guest blogger john hare
My methods of getting a quick check on feasibility of of a concept generally consist of finding something simple enough for me to figure quickly. Sometimes without even a calculator. Since it never occurred to me that you couldn’t turn 180 degrees with a gravity turn at high velocity until Doug questioned it, I had to find a method of general checking that I could understand. I don’t program computers, and have never studied higher mathematics, so that left me with the graphic methods I picked up in drafting classes twenty mumble years back.
I didn’t want to show my work as it is obviously inadequate for serious orbital calculations even though it was good enough to let me know that the comment of less than 1 degree of available gravity turn from the moon was off. Since Bob has linked a legitimate method of figuring gravity turns now, I can show why I was certain that the comment was off, even though I couldn’t prove it to a degree anybody would consider satisfactory.
With Lunar gravity of 1.62 m/s at the surface, a close flyby can reach a 1.6 m/s altitude at perilune with no atmosphere to prevent it from getting that close. During the next 100 seconds, the spacecraft will be accelerated down by just over 150 m/s and decelerated by about 15 m/s. The velocity at the end will be just under 3500 m/s with a down component of just over 150 m/s. This is well over 1 degree of turn during that segment. Each additional segment will contribute less and less turn as the vehicle climbs higher with a lower velocity gravity vector. After figuring the components after perilune, the mirror image will apply to the approach before perilune. I neverÂ went beyond three segments because this is so clumsy and inadequate, not to mention time consuming and frustrating when it was certain thatÂ better methods were available somewhere.
I will use this clumsy method and other similar stuff to make sure that I am using the real formulas correctly. I can already see that my first impression of the table Bob postedÂ was off on the pessimistic side. I think I see a way clear to use a Lunar/Earth/Lunar pattern flybyÂ to get the results of the original post Â even if more complicated.Â
Apparently something of this nature was calculated in the 1920s by a Russian. I’m certain that this work has been done properly by more than one group. The idea here is not to produce an operating mission plan, but rather to prove that one is possible for people that can use it. Then the interested parties can shake proper answers out of the ivory towers.