Gravity and Satellite Equations

[robostar]

This isn't quite a question, I've got an exam coming up and I'm compiling a notes sheet I've found gravity and satellites troubling, I know most of the general equations, but I was wondering if I could get a set of equations which have been modified to find each measure...

So far I've got Mass? =
(4(pie)^2)*(R^3)
___________
(T^2) * G
Period?
T = 2(pie)R
_____
v
T^2 = (4(pie)^2) * R^3
____________
G Constant * Mass

Has anyone got anymore modifications that I can put on my notes sheet?

 

[Cyosis]

You're trying to memorize all modifications of the same equation? Why don't you just practice combining and solving them for the variable you're interested in? Memorizing will make you forget shortly after your exam, deriving them yourself from the base principles that is $F_{centripetal}=F_{gravity}$ will last a life time!

 

[robostar]

Nah, we are aloud to bring in a A4 sheet of notes into our exam, and since I'm not very good at deriving equations, I just wanted someone to give me a basic list of equations which would make it easier for me in my exam.

 

[Cyosis]

Well in that case perhaps we should derive a few. For an orbiting satellite the centripetal force is provided by gravity, therefore $F_{centripetal}=F_{gravity}$. $F_{centripetal}=m \omega^2 r=m v^2/r$ and $\omega= 2 \pi f=2 \pi /T =v/r$.$F_{gravity}=GmM/r^2$.

Therefore the equations to solve are:
$$m\omega^2 r=\frac{GmM}{r^2}$$

and

$$m \frac{v^2}{r}=\frac{GmM}{r^2}$$

So far you have solved them for T and M, correctly. If you want all possible combinations you will have to solve them for $v,f,r, \omega$ as well. Try to start with v.