# Low altitude satellites orbiting around planet with twice radius

1. Apr 10, 2013

### totallyclone

1. The problem statement, all variables and given/known data
Two remote planets consist of identical material, but one has a radius twice as large as the other. IF the shortest possible period for a low altitude satellite orbiting the smaller planet is 40 minutes, what is the shortest possible period for a similar low altitude satellite orbiting the larger one? Answer in minutes.

2. Relevant equations
volume of sphere=4/3 ∏r3
speed=distance/time
Ek=-1/2 Eg

3. The attempt at a solution
rB=2rA

timeA=2∏r/VA
40=2∏r/VA

Don't really know how to move on from here? I know I have to find the time taken for the satellite to orbit planet B.

TB=2∏(2rA)/VB

I don't know VB, how would I find that?

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2. Apr 10, 2013

### PeterO

The larger planet will have a much larger mass [same material presumably means same density]

Radius of orbit around the larger planet is larger [just a little larger than the planet itself]

I would be looking at the effect of doubling the radius of orbit of the satellite around the smaller planet, then the effect of having a larger mass attracting the satellite.

3. Apr 10, 2013

### totallyclone

So I doubled the radius. I didn't notice their densities would be the same since they're made of the same material. Anyways:

EKA=-1/2 EGA
1/2 mvA2=-1/2(-GmMA/rA)
vA2=GMA/rA

and

EKB=-1/2 EGB
1/2 mvB2=-1/2(-GmMB/2rA)
vB2=GMB/2rA

Last edited: Apr 10, 2013
4. Apr 10, 2013

### PeterO

I was looking for an answer like: If you double the radius (while retaining the planet mass), you double/halve/quadruple/quarter the period.

You would then look at: When you double/treble/quadruple/etc the mass of the planet (independent of the radius), you (some change) the Period.

You then combine those effects:

eg if one change means halving, and the other means increasing by a factor of 12; then net result is an increase by a factor of 6.

5. Apr 10, 2013

### totallyclone

Volume of B=4/3 ∏r3
=4/3∏(2rA)3
=4/3∏(8rA3)
=8(4/3∏rA3)
=8 volume of A

So, planet B's volume is 8 times of A's....

6. Apr 10, 2013

### PeterO

I would be addressing the expression a = 4π2.R / T2
one of the more useful expressions relating to the acceleration of a body moving in a circle.

7. Apr 10, 2013

### PeterO

Given they are made of the same material (imagine if you were using two steel balls to model the situation) what effect would that have on the mass.

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