Understanding the Relationship Between Satellite Properties and Orbit Radius

[dheath90]

A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on r2 because A = πr2. Determine how the following properties of the satellite depend on r. In each case, give the power of r, i.e., if the dependence goes as rn, give n. If there is no dependence, then n = 0. (a) period, (b) kinetic energy, (c) angular momentum, and (d) speed.

I do not understand how to do this problem at all.

Help please!

 

[JaredJames]

This belongs in the homework section.

The question is fairly straight forward, how does orbital radius affect each of the four items? That is what you should do to start with.

Jared

 

[FlexGunship]

A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on r2 because A = πr2. Determine how the following properties of the satellite depend on r. In each case, give the power of r, i.e., if the dependence goes as rn, give n. If there is no dependence, then n = 0. (a) period, (b) kinetic energy, (c) angular momentum, and (d) speed.

I do not understand how to do this problem at all.

Help please!

Orbital mechanics is kind of my bread and butter. However, some users believe this to belong in the homework section. That being said, it has not been moved yet, so I will proceed cautiously.

I have given this problem in two formats before.

• using the six orbital elements
• using basic gravitation formulae

If we are assuming a simple planar orbit with definable period, then the problem can be solved with basic orbital mechanics. Again, given that this might belong in the homework section, I will be very cautious in my recommendation:

Your textbook is likely to define about four key equations that relate these variables. A hint for you is this: orbital period is not dependent upon eccentricity and kinetic energy is only dependent upon velocity and mass of the orbital object.

Since you are speaking of orbital periods, it is unlikely that you must consider the true anomaly.

Given that I cannot solve this for you, I suggest you look in your text for the four key equations relating these variables.

Heh, lastly, don't worry... no one's asking you to solve the N-body problem.