# Using ratios to obtain the weight of a person at a specific distance

1. Apr 1, 2013

### needingtoknow

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

Assuming the person weighs 980 N on the surface of the Earth, how would you use ratios to obtain the weight of a person at 128 000 km above the surface of the Earth.

2. Relevant equations

Fg is proportional to 1/d2

3. The attempt at a solution

The answer in the key says 0.072 N. I didn't know exactly where to start but by working backwards from the answer I have determined that it is 20 times the distance from the centre of Earth. I know how to solve these questions using ratios if I am given the times the distance from the centre of Earth.

For example for a previous question: Three times the distance from the centre of Earth, here is how I solve it.

Fg is proportional to 1/d^2

1x3 = 3 therefore 980 = 1/3^2

980 / 9 = 109 N

This method works everytime when I am given the times the distance from the centre of Earth. But when I am given a specific distance I do not know how to get the answer. Can someone please help? Thanks!

2. Apr 1, 2013

### Sunil Simha

Since $F\propto\frac{1}{d^2}$, You can write $F = k\frac{1}{d^2}$ where k is the constant of proportionality.

So if $F_1\propto\frac{1}{d_1^2}$ and $F_2\propto\frac{1}{d_2^2}$

then $\frac{F_1}{F_2}=\frac{\frac{1}{d_1^2}}{\frac{1}{d_2^2}}$.

The constants of proportionality cancel.

3. Apr 1, 2013

### Staff: Mentor

The radial distance from the center of the earth to the surface is ??? What is the ratio of 128000 km to this distance?

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