Gravitational acceleration of a satellite

So, the mass of the satellite does not matter for the Earth's gravitational acceleration, but the distance between the satellite and the center of the Earth does.In summary, the solution to the question about the quantities affecting gravitational acceleration is that it depends on the distance from the center of the Earth and the mass of the Earth. The mass of the satellite does not affect the Earth's gravitational acceleration.
  • #1
christyan
1
0
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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  • #2
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:
 
  • #3
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.
 

1. What is the formula for calculating the gravitational acceleration of a satellite?

The formula for calculating the gravitational acceleration of a satellite is g = G * M / r^2, where g is the gravitational acceleration, G is the gravitational constant, M is the mass of the planet, and r is the distance between the satellite and the planet's center of mass.

2. How does the gravitational acceleration of a satellite differ from that of an object on the surface of a planet?

The gravitational acceleration of a satellite is typically much lower than that of an object on the surface of a planet. This is because the satellite is further away from the planet's center of mass, and therefore experiences a weaker gravitational force.

3. Can the gravitational acceleration of a satellite change?

Yes, the gravitational acceleration of a satellite can change depending on its distance from the planet and the mass of the planet. It can also be affected by other factors such as the presence of other massive objects nearby.

4. How does the gravitational acceleration of a satellite affect its orbit?

The gravitational acceleration of a satellite determines the strength of the gravitational force between the satellite and the planet. This force is what keeps the satellite in orbit around the planet. If the gravitational acceleration is too low, the satellite may not have enough speed to maintain its orbit and will eventually fall back to the planet.

5. How is the gravitational acceleration of a satellite measured?

The gravitational acceleration of a satellite can be measured using instruments such as accelerometers or by analyzing the orbital data of the satellite. It can also be calculated using the formula mentioned in the first question.

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