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Lunar pogo hopper

8 Aug 2015, 21:46 UTC
Lunar pogo hopper
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Paul Spudis recently offered some thoughts about Drones on the Moon. He notes conventional drones would not work on an airless world.Spudis writes:Sub-orbital “hops” (ballistic flights from point-to-point) are possible, but come at fairly high cost—it takes nearly as much energy to fly hundreds of kilometers on the Moon in a ballistic hop as it does to go into orbit and then descend elsewhere.This is incorrect. Here I look at suborbital hops on airless worlds. A minimum energy ellipse going from point A to B would have a focus on the midpoint of the chord connecting A & B:The other focus would be at the moon's center, of course.The vis viva equation tells usv=sqrt(GM(2/r - 1/a)In this case GM is the moon's gravitational parameter, r is the moon's radius and a is the semi major axis of the ellipse.Let's say A is 300 km from B. That'd be  about 9.9 degrees separation. Here's a pic:.67 km/s to hop and another .67 km/s for a soft landing. For low lunar orbit that would be 1.68 km/s to take off and another 1.68 km/s to soft land. Energy goes with square of speed. (.67/1.68)2=.16. The energies differ by more than a factor of ...

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