Calculating Gravitational Force at Different Distances from Earth's Center

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To calculate the gravitational force on an astronaut at various distances from Earth's center, use the formula F = GM1M2/R^2, where G is the gravitational constant. The astronaut's mass and Earth's mass remain constant, allowing the relationship F is inversely proportional to R^2 to be applied. By setting up ratios of forces at different distances, the force at each distance can be derived from the known force at Earth's surface. Specifically, for distances of 2R, 5R, 10R, and 17.2R, the gravitational force can be calculated using the initial force of 634N. This approach avoids needing the specific values for Earth's mass and radius.
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Homework Statement


The force of gravity at Earth's surface on an astronaut is 634N. What is the force of gravity on the same person at each of the following distances, in multiples of Earth's radius, from the centre of Earth?
a) 2 b)5 c)10 d)17.2

I have no idea how to solve this, can someone please point me in the right direction of how to solve this question.
 
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Seems to me that this is a problem involving Newton's law of universal gravitation:

F=(g x mass 1 x mass 2) / (r^2) with g being the gravitational constant, 6.67 x 10^-11.
You can solve for the astronaut's mass, and use this equation (assuming the Earth's mass and radius as given, just look this up) to solve for the force of gravity on the astronaut.

Correct me if I'm wrong, I'm only another AP Physics student.
 
Last edited:
You don't need Earth's mass and radius and also G.
We have F=GM1M2/R2

As according to your problem M1 and M2 are not going to change

Use F is inversely proportional to R2

F1/F2=R22/R12
 
nil1996 said:
You don't need Earth's mass and radius and also G.
We have F=GM1M2/R2

As according to your problem M1 and M2 are not going to change

Use F is inversely proportional to R2

F1/F2=R22/R12

I don't understand how you came up with that equation.
 
oMovements said:
I don't understand how you came up with that equation.

F=GMearthMman/R2

Now according to the problem it is asked to find the force on the man when its distance from the center of Earth is 2R,4R...etc

So in the formula GMearthMman/R2 we are going to change the distance R.Right?

As everything else in the formula is going to remain constant except R
We can say that F is dirctly proportional to 1/R1

so let F1 be the force of gravity on the man at a distance R from the centre of earth.
Let F2 be the force of gravity on the man at a distance R2 from the centre of earth.

So F1=GMearthMman/R2....1
F2=GMearthMman/(R1)2......2

divide equation 1 by 2 you will get my formula.

For your firsr problem R1=2R and F1=634

put in the above equation you will get F2
 
Last edited:
nil1996 said:
F=GMearthMman/R2

Now according to the problem it is asked to find the force on the man when its distance from the center of Earth is 2R,4R...etc

So in the formula GMearthMman/R2 we are going to change the distance R.Right?

As everything else in the formula is going to remain constant except R
We can say that F is dirctly proportional to 1/R1

so let F1 be the force of gravity on the man at a distance R from the centre of earth.
Let F2 be the force of gravity on the man at a distance R2 from the centre of earth.

So F1=GMearthMman/R2....1
F2=GMearthMman/(R1)2......2

divide equation 1 by 2 you will get my formula.

For your firsr problem R1=2R and F1=634

put in the above equation you will get F2

Please don't post complete solutions. Just give the questioner a nudge in the right direction.
 
haruspex said:
Please don't post complete solutions. Just give the questioner a nudge in the right direction.


Oh,sorry for that.I will take care next time.
 
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