# A couple of gravitational problems (kelper's third law)

1. Jul 25, 2012

### Vickyvicksss

1. The problem statement, all variables and given/known data

A satellite is to be placed in orbit about the earth at an altitude of 1.6 x 10 6m. What will be its period of motion?

2. The attempt at a solution
Using kelper's third law.

R3 / T2 = R3 / T2

Radius of satellite: 6.38 x 106 + 1.6 x 106 = 7.98 x 106
Radius of earth: 6.38 x 106
Period of satellite: ?
Period of earth: 3.16 x 107

When I plugged these numbers in, I get 4.42 x 107s
I've used the formula before without any problems, so that's not the issue.

3. The problem statement, all variables and given/known data
Determine the radius of a satellite's synchronous orbit around Uranus. Your very friendly, local astronomer informs you that uranus' moon, Miranda, has an average radius of revolution of 1.24 x 105 km with a period of revolution of 1.4 earth days.

The answer is 5.8 x 107m

4. The attempt at a solution
Same thing as above, I used kelper's third law.
R3 / T2 = R3 / T2

Radius of Miranda: 1.24 x 105
Period of miranda: 1.4 days * 3600 * 24 = 120960s
Period of satellite: (I'm assuming this is period of Uranus?) 2.66 x 109

I plugged these numbers in and I got 9.73 x 107m

2. Jul 25, 2012

### Staff: Mentor

What do you mean by 'period of earth'? Where did you get this number?
Where did you get this number?

3. Jul 25, 2012

### Ibix

The correct number to plug in to Kepler's law here, given that you have plugged in Earth's radius for one of the Rs, is the orbital period of a satellite at ground level, not the orbital period of the Earth around the Sun. The numbers always must refer to orbital periods and orbital radii around the same gravitational center - the Earth, in this case.

Apart from the satellite, what goes round the Earth that has an orbital radius and period that you could look up?

For the second question, do you know what a synchronous orbit is?