# Lunar gravity assist en route to Mars

1. Sep 1, 2010

### Witan

I was wondering how feasible it would be for a spacecraft to use a lunar gravity assist on its route to Mars. Specifically, I was wondering;

1.) Would such a maneuver boost the delta-v en route to Mars?

2.) Would any such boost be possible in terms of its geometry? (i.e., would a lunar boost keep the spacecraft in the ecliptic?)

If there isn't any tangible benefit, is the effect of a lunar flyby on the trajectory at least neutral? I was thinking, even if the spacecraft doesn't get a large boost, it could at least use the close lunar flyby as a scientific bonus to help map the Moon's lumpy gravitational field before heading off to Mars.

2. Sep 2, 2010

### qraal

Possible, but tricky. However the so-called "Interplanetary Super-Highway" might allow such maneuverings for a low delta-vee cost. Very useful like that.

3. Sep 2, 2010

### Witan

What would make such a trajectory tricky?

4. Sep 2, 2010

### Jonathan Scott

If you mean using gravity assist starting from earth, try a quick calculation:

I make it that the moon's orbital speed relative to the earth is roughly 1km/s, which means that relative to the earth, the maximum theoretically possible delta-v would be twice that, 2km/s, which isn't going to help a lot, considering that Earth's escape velocity is 11.2km/s.

If instead you mean using a gravity assist after the spacecraft has already been away from the earth and come back, then using the earth would obviously be far more efficient.

5. Sep 2, 2010

### Janus

Staff Emeritus
But the escape velocity at the distance of the Moon is only 1.414 km/s, and Even a savings of 2 km/sec is fairly significant.

Unfortunately, you could never get that 2 km/sec boost is real life, as the trajectory around the Moon needed would intersect the surface of the Moon.

I think that this question came up before and I calculated about how much boost you could get from the Moon. It came out to be pretty small.

Another drawback is that in order to get the correct trajectory to reach a given planet, you have to wait until the Moon is in the right relative position in its orbit. Since minimum energy trajectories only occur when the Earth and target planet have the right relative positions in their orbits, it would be a rare occasion for both to happen at the same time.

6. Sep 2, 2010

### Jonathan Scott

Yes, I'm aware that from the Moon's orbit the escape velocity is much smaller, but I felt that rough comparison with the escape velocity needed to get away from Earth in the first place was a better indication of the relatively small gain.

Thanks. If you happen to have calculated the actual limit (for a path grazing the moon's surface) I'd be interested to know; I can't be bothered to calculate it for myself!

7. Sep 2, 2010

### Witan

Thanks for the replies. Is basically all the info you need to calculate orbits in the two sticky threads? I skimmed through them a little, but I know it's going to take me time to learn it well enough to do it myself.

8. Sep 2, 2010

### twofish-quant

There are a number of ways of doing gravitational assist. I don't think that doing a "lunar gravitational slingshot" will help you very much, but there are some very interesting things that are happening with the concept of the interplanetary superhighway.

The basic idea comes from chaos theory. There are situations with orbits where small changes in direction and speed and results in very large differences in direction. So the idea is that you find a spot near the moon and then a small change in your energy and direction will let you make very large directional changes.

The interplanetary superhighway will not get you to your destination faster, since you still need the energy to get to mars. However by making small changes, it lets you change your direction with extremely small amounts of fuel.

9. Sep 2, 2010

### twofish-quant

If you want to do a gravitational slingshot, the maths are really easy. In reality, the spacecraft is going in a hyperbolic orbit around the planet, but you can approximate things by approximating things as spacecraft bouncing off the surface of the planet. (i.e. draw the asymptotes of the hyperbolic orbit. Now draw a line in which the spacecraft just bounces off the surface of the planet as if the spacecraft and the planet were made of rubber), at long distances the two orbits are very close.

The calculations for doing interplanetary superhighway routes is much more complex, which is why people didn't realize it could be done until the 1990's.