The figure below shows a picture of American astronaut Clay Anderson experiencin

Question

The figure below shows a picture of American astronaut Clay Anderson experiencing weightlessness on board the International Space Station. Most people have the misconception that a person in a spacecraft is weightless because he or she is no longer affected by gravity. Show that this premise cannot be true by computing the gravitational field of the Earth at an altitude of 200 km, the typical altitude of a spacecraft in orbit. (Give the magnitude.) m/s^2 Compare this result with the gravitational field on the surface of the Earth. g_200 km/g_Surface = Why would astronauts in orbit experience weightlessness even if they are experiencing a gravitational field (and therefore a gravitational force)?

Explanation / Answer

h = 200 km = 2 x 10^5 m

acceleration due to gravity is given by:

g = GM/(r + h)^2

g(200) = 6.67 x 10^-11 x 5.97 x 10^24 / (6.37 x 10^6 + 0.2 x 10^6)^2 = 9.23 m/s^2

Hence, g(200) = 9.23 m/s^2

g(200)/g(surface) = 9.23/9.81 = 0.941

Hence, g(200)/g(surface) = 0.941

b)Because, the astronauts have the same acceleration as the space shuttle has, they feel weightlessness.

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