Force of gravity on a spaceship - can't get right answer.

[confusedbyphysics]

This seems like it should be very easy but I keep getting the wrong answer. Here is the problem.

"Calculate the force of gravity on a spacecraft 32000 km (5 Earth radii) above the Earth's surface if its mass is 1300 kg."

In my book there is problem very similar so I tried doing the same thing, but it did not work. What I did was:

Force of Gravity decreases with a square of the radius so 1/5^2 = 1/25 as strong. Then just F = 1/25mg, 1/25 X (1300)(9.8) = 509.6 N. My online homework submission Webassign says that is wrong. The bookk says I can solve it doing the long way also..

So I trie doing it the long way. F = G (mass 1 X mass 2) / (radius ^2)...soooo... G is a constant, 6.67 X 10^-11 Nm^2. mass 1 is the spaceship, so 1300 kg. mass 2 is earth, the constant being 5.98 X 10^24 kg. Change radius from km to m, so 32000 km = 32000000 m. or 3.2 X 10^7

F = 6.67 X 10^-11 X 1300 X (5.98 X 10^24) / ((3.2 X 10^7)^2) = 506 N which is wrong as well!

Please help, thank you so much!

 

[Grogs]

I think I see where you went wrong. Look at the part I made bold in your quotation below:

This seems like it should be very easy but I keep getting the wrong answer. Here is the problem.

"Calculate the force of gravity on a spacecraft 32000 km (5 Earth radii) above the Earth's surface if its mass is 1300 kg."

In my book there is problem very similar so I tried doing the same thing, but it did not work. What I did was:

Force of Gravity decreases with a square of the radius so 1/5^2 = 1/25 as strong. Then just F = 1/25mg, 1/25 X (1300)(9.8) = 509.6 N. My online homework submission Webassign says that is wrong. The bookk says I can solve it doing the long way also..

So I trie doing it the long way. F = G (mass 1 X mass 2) / (radius ^2)...soooo... G is a constant, 6.67 X 10^-11 Nm^2. mass 1 is the spaceship, so 1300 kg. mass 2 is earth, the constant being 5.98 X 10^24 kg. Change radius from km to m, so 32000 km = 32000000 m. or 3.2 X 10^7

F = 6.67 X 10^-11 X 1300 X (5.98 X 10^24) / ((3.2 X 10^7)^2) = 506 N which is wrong as well!

Please help, thank you so much!

 

[confusedbyphysics]

Oh. So would the radius be 6 and the force of gravity would be 1/36th??

EDIT: Yup, that was it. Thank you for the help Grogs. That one little thing that I missed screwed me up. I need to read more closely, lol.