Posted by Mike on Monday, April 5, 2010 at 2:11am.
15 m/s and catch it 2.4 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 240 min.
===================================
t up = 1.2s
a = -gphysics
v = 15 - g t
0 = 15 - gphysics (1.2)
g physics = 15/1.2
gphysics = 12.5 m/s^2
on surface
F = m gphysics = G m Mphysics/Rphysics^2
so
12.5 = G Mphysics/Rphysics^2
in orbit
F = G mship Mphysics/4Rphysics^2 = mship v^2/2 Rphysics
12.5 = 2v^2 /( Rphysics)
T = 240*60 = 2 pi (2Rphysics)/v
so
v^2 = [4 pi Rphysics/(240*60)]^2
so
12.5 = 2[4 pi Rphysics/(240*60)]^2/Rphysics
solve for Rphysics and go back for Mphysics
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