You are watching a TV news program when they switch to some scenes taken abroad

Question

You are watching a TV news program when they switch to some scenes taken abroad the space shuttle which circles 500 miles above the Earth once every 95 minutes. To allow the audience to appreciate the distance involved, the announcer tells you that the radius of the Earth is about 4000 miles and the distance from the Earth to the Moon is about 250,000 miles. When an astronaut drops her pen it floats in front of her face. You immediately wonder how the acceleration of the dropped pen compares to the acceleration of a pen that you might drop here on the surface of the Earth.

Explanation / Answer

here,

the gravitational force on the surface of earth is g = 9.8 m/s^2

accelration due to gravity , g = G * m /r^2

as r is distnace from the centre of earth

r = 250000 + 4000

r = 254000 miles

r = 4.088* 10^8 m

g = 6.67 * 10^-11 * 5.97 * 10^24 /( 4.088 * 10^8)^2

g = 2.38 *10^-3 m/s^2

the accelration due to gravity is very less

so the pen wil float

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