Question

Deimos, a moon of Mars, is about 12 km in diameter with mass 1.5×1015 kg. 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?

I am stuck on how to solve this problem. Thanks!

Answer 1

Answer:

a)  v = 4.08 m / s , b)     T = 2.58 h

Explanation:

For this exercise, let's start by using Newton's second law where force is the attraction of gravity

          F = m a

Force is

          F = G m $M_{D}$ / r²

The acceleration is centripetal

         a = v² / r

Let's replace

        G m $M_{D}$  / r² = m v² / r

        G $M_{D}$  / r = v²

        v = √ G $M_{D}$  / r

The radius is half the diameter

        r = d / 2

        r = 12 10³/2 = 6.0 10³ m

       v = √ (6.67 10⁻¹¹ 1.5 10¹⁵/6 10³

       v = √ 16,675

       v = 4.08 m / s

If you throw the ball with this speed, take a full turn

c) The constant speed module only changes the direction, so we can use the relationship

        v = d / t

The time is

       t = d / v

The distance along the circle and this time is called Period

       d = 2π r

       d = 2π 6 10³

       d = 37,70 10³ m

Let's calculate

       T = 37.70 10³ / 4.08

       T = 9.24 10³ s

Let's reduce to hours

     T = 9.24 10³ s (1h / 3600 s)

     T = 2.58 h