# Gravitational Potential Energy of a satellite

• Victorian91
In summary, a satellite of mass 100kg needs an energy of approximately 5.2x10^8 J to be moved from its old orbit of radius 2R to a new orbit of radius 3R around the Earth. This can be calculated using the formula U = Uf - Ui, where Ui is the gravitational potential energy in the old orbit and Uf is the gravitational potential energy in the new orbit. It is important to note that the textbook may have a printing error, as the correct formula should not have an extra 2 in the denominators.
Victorian91
Can someone help me..

A satellite of mass 100kg revolves round the Earth in a circular orbit of radius 2R where R is the radius of the Earth. Determine the energy needed to move the satellite to a new orbit of radius 3R.

Thanks alot.

Victorian91 said:
Can someone help me..

A satellite of mass 100kg revolves round the Earth in a circular orbit of radius 2R where R is the radius of the Earth. Determine the energy needed to move the satellite to a new orbit of radius 3R.

Thanks alot.

Hi Victorian91! Welcome to PF

You have to show what you've done/tried first before we can help.

Okay..
This is how i did my solution to this problem..

In the old orbit, Ui = - GMm/2(2R)

In the new orbit, Uf = - GMm/2(3R)

Energy needed U = Uf -Ui

= GMm/ 12R

= 5.2X10^8 J

Is this correct?

Or it should be just putting in 2R and 3R..

Thanks..

Victorian91 said:
In the old orbit, Ui = - GMm/2(2R)

In the new orbit, Uf = - GMm/2(3R)
Why do you have the 2 in the denominator of each? I think you should have Ui = -GMm/2R and Uf = -GMm/3R. I'm curious why you thought the extra 2 came in.

Yes I agree with you..

Just that I was skeptical when my textbook included the 2(2R) and 2(3R)

That is why I post this ..

Could anyone know why?

I have no idea why the textbook included the extra 2. Are you sure that's exactly the problem in the book?

Also, out of curiosity, which textbook is it?

Well,

Its PRE - U Text STPM
Physics (Volume 1 )

Maybe a printing error..

Victorian91 said:
Okay..
This is how i did my solution to this problem..

In the old orbit, Ui = - GMm/2(2R)

In the new orbit, Uf = - GMm/2(3R)

Energy needed U = Uf -Ui

That is correct but without the 2* that just seems weird, when i calculated the energy required i got an answer of 1.04x10^9J... What is the correct answer?

## 1. What is gravitational potential energy?

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is the energy that is required to move the object from its current position to a reference point, typically infinity, without any acceleration.

## 2. How is the gravitational potential energy of a satellite calculated?

The gravitational potential energy of a satellite is calculated using the formula U = -GmM/r, where G is the universal gravitational constant, m is the mass of the satellite, M is the mass of the planet, and r is the distance between the satellite and the planet's center of mass.

## 3. How does the distance between a satellite and a planet affect its gravitational potential energy?

The gravitational potential energy of a satellite is directly proportional to the distance between the satellite and the planet's center of mass. As the distance increases, the potential energy also increases.

## 4. What happens to the gravitational potential energy of a satellite as it moves closer to a planet?

As a satellite moves closer to a planet, its gravitational potential energy decreases. This is because the distance between the satellite and the planet decreases, resulting in a smaller value for r in the gravitational potential energy formula.

## 5. Can the gravitational potential energy of a satellite be negative?

Yes, the gravitational potential energy of a satellite can be negative. This can occur when the satellite is at a distance less than the reference point (usually infinity) and is moving towards the planet. In this case, the potential energy is considered to be "lost" or converted into kinetic energy as the satellite falls towards the planet.

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