Hello Guys.. I have a question and I know it might be easy to solve but I'm really stuck.
What is the ratio between the weight of a body 100 km above the surface of the earth and on the surface of the earth?
P.S:
the answer 97% and acceleration of gravity is 9.8 m/sec2 and no other information is provided

Question

bahrom7893 · Answer

You need to use F = G(m_1)*(m_2)/(r^2)

bahrom7893 · Answer

in both cases m_2 is the mass of earth

bahrom7893 · Answer

In the first case, 100 km above the surface of the earth, the radius, r is the earth's radius + 100 km

anonymous · Answer

but the r of earth isn't provided!

bahrom7893 · Answer

In the second case r is just the radius of the earth.

bahrom7893 · Answer

You can look it up, it's just a constant

anonymous · Answer

yea but in our text that means you need to solve in with r unknown

bahrom7893 · Answer

Actually you don't. Anything that involves the mass of earth, the radius of earth, etc.. u don't

shane_b · Answer

You can do it simpler than that.  Let R be the radius of the Earth and r be the radius of the earth + 100km.
$$g_r=\frac{R^2}{r^2}g_{surface}$$$$g_r=\frac{R^2}{(r+100)^2}g_{surface}$$$$g_r=\frac{(6378.1km)^2}{(6478.1km)^2}(9.8m/s^2)=0.969 \text{ or about 97%}$$

anonymous · Answer

Excellent... Thank you a lot :)

shane_b · Answer

In the second equation I guess that should have been a big R since I showed the addition of 100km.

You're welcome :)