How Do You Calculate the Orbital Period of a Satellite?

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Homework Help Overview

The discussion revolves around calculating the orbital period of a satellite, specifically a space station orbiting the Earth at an altitude of 225 km. Participants are examining the relationship between orbital speed, radius, and period using gravitational equations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the equation Te^2/ Re^3 = Ts^2/ Rs^3 to relate the periods and radii of the Earth and the satellite. Questions arise regarding the units for time and how to accurately determine the satellite's radius. There is also confusion about the initial calculation of speed without a clear definition of the radius.

Discussion Status

Some participants have provided guidance on significant figures and have prompted the original poster to clarify their calculations. There is an ongoing exploration of the relationship between speed and orbital radius, but no consensus has been reached on the orbital period calculation itself.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can provide. The original poster's understanding of the orbital radius and speed is questioned, indicating potential gaps in their reasoning.

Havenater23
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Homework Statement


If the space station orbits the Earth 225 km above the surface , what are the satellites orbital speed and period ? The mass of the Earth is 5.97 E24 kg and the radius is 6.38 E6 m.


Homework Equations





The Attempt at a Solution


I already have the speed ( v ) , I just don't understand how to find the orbital period

Te^2/ Re^3 = Ts^2/ Rs^3

I know the Earth's radius and orbital, but do I put the t in hours or seconds ?
How do I find the satellites radius ?
If anyone could help it would be appreciated.
 
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Havenater23 said:
I already have the speed ( v ) , I just don't understand how to find the orbital period

Te^2/ Re^3 = Ts^2/ Rs^3

I know the Earth's radius and orbital, but do I put the t in hours or seconds ?

Just use the correct significant figures for either.

What's Te?

How do I find the satellites radius ?
? How did you find the speed without the orbital radius? You said you had the orbital radius. :confused:

Maybe you should show your work so far.
 
Well I got the orbital radius by take the 225km + 6.38 * 10^6 m .
Converting 225 km to m. I used that as the R in the problem to find the speed.
 
Havenater23 said:
Well I got the orbital radius by take the 225km + 6.38 * 10^6 m .
Converting 225 km to m. I used that as the R in the problem to find the speed.

I'm confused then. Apparently you have the orbital radius, yet you asked how to find it.

Well, moving on. What did you determine the speed to be?
 
Like 7761 m/s
 
Okay, you have a speed. What is the circumference of the orbit?
 

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