# Propellantless propulsion in gravity field

I have a proposal for a following propellantless maneuver. It is propellantless in sense that no mass is lost from spacecraft. It is not reactionless as spacecraft interacts with planet through gravity field. Also law of conservation of energy stands and spacecraft needs an energy source.

Lets assume spacecraft is orbiting planet on an elliptic orbit(orbit is in plane z=0). Spacecraft consists of ejectable reaction mass and main spacecraft - both are of same mass.

At some place in the orbit spacecraft ejects the reaction mass perpendicular to original orbital plane. As both are of same mass following observations can be made:

1. both new orbits are symmetric around original orbital plane
2. because of symmetry both new orbits will intersect, and the point of intersection will be on the original orbital plane
3. because of symmetry both spacecraft and reaction mass will meet at the same the same time at this point

Lets now assume that the spacecraft captures the reaction mass at this point. Because of symmetry Vx and Vy components of both parts(main spacecraft and reaction mass) will be the same. Vz vectors will be in opposite directions with equal magnitudes, so for capturing Vz has to be absorbed. After capture new orbit will be formed and spacecraft will have the same mass as in the beginning. Also the new orbit will be in the same plane as original orbit.

Now if the speed of ejection is greater than the speed of capture it means that some energy from ejection is left in the orbit. Opposite is true for case when energy absorbed at capture is greater than ejection energy.

Same maneuver can also be completed with hyperbolic escape trajectories(and if capture point tends to infinity efficiency tends to 1 - all energy of ejection is transferred into the new trajectory).

For specific examples tools like NASA GMAT can be used.

Edit: I created a demonstration for the maneuver: https://andrisa1.github.io/propellantless.html

• Ejecting the reaction mass perpendicular to the orbit will require a huge energy expenditure to achieve that much momentum change. How do you think that would be done, without some kind of propellant? Commented Feb 6, 2023 at 18:09
• I meant that force of ejection is perpendicular to orbital plane(and is applied for a brief period), not the new trajectories or speed vectors. Commented Feb 6, 2023 at 18:20
• If you never plan to meet up again with the reaction mass slug you throw out, you will always get more orbital energy benefit to the rest of your spacecraft from it by throwing it out backwards along your current velocity vector than you do by throwing it perpendicular. Commented Feb 6, 2023 at 18:56
• Yes, but if reaction mass is not lost, it can be reused multiple times and in the end it can be usable cargo. Commented Feb 6, 2023 at 19:06
• Can you explain to me how you think ejecting and recapturing will provide a net "propulsion," as it strikes me that will not happen. Commented Feb 6, 2023 at 20:03

I see no particular problem here. Throwing masses around and capturing them to redistribute momentum and energy is completely fine.

Let's consider a simplified planar version of your scheme.

1. The two parts of the spacecraft (red and blue) are sitting on the surface of some airless world.
2. Supplying some energy, these are pushed apart with great force in equal and opposite directions.
3. They travel outwards in equal but mirrored elliptic orbits, loosing speed along the way.
4. At the apoapsis, they recombine, gently touching at the much lower orbital velocity.

You invest some kinetic energy, getting it back as potential energy by moving the spacecraft further out the gravitational field. The opposite is of course also possible, turning potential energy into kinetic energy.

In practice, much greater velocities can be achieved from burning chemical fuels and expanding the combustion gasses. And gasses are hard to catch and reuse.

• Also just to note the obvious - once recombined, the ejection-capture sequence can be performed again and again. Commented Feb 7, 2023 at 10:40