Question

Deimos, a moon of Mars, is about 12 km in diameter with mass 1.5×1015kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter!
Part A
With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?
Express your answer with the appropriate units.
Part C
How long (in hours) after throwing the ball should you be ready to hit it?

Answer 1

Answer:

A) 4.1 m/s C) 2.6 hrs

Explanation:

(Ignore the As in the equation, I don't know why those are showing up)

A) The force of gravity equals $\frac{Gm_{1} m_{2} }{r^{2} }$

The force of gravity also equals $\frac{v^{2}m_{1}  }{r}$

Set these equations equal to one another, let $m_{1}$ be the mass of the ball and $m_{2}$ be the mass of Deimos.

G is $6.67*10^{-11}  \frac{Nm^2}{kg^2}$

Use 6000 m for r (diameter divided by 2)

After plugging in numerical values (the mass of the ball cancels out

) the answer is 4.1 m/s

C) $T=\frac{2\pi r}{v}$

Use the value obtained from part A for v. Use 6000 m for r. Divide the answer from this formula by 3600 to get the correct units (hours).