium in there. You wouldn't be the first. Larry Niven's Outsiders use such a technology, though he doesn't name it as such.

• A momentum and potential energy battery, not inertia: see my Answer below! Mar 4, 2017 at 17:31

Yes, something similar to this is indeed somewhat possible.

By throwing out a ball (propellant) on a really long rope. Unfortunately (or fortunately?), you will stop as soon as you run out of rope, and you'll move back to your starting point if you reel the rope back in.

BenRW mentioned Warp Drive. I'm going to clarify a few things regarding that. The way warp drive works is by causing mass to invert without affecting volume. Imagine a 10KG ball traveling at 1KMps. If you cut its mass in half without removing the energy in its momentum, you can double its velocity. All you have to do is figure out how to reduce the mass without changing anything regarding its composition.

Warp drive works on an asymptote on the reverse curve. By creating a negative mass, you can never mathematically go below the speed of light. A common theoretical particle that does this is called a tachyon which can travel the length of infinity instantly due to it's own mathematical quark.

So in short; to speed up, reduce your mass. To slow down, restore it. You'll still incur an energy penalty depending on how you accomplish this.

• Please review my edit for future reference. Mar 4, 2017 at 17:33
• I think you are confused here. A negative mass would be limited to light speed in the normal way, but allow a pair of matched pos/neg masses to accellarete for no energy cost. imaginary mass would be limited to speeds greater than light. Mar 4, 2017 at 17:36
• I started reading through Einstein's work regarding the theory of relativity and stress–energy tensor. Then I remembered that this is for fiction and I'm not trying to build a real warp drive. Also, my head hurts. So I'll go with what you said. I think the only way Warp drive will be possible is if someone builds a prototype before establishing a sound theory. On that note, I think Hyper Gates are a better way to travel. Mar 5, 2017 at 18:20
• This Answer is not the way to go in a story: it is mixing up two completely different ideas. See negative mass on Wikipedia. If you want a warp drive (usually for FTL travel) then that's something else. This question is asking about not expending energy when travelling — which is indeed what a negative matter drive as imagined by Forward would do, but that's not what’s described in this Answer. Mar 5, 2017 at 18:48
• I suggest this book to read if you want to understand relativity. Mar 5, 2017 at 18:51

Low energy travel within the solar system is possible, as long as you can wait long enough.

Once you reach the Earth-Sun L2 Lagrange point, there are very low energy transfers available to take you to other Lagrange points within the solar system. The downside is that these may take so long that they are not only restricted to cargo, but also not usable for cargo that has to get there in a reasonable time - materials for building your Mars base for example.

• Note that you can include links in your post—in fact, most do, and Wikipedia is often the target. Look at the toolbar and associated help when editing. Mar 5, 2017 at 19:23
• Oh, and welcome to Worldbuilding! Mar 5, 2017 at 19:25

If the universe wraps around on itself then if you expell a mass opposite your trajectory to get you going, you can encounter that mass later in time when it flies around the closed universe. You can exchange momentum with the "propellent" again to come to a stop at the destination.

You don't actually expend any propellent because you reabsorb it later when it wraps back around. In such a setup you could hypothetically reuse your reaction mass.
You'd have to vary the mass of your ship & propellent and take into account the size of the universe in order to plot trajectories & travel times accurately--and have some foreknowledge as to whether the space you launch your propellent into is clear of debris that could potentially destroy it or set it off-course.

You probably couldn't do this in our universe. Even if our universe were closed, unless you could halt the expansion of space your reaction mass would never be able to complete a circuit.
It would be easy and maybe even preferred in a smaller closed-universe, maybe millions of AU to a few dozen or light-years "around". I'm imagining a spacecraft with an immense coilgun hundreds or thousands of kms long, accelerating large masses toward its destination opposite it's direction of travel, flipping, and then rendezvousing with those masses, capturing them within the coilgun and then decelerating them, recapturing that momentum and coming to a halt.

For a universe nearly the size of ours, you'd want to achieve seriously high fractions of c to get anywhere in a reasonable amount of time. We're talking condensing billions or even trillions of years down to a hundred or less via time dilation. At that point, you're likely flinging stellar masses around to travel a regular size spacecraft.

## Attach a Flywheel to a Space Elevator

JDługosz's answer does such a great job of describing how a flywheel can be used to recapture energy that I feel no need to elaborate on that part further... however, his answer does not resolve the question of how to keep your flywheels somewhere useful.

Instead of tethering your two flywheels to each other, you just need to teether them to an adequately massive, spinning nearby object like a planet or large asteroid. A space elevator uses a counterweight that extends far enough into space that the angular momentum caused by the planet's rotation exceeds the acceleration of gravity. This causes your counterweight to "fall" away from the planet creating tension to hold its tether taught. Because the counterweight is constantly pulling the teether in the opposite direction of the planet's gravity, when your flywheel catches a cargo pod and gets pushed off to the side, it will immediately begin to fall back to its geosynchronous resting location. Because you add the inertia of an entire planet to your system, the reaction's center of gravity only experiences a very marginal change in velocity allowing you to stop a fast moving object without sending your flywheel station hurdling off into deep space or needing to spend its own fuel to maintain a proper orbit.

Also, space elevators are a GREAT way for getting things onto and off of planets without having to fight with any tyranny of rocket equations; so, not only do you gain a ton of cost efficiency with the flywheel, but you also save tons of energy getting stuff onto and off of the planet itself.

I will try to give an easy to understand explanation of why it won't work. First of all, you need to understand that everything can be seen as a 'system' with a center of mass. Imagine a solid sphere. Its center of mass is exaclty in the middle.

(the center of mass is represented with a blue dot)

Now imagine you have two of those spheres.

Both the spheres have a center of mass. However, the system as a whole, consisting of both spheres, has its own center of mass. (represented with the red dot in the picture above) This doesn't necessarilly have to be inside an object.

Whatever you do, the center of mass of the entire system will always remain at the same spot, unless something from outside the system interacts with it. When one of the objects pushes itself away from the other object, both objects will fly away at such speeds that the center of mass of the entire system is still at the same spot.

When one of the objects goes to the right, the other goes to the left. When one of the objects stops the other, both objects will stop. This is called conservation of momentem. When a system goes at a certain speed (in our example 0 m/s), nothing inside that system can cause the center of mass of the entire system to change velocity. The reason we can still say that a rocket changes speed is because we constantly redefine the system to be only the rocket itself and the fuel it hasn't used yet. This way we end up with a system with a center of mass that is moving relative to the original system, but with less mass.

This is the reason why it isn't possible to change speed without the loss of mass.

• You are saying “it won't work” but explaining what it needs to work (e.g. the momentum transfer devices in my earlier answer). Mar 11, 2017 at 23:51

I would say no to energy, but yes to propellant.

Scifi: Gravity Drives could be used to move from place to place if the mass can be localized enough, (I'm pulling this from the video game "Space Engineers")

Real science: I remember coming across a boat that allowed movement by slowly winding up a massive weight and then ramming it forward to accelerate the mass and by its extension... the boat.

Newton's laws will come to play but don't expect to get anywhere soon, especially in the presence of gravity

• Your “Real science” example is not. That kind of thing only works in a viscus medium (poorly; oars are more efficient), not in a vacuum. Mar 4, 2017 at 17:30