## Physics 211, Quiz 17

Question 1: The Mir space station orbits the earth about 400 km above the Earth's surface. It has a mass of M = 90,000 kg.

Ivan the cosmonaut finishes a bottle of vodka aboard Mir. He opens the hatch, places the empty bottle (m = 0.5 kg) outside, and closes the hatch.

Two days later, Ivan looks outside. Where is the bottle?

• ahead of Mir in its orbit
• just outside the hatch
• behind Mir in its orbit
```  Answer: Mir and the bottle both feel the gravitational force of
the Earth.  The force on Mir is stronger

G * M(Earth) * (90,000 kg)
F(Mir)    = -----------------------------
(6370 km + 400 km)^2

G * M(Earth) * (0.5 kg)
F(bottle) = ---------------------------
(6370 km + 400 km)^2

but the acceleration of both objects is the same

F(Mir)           G * M(Earth)
a(Mir)    =  --------   =  --------------------
90,000 kg     (6370 km + 400 km)^2

F(Mir)           G * M(Earth)
a(bottle) =  --------   =  --------------------
0.5 kg      (6370 km + 400 km)^2

Therefore, if the bottle and Mir are side-by-side at
one moment, sharing the same velocity, then, since they
experience the same acceleration, they will continue to
move together.

The bottle will still be just outside the hatch.

```