Homework Help: Universal law of gravity involving ratios

1. Oct 6, 2007

Rgonzales

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

It basically evolves around:

Fg = G x m1 x m2
r(squared)

Fg = force of gravity
G = constant gravitional 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

3. 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.

2. Oct 6, 2007

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.

3. Oct 6, 2007

Rgonzales

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

4. Oct 6, 2007

Timo

Well, in this case:
1)
2)
3)

5. Oct 6, 2007

Rgonzales

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

Last edited: Oct 7, 2007
6. Oct 7, 2007

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.

7. Oct 7, 2007

Rgonzales

ops sorry i meant 980N.