# Could the Moon's gravitational anomalies be used constructively?

The moon has a habit of de-orbiting passive satellites in low orbit because it is not a homogeneous ball. Any orbit therefore passes through different sections with different surface gravities. This appears chaotic enough that eventually the small disturbances of a lunar orbit accumulate and the orbit then intersects with the surface. I'd call this destructive.

I'm wondering two things.

1. If we had very detailed maps of this gravitational field, could a super computer come up with a medium-high circular orbit that at some point "degrades" to a highly elliptical orbit with the same potential energy, which is oriented in a way to facilitate a transfer to Earth (and vice versa!)?
2. Could we even gain (or lose) potential energy similar to a classical gravity-assist? Basically stealing a small fraction of the Moon's angular momentum to first park an arriving vessel in orbit and later depart the vessel again for almost free.

I'm not sure how detailed the maps are that we have of the gravitational anomalies, but I suspect they are not detailed enough for any of this. And I also wonder how long it would take for the Moon to change orbits of a craft in this way.

• Great question. Way above my pay grade. Commented Aug 29, 2022 at 18:06
• Intuitively I would guess no, because the differences are so small they are usually measured in (countable) wavelengths of microwaves - about 1/10th the width of a human hair over a single orbit. source
– Wyck
Commented Aug 29, 2022 at 19:04
• GRAIL made a pretty good gravity map. en.wikipedia.org/wiki/GRAIL moon.nasa.gov/resources/55/grails-gravity-map-of-the-moon space.stackexchange.com/q/26986/38535 Commented Aug 29, 2022 at 19:17
• @Wyck Yet eventually these accumulate to such an extent that a satellite can be lost. Commented Aug 29, 2022 at 23:01
• Gravity maps of the moon are good enough that we can find and use an orbit that is stable because all the gravitational perturbations cancel out. So if this can be done, we might well have detailed enough information already to do it. Commented Aug 30, 2022 at 5:17

I’d say “No” to both questions.

It is bewitching to think of a lunar satellite surfing the gravity potentials like a soaring sea-bird, higher and higher…

But my intuition says “no”. A frictionless rollercoaster will never gain energy (potential + kinetic) no matter how cleverly the track is designed. Energy cannot be transferred, but momentum can be.

Kinetic energy and gravitational potential energy are both scalar. Their sum is usually conserved in orbital mechanics unless another form of energy is inputted or removed.

Momentum is a vector quantity and is always conserved. Surfing the gravitational anomalies will never transfer energy to a satellite. But it could possibly transfer momentum. Can enough momentum be transferred to significantly favor an earth transfer orbit? Unlikely.

To see the effect of momentum transfer, compare 4 orbits which (by definition) all have the same total kinetic and potential energy:

“A” is a circular orbit. “D” is a highly elliptic orbit which intersects with the lunar surface.

All orbits have (by definition) the same energy. And they must all have the same potential energy at the same elevation. So their velocity must be the same when they are at the same distance from the Moon. This enlargement shows equal velocity vectors (red) for satellites on Orbits A B and C at the orbital distance of A.

There are an infinite number of other orbits in this set of orbits which differ only in momentum, not energy. The range of eccentricities of these orbits is limited by how near the radius of “A” is to the Lunar surface. The lower the orbit, the smaller a change in eccentricity before cratering.

To surf the Moon’s gravitational anomalies, the satellite would need to be in a very low orbit. Any change in orbital eccentricity would either raise the altitude (taking the satellite out of the surf zone) or lower the orbit and end the experiment.

• I don't see how this contradicts the hypothesis of the question. Even if the satellite cannot gain energy, changing the orbit from A to C/D would already be beneficial to a return home (if the vessel does not intersect the surface). A change from C to A would also be beneficial for arriving at the Moon. The red arrows you drew are not wrong, but irrelevant. The velocity at periapsis is. The argument that energy cannot be transferred doesn't make sense to me either. In a gravity assist, that is precisely what happens. Commented Aug 29, 2022 at 23:11
• @bitmask I think the answer is contending in the last paragraph that a satellite in a medium-circular orbit (as you the OP propose) would only be negligibly affected by the Moon's gravitational anomalies. But I agree the argument for this particular point is somewhat lacking. Commented Aug 30, 2022 at 5:16
• I fully agree with the energy aspect. But at least the "which is oriented in a way" part of the question should be possible. Commented Aug 30, 2022 at 7:38