Why does a satellite at 160 km have greater total energy than at 144 km?

[krypt0nite]

Which is larger - the total energy of the 2.00 kg satellite in its 160. km orbit or the total energy in its 144 km orbit. Explain why the two answers are different.

Ok the total energy of 2.00 satellite in 160km orbit is -6.09x10^7 J and the total energy of 2.00 satellite in 144km orbit is -6.12x10^7 J.

How do I do the explaining part? I dont' think its simple as just saying their at different distances. Why is the satellite in the 160km orbit have a greater Etotal than the satellite in the 144km orbit?

 

[dextercioby]

Can u show us the resoning (not necessarily the calcuations) that led to the 2 different answers?

Daniel.

 

[wais]

The total energy of a satellite in orbit is determined by its position and velocity, which are affected by the gravitational force of the planet it is orbiting. As the distance between the satellite and the planet changes, the strength of the gravitational force also changes.

In this scenario, the satellite in the 160km orbit is further from the planet compared to the satellite in the 144km orbit. This means that the gravitational force acting on the satellite in the 160km orbit is weaker than the force acting on the satellite in the 144km orbit. As a result, the satellite in the 160km orbit has a lower velocity and therefore a lower kinetic energy compared to the satellite in the 144km orbit.

However, the potential energy of the satellite is directly proportional to its distance from the planet. This means that the satellite in the 160km orbit has a higher potential energy compared to the satellite in the 144km orbit. When these two energies (kinetic and potential) are combined, we get the total energy of the satellite.

Since the potential energy of the satellite in the 160km orbit is higher, it compensates for the lower kinetic energy, resulting in a higher total energy compared to the satellite in the 144km orbit. In other words, the satellite in the 160km orbit has a higher total energy because it is further from the planet and therefore has a higher potential energy.

In conclusion, the difference in total energy between the satellite in the 160km orbit and the satellite in the 144km orbit is due to the difference in their distances from the planet and the resulting difference in their potential energies.