# Geosynchronous orbit problem

ok, so i've got an idea on what to do, but i cant seem to get the right answer, heres the question:

One of Jupiter's moons has a mass of 2.2x10^23kg and radius of 4600km. How high above the surface of the moon should a satellite of mass 112kg be so that it undergoes geosynchronous orbit about the moon? The rotational period of the moon is 0.7402 days.

So, I used T = [2*pi*(4600-r)^(3/2)] / [root (Gmp)], where mp is mass of planet (in this case the moon being orbited) and G is 6.67x10^-11. I converted the period into seconds, whereby 0.7402 days is 17.7648 hours, which is 63953.28s. I've also converted 4600km into 4,600,000m and kept mass in kilograms.

I plug in the numbers and keep getting 7.699x10^15m, which isn't correct. I'm not sure of the correct answer however, would just appreciate a shove in the right direction.

-Twiztidmxcn

## Answers and Replies

dextercioby
Science Advisor
Homework Helper
U shouldn't include in your calculations of the distance the radius of the moon.

How about posting the derivation of the formula which u are supposed to use...?

Daniel.

derivation of the formula im supposed to use?

i don't even know if im using the right formula, let alone what derivations im supposed to do

dextercioby
Science Advisor
Homework Helper
What are/is the force acting on the satellite...?

Daniel.

P.S.Then how are u supposed to do it...?

Janus
Staff Emeritus
Science Advisor
Gold Member
Your formula:

$$T = 2 \pi \frac{(4600-r)^{\frac{3}{2}}} {\sqrt {Gm_p}}$$

Is not quite correct. The problem is in the (4600-r) part. Why did you use this particular term?

sorry, i meant to put 4600 + r, because you have the radius of the moon plus the radius from the surface to the satellite

it doesnt even matter if that number is there, it makes no difference when solving for the radius needed

i know there is a gravitational force from the moon to the satellite but I cannot solve for force or radius

i actually have no clue in hell how to do this, this is in my physics homework but our physics profs just mentioned it, and the book has helped not a damn bit. their style of learning is force you to learn it yourself, which obviously hasnt helped me

dextercioby
Science Advisor
Homework Helper
Can u apply the second principle for the motion of the satellite...??

Daniel.