Gravitation

[MedPR]

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If a space station is located a distance of twice the radius of the Earth away from the surface of the Earth, the acceleration due to gravitational attraction from the Earth on the space station is:

A. 1/9 of that on the earth
B. 1/4 of that on the earth
C. 1/2 of that on the earth
D. equal to that on the earth

Will post the answer after a while.

 

[dmf2682]

a?

 

[MedPR]

a?

Yea, it's A. I thought it would be B, since gravity on earth already takes into account its radius, but then I reread the question and realized I read it wrong the first time.

 

[gettheleadout]

IIRC, the force of gravity is inversely proportional to the square of the distance from the center of mass, and since that's the center of the earth, two radii away from the surface is three radii total, so with r = 3 and (3)^2 in the denominator, the force should be 1/9 of that on the earth, so A.

Edit: Dang, you confirmed the answer before I actually posted. Anyway, the radius is taken into account for calculating the force of gravity on earth's surface because the radius is 1, right? So a denominator factor of (1)^2 leaves you with the standard force of gravity, and increasing that denominator factor to 9 still gives you 1/9 the original.