# Homework Help: Help with gravity Question

1. Jan 23, 2009

### Stratosphere

1. The problem statement, all variables and given/known data
How high above the surface of the earth should a rocket be
in order to have 1/100 of its normal weight? Express your answer
in units of earth radii.

2. Relevant equations
F=GMm/r2
F=mg

3. The attempt at a solution
r = √(( 6.67 x 〖10〗^(-11) x 5.97 x 〖10〗^24 )/0.098)
then divide by 6.37*106

I asked for help from one of my friends and he emailed me this but I think he might have messed somthing up. I keep getting a really big number.

I also know the answer its 9 radii but i dont understand how to get that answer.

Last edited: Jan 23, 2009
2. Jan 23, 2009

### mgb_phys

You don't need to use the actual mass of the Earth or the value of G.

You know that the weight is F = GMm/r^2
You know 'GMm' doesn't change,
So all you are asking is what do you have to do to 'r' to make 'r^2' 1/100 as big

ps. Careful with the final answer, r is from the centre of the Earth but the question asks for height above surface.

Last edited: Jan 23, 2009
3. Jan 23, 2009

### Stratosphere

So i have to make r^2=1/10 of r^2?

4. Jan 23, 2009

### mgb_phys

yes - it migth help to label them rinitial and rfinal to avoid confusing yourself !

5. Jan 23, 2009

### Stratosphere

so how do i do that i tried r^2/10 its not right.

6. Jan 23, 2009

### Stratosphere

i think i got it, so I did r*10 then subtract 1 to get distance from earths surface not its center. Thnx for the help.

7. Jan 23, 2009

### mgb_phys

More formally you would write
ri2 = 100 rf2

Take square root of both sides, it also helps to know that sqrt(ab) = sqrt(a) * sqrt(b)