Question

You are in a 5.000x106 kg spherical spaceship (R = 100.0 m) and you notice that there is a 2.000 kg ribeye
steak in a perfectly circular orbit around your spaceship! You really want that steak.
You measure the steak’s orbital period to be 94.01 hours. Your mass is 80.00 kg.
a) What is the height of the steak above the surface of the
spaceship (H)?
b) You jump from the surface to catch the steak.
What initial speed do you need so that you stop at the
same height as the steak before you fall back?
c) You catch the steak and tried to cook it but burned it and
are now very angry.
With what minimum speed do you have to throw the steak
away from the surface of the spaceship so that it never
comes back?

Answer 1

1) so centripetal force in circular orbit of thatsteak is equal to gravitational force between steak and spaceship and steak and you

so

Ms is mass of space ship and My is mass of you

r is distance frpom center to steak

T= 94.01 hr=338436 s

so plug in all values we get

so height from surface= -1.1 m it is inside spacership

i think some of data given is wrong please check

2) so initial speed must be

3)and escape velocity is when total energy is become equal to kinetic energy so

so,

so we get