# Finding gravitational acceleration near the surface of a planet with a satellite

1. Nov 27, 2012

### katy123

1. The problem statement, all variables and given/known data
find acceleration due to gravity near the surface of a planet with a satellite by finding the mass of the planet and substituting it into the formula for the law of universal gravitation

2. Relevant equations
fc=mac
fg=GMm/R^2
fg=fc
fg=mg

3. The attempt at a solution
my question is a general one, I have solved for the mass of the planet finding that 4pi^2r^3/t^2G= Mass of planet
Then, you substitute it into Fg=GMm/R^2
set this equal to mg
mg=GMm/R^2

my teacher has done this on two separate occasions once that results in
acceleration due to gravity=4pi^2r/t^2
and another where it is = 4pi^2r^3/(R^2)(T^2)
r= distance from center to center
R=radius of the big planet
how do you know which radius to use in these equations, and why did it cancel out in one and not in the other?

2. Nov 27, 2012

### SHISHKABOB

hi katy, try using the X2 and X2 buttons

It looks like in the first equation for the acceleration due to gravity your teacher approximated r ≈ R, which would be the case if you were on the surface of the Earth.

If you want to find the acceleration due to gravity on a satellite that is not near the surface of the earth, then r ≠ R.

r will just be the altitude of the satellite plus the radius of the Earth, which is R.

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