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[ 3.6 ms ] story [ 20.7 ms ] thread
Problem is, it doesn't discuss much on what those savings might be, only that they exist.
I think they are speaking of the Oberth Effect: http://en.wikipedia.org/wiki/Oberth_effect about which I know nearly nothing, but the multiplier at the end of the Wikipedia example is 3.3.

In brief, you let a planet pull you in to its gravity well, then while you are going very fast burn your fuel to get your Δv.

At this point my physics falls apart. You either…

1) Gain the energy from the propellent coming down and not having to go back up. (f=ma doesn't help me here)

2) Gain extra energy because the rocket force is constant and with a greater 'v' the kinetic energy is greater. (says whose frame of reference?)

3) Gain energy because you balance some equation and realize you left the exhaust at a lower altitude. (Dr. Carl Bender tried to pull this stuff on me in freshman physics. It looked good on him.)

John Crighton did this on farscape...it worked really well!
I recently heard a talk on a similar idea: http://en.wikipedia.org/wiki/Aerogravity_assist

A lot of technology still needs to be developed before something like this is viable, but if it were possible a trip to mars travel time would be cut down tremendously. If I remember right there were two launch windows a year using that method.