Geostationary Satellite and Orbiting Satellite problem

1. May 12, 2014

agnibho

1. The problem statement, all variables and given/known data
A satellite GeoSAT is in a circular geostationary orbit of radius RG above a point P on the equator. Another satellite ComSAT is in a lower circular orbit of radius 0.81RG. At 7 P.M. on January 1, ComSAT is sighted directly above P. On which day among the following can ComSAT be sighted directly above P between 7 P.M. and 8 P.M. ??
(a) Jan 3
(b) Jan 9
(c) Jan 15
(d) Jan 21

2. The attempt at a solution
I am sorry but I am unable to think of any possible way to solve this problem. Will Keplar's equations help?? I am totally confused!! Please help!!

Last edited: May 12, 2014
2. May 12, 2014

phyzguy

What is the period of a geosynchronous orbit with radius RG? Using Kepler's laws, what is the period of an orbit with radius 0.81 RG?

3. May 18, 2014

agnibho

Umm...would that help?? :/

4. May 18, 2014

phyzguy

Yes, it will help - that's why I asked the questions. Can you answer them?

5. May 19, 2014

agnibho

Well, the formula to be applied can be.....
T2/R3 = (4 * π2) / (G * M)

where M= 5.98x1024 kg i.e. the mass of the Earth.
Would it help now??

6. May 19, 2014

agnibho

The above formula is for geosynchronous as I found out.... but the question tells about geostationary orbit.....

7. May 19, 2014

phyzguy

Geosynchronous and geostationary really mean the same thing. Do you know what a geostationary orbit is? If you do, you should be able to tell me the period of a geostationary orbit without doing any calculations.

8. May 19, 2014

agnibho

As Wikipedia states, the time period can be
T = 2π √(r3/μ)

What say??

9. May 19, 2014

agnibho

okay

10. May 19, 2014

agnibho

Yeah it's 24 hours! :tongue:

11. May 19, 2014

phyzguy

OK, good. It's actually 23 hours and 56 minutes, but 24 hours is probably close enough. So if the period of the satellite at radius R = RG is T = 24 hours, and if we know from what you wrote earlier that
$$\rm \frac{T^2}{R^3} = constant$$
then what is T when R = 0.81RG?

12. May 19, 2014

D H

Staff Emeritus
You don't need to know M or G. What you need to do is to answer phyzguy's questions.

What's the period of a geostationary satellite?
What do Kepler's laws say about the period of a satellite? Hint: Only one law says anything about the period.

From that, what is the period of that satellite whose orbital radius is 0.81 RG?

13. May 19, 2014

agnibho

oh okay got it now..... so all I have to do is to find out the periods for both the satellites and then calculate the time difference to get the number of days, right?

14. May 19, 2014

phyzguy

Right.

15. May 19, 2014

D H

Staff Emeritus
There's more to it than that. The satellite will be directly overhead after an integral number of orbits.

Here's what you need to solve for: For what integers N is the time needed to make N orbits between M days and M days plus one hour, where M is another integer?