Question

A spaceship is in orbit around the earth at an altitude of 400 miles.

a) Draw a Force Body Diagram for an 80 kg astronaut.

b) Describe (or calculate) the astronaut's weight at this location.

c) Explain why the astronauts on the ship experience "weightlessness."

Answer 1

First, I will find the value of g at 400 miles

400 miles = 643.738 km

g = Gm / r²

here r is the distance from center of earth to the spaceship

radius of earth = 6370 Km

r = 6370 + 643.738 = 7013.738 Km

g = 6.67e-11*5.98e24 / (7013.738 * 1000)²

g = 8.108 m/s²

Thereforem weight of astronaut is

W = mg

W = 80 * 8.108

W = 648.66 N

astronauts on the ship experience "weightlessness because there are no external objects touching our body and exerting a push or pull upon it. Weightlessness exist when all contact forces are removed. This is common when we are in a free fall.