Gravitational acceleration of a satellite

[christyan]

I don`t understand the solution for the following question:
A satellite is in orbit around the earth. Consider the following quantities:
1. distance from the center of the earth
2. mass of the earth
3. mass of the satellite

The gravitational acceleration g depends on which of the above?

The solution is 1 and 2.

Newton's law of universal gravitation states that every mass in the universe attracts every other mass in the universe.
the equation is F= Gm1m2/r² where m1 is the Earth and m2 should be the satellite.
thank you.

 

[tiny-tim]

Welcome to PF!

Hi christyan! Welcome to PF!

Newton's law of universal gravitation …

How about Newton's other law (about acceleration)?

 

[rcgldr]

From an inertial (non-accelerating) frame of reference, then the rate of acceleration of the satellite towards the Earth is

g_earth = F / m₂ = G m₁ / r^2.

g_earth = 6.67428 x 10^-11 x 5.9736 x 10^24 / r^2 = (3.9869479008 x 10^14 / r^2) m / s^2

At the mean radius of the Earth (it's surface), 6371000 m, g ~= 9.8226 m / s^2.