What is the gravitational force on the satellite?

In summary, we are trying to find the fraction of the weight of a satellite in orbit compared to its weight on Earth's surface. Using the given values for gravitational constant, mass of Earth, and radius of Earth, we can calculate the gravitational force on the satellite to be 1.51*10^4 N. To find the fraction, we use the formula g' = g[Re/(Re+h)]^2, where g is the free fall acceleration, Re is the radius of Earth, and h is the height of the satellite. When we plug in the values, we get a fraction of approximately 0.814, meaning the weight of the satellite in orbit is about 81.4% of its weight on Earth
  • #1
badman
57
0
A satellite of mass 1900 kg used in a cellular telephone network is in a circular orbit at a height of 690 km above the surface of the earth.

What is the gravitational force on the satellite?
Take the gravitational constant to be G = 6.67×10−11 N*m^2/kg^2, the mass of the Earth to be m_e = 5.97×1024 kg, and the radius of the Earth to be r_e = 6.38×106 m.


my answer was 1.51*10^4 {\rm N} which was correct, but I am confused on the next question: What fraction is this of its weight at the surface of the earth?
Take the free fall acceleration to be g = 9.80 m/s^2.
 
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  • #2
The value of g changes with height. 690 Km is comparable to the radius of the Earth. Have you considerd this.

Hint g' = g[Re/(Re+h)]
 
  • #3
so for that equation doi use the answer times the mass of the Earth to find the fraction, theyre talking about?
 
  • #4
yes
weight of the settelite is mg,
hence ratio of the weights will be mg'/mg=g'/g
where g' is accelerationdue to gravity at height h and g is that at the surface of earth.
 
  • #5
You needed the mass of the Earth to find the gravitational force on the satellite in orbit but you don't to find the gravitational force on the satellite on Earth (its weight). Just use F= mg where g= 9.81 m/s2 and m= 1900 kg, as given.

Divide the two to find the fraction.
 
  • #6
i did what you guys told me but i keep getting wrong. i tried what mukundpa and halls suggested but i ended up wrong.
 
  • #7
wouldn't the second part of the question just be [tex]\frac{r^2_{orbit}}{r^2_{earth}}[/tex]?
 
  • #8
nvm i already solved it. i used the number i got as the wrong numerator
 
  • #9
I am extremely sorry for mistype and not looking back seriously
Actually the derivation is like that

at the surface of Earth acceleration due to gravity is

g = GM/Re^2 Re is radius of earth

and at a height h from the surface
g' = GM/(Re+h)^2

Hence g' = g [Re/(Re+h)]^2

Therefore the required fraction is mg'/mg = [Re/(Re+h)]^2
=[6380/(6380+690)]^2 = 0.814
is it correct
sorry again
 

1. What is the gravitational force on the satellite?

The gravitational force on a satellite is the force of attraction between the satellite and the planet or object it is orbiting. It is responsible for keeping the satellite in its orbit and is determined by the mass and distance between the satellite and the planet.

2. How is the gravitational force on a satellite calculated?

The gravitational force on a satellite can be calculated using Newton's Law of Universal Gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

3. Does the gravitational force on a satellite change?

Yes, the gravitational force on a satellite can change depending on its position in orbit. It is strongest when the satellite is closest to the planet and weakest when it is farthest away. The gravitational force can also change if there are other objects nearby exerting their own gravitational force.

4. How does the mass of the satellite affect the gravitational force?

The mass of the satellite does not affect the gravitational force on it. However, the mass of the planet or object it is orbiting does affect the force. The greater the mass of the planet, the stronger the gravitational force on the satellite will be.

5. What happens to the gravitational force on a satellite as it moves farther away from the planet?

The gravitational force on a satellite decreases as it moves farther away from the planet. This is because the distance between the satellite and the planet increases, according to the inverse square law, resulting in a weaker force of attraction between them.

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