guest blogger john hare
In my last couple of posts involving gravity turns, there seems to be some legitimate doubt whether useful maneuvers can be done with Lunar gravity turns. My numbers are quite different from those obtained by others and my methods are probably unacceptable for serious further debate. I believe there are some clear relationships in gravity turn mechanics just as there are in escape velocity relative to orbital velocity.
If a particular altitude has an orbital velocity of x, then escape velocity will be 1.41x for any gravity field or velocity. A 1,500 m/s circular orbit has an escape velocity of 2,115 m/s whether it is low Lunar orbit, high Earth orbit, or extremely distant Solar orbit. That is a constant relationship.
Somewhere, somebody has derived constant relationships for gravity turn angles relative to local orbital velocity. A useful table for this could fit on an index card. Something like this.
Orbital velocity 1.0x
escape velocity 1.41x
170 degree turn velocity 1.4-x
160 degree turn angle 1.5-x
150 degree turn angle 1.5-x
The real tables are out there somewhere because they are too obvious and useful to not exist. I will put up $100.00 to the first person that finds a reliable, citable source for this information. I think my reasons are obvious.
I said it was a cheap contest.