Hey everyone! I'm trying to look at gravity assists. One homework problem in my physics class was the following:
A satellite (with mass negligible compared to that of the Earth) is making a fly-by of the Earth on a hyperbolic orbit. Let the velocity of the Earth be ve. The satellite originally approaches from the negative x-direction, does a loop around the earth, and then flies off in the same direction it came from. Far from the Earth, the magnitude of the satellite's x-component of velocity is vi when approaching and vf when receding. For the case where vi=4ve, what is the final speed vf of the satellite in terms of the speed of the earth ve?
So, for the class, the answer was 2ve. Simple enough. I wanted to visualize this in KSP. The first thing I did was I switched the wording from "earth" to "mun" - don't want to deal with any annoying atmospheric effects. Then I did a bunch of math to get the following HyperEdit parameters:
Inclination: 0
Eccentricity: 15.292
Semi-major axis: -855000
Lon. of asc. node: 344.657
Argument of periapsis: 216.221
Mean anomaly at epoch: -9.705
Epoch: 36643.375
These numbers should put you in a gravity assist with mun at around 9,000 m closest approach. The velocity of the mun is 542 m/s. Thus, to fit with the problem's value of 4 times the velocity of the body, we want to be going around 2168 m/s. Time warping until just before mun capture confirms this number. Once we're into the mun's SOI, we have a velocity of 1625. Once we escape the mun, we're going 1625 relative to the mun - to be expected. Once we get back out to Kerbin's SOI, we expect our velocity to be 2*542, or 1084 m/s. But we look and we're at 2165. This gravity assist only took off 3 m/s from our velocity. Nothing, really. Why is this? I think it lies in the fact that I'm not fulfilling the "does a loop around the [mun]" that existed in the original problem. But how could I possibly make it do a loop? It seems like my speed is too high to really be affected. Can anyone explain where I'm going wrong here? If there are any true saints around here, it would be excellent to get a modified set of orbital parameters, but if not, that's fine, I can do it myself. I just need to have a nudge in the right direction to understand what's wrong with my maneuver.