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

[katy123]

Homework Statement

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

Homework Equations

fc=mac
fg=GMm/R^2
fg=fc
fg=mg

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?

 

[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.