Calculate Radius of Orbit Around Planet Zeron

[rlmurra2]

A satellite circles planet Zeron every 98 min. The mass of the planet is known to be 5.0 x 10^4 kg. What is the radius of the orbit?

I don't know what I'm doing wrong, I am using the formula T^2=(4(pi)^2/GM)r^3...and I am not coming up w/ the right answer, I have like 5 choices to choose from and theire all x10^6...

 

[Astronuc]

Balance centripetal force with gravitational force - both are proportional to the mass of the satellite.

Remember the angular frequency, \omega = 2\pi/T, where T is the period.

And tangential speed, v = \omegar

 

[Chi Meson]

did you convert the period (T) to seconds?

 

[rlmurra2]

I tried converting it to seconds and leaving it in minutes...still the answer is way off.

 

[Doc Al]

The mass of the planet is known to be 5.0 x 10^4 kg.

That's an awfully tiny planet. Are you sure of that number?

 

[rlmurra2]

Yep, that's what it says in the problem. Are we supposed to use Kepler's third law or whatever to solve this? It seems really easy that way, but when you plug in the numbers, it just doesn't work out.

 

[Doc Al]

You can use Kepler's third law, or figure it out for yourself using what Astronuc posted. Either way, you'll get the same answer.

 

[rlmurra2]

I've been using Newton's third law all along, and its not working. I'll try again. What is it, just to make sure I am using the right formula?

 

[Doc Al]

I assume you mean Kepler's third law. Read about it here: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

 

[rlmurra2]

yeah, that's the one I am using...wow I really don't think this problem is that hard. even tried it with period in minutes and seconds. oh well thanks anyways

 

[Chi Meson]

The period should be in seconds, not minutes. And I agree with DocAl's question: a truck has a mass on the order of 10^4 kg. A planet would not be a planet unless it had a mass of at least 10^20 kg. Methinks there is a typo in your question.