Physics Gravitational Force Question

[neoking77]

At a distance H above the surface of a plane, the true weight of a remote probe is one percent less than its true weight on the surface. The radius of the planet is R. Find the ratio H/R.

Work:
Let Mp be mass of planet and Ms be the mass of space probe

(true weight) Ft = GMpM/(r+h)^2

(surface weight) Fs = GMpM/r^2

Ft = GMpMs/r^2 - GMpMs/r^2(0.01)

Ft = GMpMs/r^2 - GMpMs/r^2(0.01) = GMpMs/(r+h)^2

i don't know where to go from here

thanks in advance.

 

[Tide]

Multiply both sides by r^2 and write

\frac {r^2}{(r+h)^2}

as

\frac {1}{\left(1 + \frac {h}{r}\right)^2}

You should be able to handle the rest.

 

[neoking77]

thank you very much for your help