Change in energy in orbiting satellite.

[Gianf]

Homework Statement

A satellite of mass 45.5 kg orbiting the Earth moves from an orbit of 7271 km to an orbit of 7356 km.
what is the work done by all forces acting on it?

Homework Equations

U=GMm/r

The Attempt at a Solution

I calculated the total energies of the satellite in both orbits which is -1/2GMm/r
This gave -1.2458Gj for the lower orbit and -1.2315 for the higher one.
Should the difference be the total work done?

 

[rude man]

Homework Statement

A satellite of mass 45.5 kg orbiting the Earth moves from an orbit of 7271 km to an orbit of 7356 km.
what is the work done by all forces acting on it?

Homework Equations

U=GMm/r

The Attempt at a Solution

I calculated the total energies of the satellite in both orbits which is -1/2GMm/r
This gave -1.2458Gj for the lower orbit and -1.2315 for the higher one.
Should the difference be the total work done?

It says find the work done by all the forces acting on it.

Contemplate the possibility that this is a 'trick' question.

 

[Gianf]

I've been thinking about this question all day... still don't get it
what would the trick be?

 

[rude man]

Sorry, I think I misread the question. Actually, it's a bit misty. My reading of it now is that there was a circular orbit of 7272 km which gets moved to a NEW circular orbit of 7356 km.

Just use conservation of energy but remember to include potential and kinetic energies.

 

[HalfLostAndSearching]

I would like to clarify a few things about the concept of energy in orbiting satellites. First, it is important to note that in an orbit, the total energy (kinetic + potential) remains constant. Therefore, the change in energy in an orbiting satellite can be better understood as a change in the distribution of energy between kinetic and potential energy.

In this case, we can say that the satellite has gained potential energy as it moved from a lower orbit to a higher orbit. This change in potential energy is due to the work done by the gravitational force between the Earth and the satellite. The work done in this case can be calculated using the formula W = ΔU = mΔh, where m is the mass of the satellite and Δh is the change in altitude between the two orbits.

Therefore, the work done by all forces acting on the satellite in this scenario would be mΔh = (45.5 kg)(7356 km - 7271 km) = 387.5 kJ. This work is done by the gravitational force and is responsible for the change in potential energy of the satellite.

It is also worth noting that in an orbit, there are other forces acting on the satellite such as air resistance and solar radiation pressure. However, these forces are usually very small compared to the gravitational force and can be neglected in this scenario.

In conclusion, the change in energy in an orbiting satellite can be understood as a change in the distribution of energy between kinetic and potential energy. The work done by all forces acting on the satellite in this case can be calculated using the change in altitude between the two orbits and the mass of the satellite.