Calculating Gravitational Force at Different Distances from Earth's Center

[oMovements]

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.

 

[nkentros7]

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.

 

[nil1996]

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

 

[oMovements]

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.

 

[nil1996]

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

F=GM_earthM_man/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 GM_earthM_man/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=GM_earthM_man/R²....1
F2=GM_earthM_man/(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

 

[haruspex]

F=GM_earthM_man/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 GM_earthM_man/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=GM_earthM_man/R²....1
F2=GM_earthM_man/(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.

 

[nil1996]

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.