Reverse gravity-assist, using the moons of a planet

[ScottVal]

Hello,
We hear a lot about gravity-assist, which usually means using a planet like Jupiter to speed a spacecraft on its way to another destination, like Pluto. But what about using a moon of a planet as a reverse gravity-assist?

For example, if you wanted to place a spacecraft in orbit around Pluto, you could approach its moon Charon at just the right angle, to result in a decrease in the spacecraft 's velocity, so you would need less fuel to slow down. Maybe this sort of thing is already being done, but I don't recall hearing anything about it.

Or maybe the effect would be negligible. I guess it would require a moon which resides close to its planet (so its velocity would be high), and has sufficient mass to effect the trajectory of the spacecraft . You could also fly past the moon more than once, to help achieve the desired orbit.

Similarly, Venus could be used to change the orbit of a spacecraft intended to study the sun. The spacecraft could achieve a very low perihelion. The proposed Solar Orbiter spacecraft will be using this technique.
-Scott

 

[mfb]

Similarly, Venus could be used to change the orbit of a spacecraft intended to study the sun. The spacecraft could achieve a very low perihelion.

Parker Solar Probe is doing this at the moment. It made a first Venus fly-by in November last year, its next one will be December 26. It will do five more fly-bys in 2020 to 2024, lowering its perihelion every time. Here is a timeline.

Most of the time you don't gain much - the moons are too small, they don't deflect a spacecraft much that is not already in orbit around the planet.

 

[Vanadium 50]

the moons are too small

I don't think that's the problem. I think it's velocity, not size.

A gravity assist is essentially an elastic collision. From the moon's frame, the spacecraft comes in at velocity v in a hyperbolic orbit, and goes out in a different direction, still at velocity magnitude v.

The problem with a moon is that it is already in orbit, so it is already going at the right speed to be in orbit. How could it not? So the probe has to come in at already almost the right velocity. If you can do that, you probably can place it at exactly the right velocity, so you don't need the moon.

 

[mfb]

You don't need to enter the same orbit as the moon. If you could have arbitrary hyperbolic trajectories you could approach the moon with nearly three times its orbital velocity from behind, make a nearly 180 degree turn and leave it in a counter-rotating orbit. Other directions work for slower approach speeds or other outgoing trajectories.

For the Moon this would mean a velocity of ~3 km/s relative to Earth, but if you approach the Moon with that velocity (2 km/s relative to the Moon) you can't turn by anything close to 180 degrees because it is not massive enough ("too small"). And the Moon is one of the best targets for such a maneuver*. For Europa this would mean a velocity of 27 km/s relative to Europa - that's too fast even for Earth.

If Deimos would be the size of Europa it would make an excellent fly-by target to slow down, but a moon with an escape velocity of 6 meters per second is just not useful for orbit changes.*Charon might look better, but if you approach Pluto slow enough to use that you'll have to wait decades for the probe to arrive.

 

[Vanadium 50]

you can't turn by anything close to 180 degrees because it is not massive enough ("too small").

Isn't the problem that you can't get close enough to the center of mass without hitting the surface? Maybe it's too big.

 

[mfb]

A black hole with the same mass would work, of course.
Objects in the Solar System differ in size much more than they differ in density.

 

[Janus]

*Charon might look better, but if you approach Pluto slow enough to use that you'll have to wait decades for the probe to arrive.

Assuming that you use a minimum energy transfer orbit, your probe would be moving at ~1 km per sec relative to the Sun, compared to Pluto's 4.74 km/sec Charon orbits at something like 0.2 km/sec . So even if you ignore speed picked up from falling towards Pluto, you end up with a minimum relative probe velocity of 3.54 km/sec with respect to Charon. It would take about 45.6 years to reach Pluto this way.
New Horizons, by starting with a greater than minimum energy trajectory and using a gravity assist from Jupiter was able to make the trip in 6 1/2 years, flying by Pluto at a relative velocity of 13.78 km/sec.

Now, even if we assume, that Charon was a equally massed Black hole, and you could do the 180 degree turn around it, the maximum velocity change you could get with respect to Pluto would be twice Charon's orbital speed or ~0.4 km/sec. To effect capture by Pluto, you have to at the very least get it below escape velocity or 0.28 km/sec Thus the probe's velocity with respect to Pluto during the flyby of Charon, can not be any greater than 0.68 km/sec. This in turn means that you would need to keep its initial approach velocity to Pluto to under ~0.61 km/sec. I'm not sure that is possible without burning up more fuel than you would save by the Charon BH gravity assist.