Calculate Radius of Orbit Around Planet Zeron

In summary, a satellite circles planet Zeron every 98 min. The mass of the planet is known to be 5.0 x 10^4 kg. The radius of the orbit is x10^6.
  • #1
rlmurra2
19
0
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...
 
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  • #2
Balance centripetal force with gravitational force - both are proportional to the mass of the satellite.

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

And tangential speed, v = [itex]\omega[/itex]r
 
  • #3
did you convert the period (T) to seconds?
 
  • #4
I tried converting it to seconds and leaving it in minutes...still the answer is way off.
 
  • #5
rlmurra2 said:
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?
 
  • #6
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.
 
  • #7
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.
 
  • #8
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?
 
  • #10
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
 
  • #11
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.
 

1. How do I calculate the radius of orbit around Planet Zeron?

To calculate the radius of orbit around Planet Zeron, you will need to know the mass of Planet Zeron (M) and the distance between the planet and the orbiting object (r). Then, you can use the formula r = √(GM), where G is the gravitational constant. This will give you the radius of the orbit in meters.

2. What is the gravitational constant and where can I find its value?

The gravitational constant (G) is a fundamental physical constant that is used to calculate the force of gravity between two objects. Its value is approximately 6.67 x 10^-11 Nm^2/kg^2. You can find this value in most physics textbooks or online resources.

3. How does the mass of the orbiting object affect the radius of its orbit around Planet Zeron?

The mass of the orbiting object does not affect the radius of its orbit around Planet Zeron. The radius of orbit is only affected by the mass of Planet Zeron and the distance between the planet and the orbiting object.

4. Is the radius of orbit always constant around Planet Zeron?

No, the radius of orbit around Planet Zeron can vary depending on the velocity of the orbiting object and any external forces acting on it. However, if the velocity and external forces remain constant, the radius of orbit will also remain constant.

5. Can I use the same formula to calculate the radius of orbit around other planets?

Yes, the formula r = √(GM) can be used to calculate the radius of orbit around any planet, as long as you have the mass of the planet and the distance between the planet and the orbiting object. However, keep in mind that the value of G may vary slightly for different planets.

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