how do i calculate gravitational force of a body?

Question

i know about distance and mass blah blah... but assuming i know the mass of the planet, and i want to measure the force of attraction AT ITS SURFACE.. how would i do it?

Answer 1

I assume that you are looking for the acceleration due to gravity at the surface of the planet. You use the Newton's formula for graviational attraction.



F = G*M.Planet*M.Object/r.Planet^2 = M.Object*a.Planet



Therefore, a.Planet= G*M.Planet/r.Planet^2



Where

G is the gravitational constant

M.Planet is the mass of the planet

r.Planet is the radius of the planet



Let's use the Earth as an example.



a.Planet= 5.9742*10^24*6.6742*10^-11/(6378km)^2

a.Planet = 9.8 m/s^2

Answer 2

Gravity at the surface of a body is an acceleration, not a force. It becomes a force when you consider two bodies, such as yourself standing on the earth. The force would be your weight. the formula that most people know:

F =GM1M2/r^2

can be used to calculate that force.

Lets consider the earth again as an example. The acceleration of gravity on the earth's surface is 9.8 m/s^2. And let's say you weigh 220 pounds, that's a mass of 100 kilograms.

Using the formula f = ma we can calculate the force of gravity acting on you. That would be your weight in SI units.

f = ma = 100x9.8 = 980 N

That's newtons.

To calculate the acceleration of gravity on the surface of a body, say another planet, we would use this formula:

a(gravity) = GM/r^2

Where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

The value of G is 6.67 x 10^(-11) Nm^2/kg^2

That's the value in exponential notation. As a regular decimal it would be:

0.0000000000667

Now in the above formula the mass must be in kilograms and the radius must be in meters.

Answer 3

This problem is not easy.

The end result is that acceleration of free fall is the same as if entire mass of the planet was concentrated at its center, and

accleration g=GM/R², and

force F = gm = GMm/R².



Newton was the first to solve this problem, with great effort. Nowdays textbooks rely on Gauss theorem of flux of 1/R² to obtain this result in somwhat easier and more generalized way.