Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.

##
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.

Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.