Gravitational acceleration of a satellite

AI Thread Summary
Gravitational acceleration of a satellite in orbit depends on the distance from the center of the Earth and the mass of the Earth, according to Newton's law of universal gravitation. The formula F = Gm1m2/r² illustrates this relationship, where m1 is the Earth's mass and m2 is the satellite's mass. The gravitational acceleration can be calculated as gearth = Gm1/r², leading to a specific value at the Earth's surface of approximately 9.8226 m/s². The mass of the satellite does not influence the gravitational acceleration experienced by it. Understanding these principles is essential for grasping satellite dynamics in orbit.
christyan
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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.
 
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Welcome to PF!

Hi christyan! Welcome to PF! :smile:
christyan said:
Newton's law of universal gravitation …

How about Newton's other law (about acceleration)? :wink:
 
From an inertial (non-accelerating) frame of reference, then the rate of acceleration of the satellite towards the Earth is

gearth = F / m2 = G m1 / r^2.

gearth = 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.
 

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