Physics Find mass and radius of planet.
posted by Mike on .
While visiting Planet Physics, you toss a rock straight up at 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.
What is the mass of Planet Physics?
What is the radius of Planet Physics?

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.
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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