Discrete question with gravitational force ratios

[Tokspor]

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This is a discrete question which I'm confused about because of possible missing information. Let's say there are two satellites, A and B. Satellite A is resting on the surface of Earth and satellite B is orbiting Earth from an altitude of R, directly over Satellite A. Satellite B is twice the mass of Satellite A. The question then asks for the ratio of Earth's gravitational force on A over its force on B.

A) 1/4
B) 1/2
C) 1
D) 2

I was thinking that I could solve this problem by using F=GmM/r^2. I could plug in r = (R) for F(B) and r = (radius of earth) for F(A). But I wouldn't know exactly by how much "R" and "radius of earth" differ.

Apparently, to solve this, you set up the ratio F(A)/F(B) as I had thought about, but here are their values according to the text:

F(A) = GMm(a)/R^2
F(B) = GMm(b)/(2R)^2

The question stem clearly says that the altitude of B from the surface of Earth is R. Why is R plugged into F(a), and 2R plugged into F(b)?

 

[G1SG2]

This is a discrete question which I'm confused about because of possible missing information. Let's say there are two satellites, A and B. Satellite A is resting on the surface of Earth and satellite B is orbiting Earth from an altitude of R, directly over Satellite A. Satellite B is twice the mass of Satellite A. The question then asks for the ratio of Earth's gravitational force on A over its force on B.

A) 1/4
B) 1/2
C) 1
D) 2

I was thinking that I could solve this problem by using F=GmM/r^2. I could plug in r = (R) for F(B) and r = (radius of earth) for F(A). But I wouldn't know exactly by how much "R" and "radius of earth" differ.

Apparently, to solve this, you set up the ratio F(A)/F(B) as I had thought about, but here are their values according to the text:

F(A) = GMm(a)/R^2
F(B) = GMm(b)/(2R)^2

The question stem clearly says that the altitude of B from the surface of Earth is R. Why is R plugged into F(a), and 2R plugged into F(b)?

Because the problem says that A is "resting on the surface of Earth" (aka it's at a distance of 1 earth radius, or 1r from the center of the earth) and for B, it says "is orbiting Earth from an altitude of R, directly over Satellite A" meaning B is 1 R away from the SURFACE OF THE EARTH (where A is hanging out) so it's R1 (distance from earth's center to the surface where our friend satellite A is hanging out) + R2 (distance from surface of the earth/where satellite A is hanging out to satellite B). So we have earth's center, satellite A at a distance of R away from the center, and satellite B is a distance of R away from the surface, so you have to add another R.

Earth's Center---R---Satellite A (surface of the earth)---R---Satellite B

So, satellite B is TWO Rs away from the earth's center. Always refer back to the earth's center.

Is the answer D? If it is, then another way of looking at the problem would be to just manipulate F=GmM/r^2. If you double m (since B is twice the mass of A) and double r in the denominator (which would give us 4, since 2^2=4), we would end up with F=GM2/4=1/2, so the force exerted on B is half of that exerted on A, or the force exerted on A which is twice that of B, 2:1, which is choice D. Unless I'm wrong and the answer isn't D, in which case I suck. lol.

 

[Tokspor]

Because the problem says that A is "resting on the surface of Earth" (aka it's at a distance of 1 earth radius, or 1r from the center of the earth) and for B, it says "is orbiting Earth from an altitude of R, directly over Satellite A" meaning B is 1 R away from the SURFACE OF THE EARTH (where A is hanging out) so it's R1 (distance from earth's center to the surface where our friend satellite A is hanging out) + R2 (distance from surface of the earth/where satellite A is hanging out to satellite B). So we have earth's center, satellite A at a distance of R away from the center, and satellite B is a distance of R away from the surface, so you have to add another R.

Earth's Center---R---Satellite A (surface of the earth)---R---Satellite B

So, satellite B is TWO Rs away from the earth's center. Always refer back to the earth's center.

Is the answer D?

Thanks for your response. I understand it now that you pointed R out to be the distance from the center of Earth to its surface. I'm looking at the question again and I see that I overlooked R being written as R(e), which is probably their way of indicating that its exact value is 1 Earth radius.

Oh, and yes, the correct answer is D.