Universal law of gravity involving ratios

[Rgonzales]

Homework Statement

For this problem, use ratios only to obtain the weight of a person at the following distances. Assume the person weighs 980N on the surface of Earth.

a) 128 000km above the surface of Earth
b) 4.5 times the distance from the centre of Earth
c) 745 400km from Earths Centre.

Homework Equations

It basically evolves around:

Fg = G x m1 x m2
r(squared)

Fg = force of gravity
G = constant gravitational force
m1 and m2 = mass
r = distance

however,

we are using a ratio so the teacher told us that it is:

fg1 x r1(squared) = fg2 x r2(squared)

r = distance
fg = force of gravity

The Attempt at a Solution

We started this yesterday in class and he told us to try it so I am not sure how to attempt this. I tried doing a FBD ( Free body diagram ) to make the question abit easier, but no success. Please help me.

 

[Timo]

What exactly is your question/problem? Proving $$F_{g1} r_1^2 = F_{g2} r_2^2$$ or applying it to the problem you stated?
For proving: Take a close look at the general expression for the gravitational force - maybe you get the idea (I don't want to reveal too much and there's several possible attempts).
For solving the stated problem using the relation: Just do it. Which of the four appearing variables do you know, which don't you know? Solve the equation for the one you don't know and plug in the numbers.

 

[Rgonzales]

I need to find the weight at of the object at each distance using the ratio that you stated.

 

[Timo]

Well, in this case:
1)

Which of the four appearing variables do you know (the value of) ?

2)

Which of the four appearing variables don't you know (the value of)?

3)

Solve the equation for the one you don't know and plug in the numbers.

 

[Rgonzales]

k well fg1 = 980 N , we have r1 = 128,000, what will be r2?

 

[Timo]

I don't know where the 500 N come from, you seem to be ignoring the statement "assume the person weighs 980N on the surface of Earth" which fixes two of the variables.

 

[Rgonzales]

ops sorry i meant 980N.