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

[Vickyvicksss]

Homework Statement

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?

The answer is 7.2x 10³s

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. Homework Statement
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
Radius of satellite: ?
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



Thank you in advance!~~ :)

 

[Doc Al]

Period of earth: 3.16 x 10⁷

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

Period of satellite: (I'm assuming this is period of Uranus?) 2.66 x 10⁹

Where did you get this number?

 

[Ibix]

The correct number to plug into 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?