Calculating the Period of an Orbit around Earth

In summary, Claire is trying to find the period of a space station orbiting Earth at a radius of 30,000km. She initially tried to use an incorrect equation and then questioned the relevance of the 30,000km radius. Another user suggests using Kepler's 3rd Law and helps Claire derive the correct equation, including the use of the Standard Gravitational Parameter for Earth. Claire thanks the user for their help and apologizes for the delayed response due to holiday preparations.
  • #1
gemini2904
15
0

Homework Statement



A space station is placed in an orbit of radius 30 000km. What is the period of the station's orbit around the Earth?

(I previously worked out the period of rotation of the space station as 22 secs but I didn't think it was relevant to this part of the question besides it's probably wrong anyway! For that question the wheel shaped station, with radius 20m, rotating around a central hub. astronaunt standing on rim head facing forward , feels force on feet, to stimulate 1/6 of the magnitude of gravity on earth)?

Homework Equations



I was looking to use T = 2pi[tex]\sqrt{}Rearth/g[/tex]

but Instead of Rearth do I need to use the radius 30 000? Or have I got the wrong equation again??

Many thanks,

Claire

The Attempt at a Solution



T = 84mins opps not 5! I don't understand how the radius of 30000 fits in, should I take it as distance?
 
Last edited:
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  • #2
What do you know about how force from perfect spheres can be modeled? What is the distance between the space shuttle and the "origin" of the gravitational force?

~Lyuokdea
 
  • #3
I guess the distance is the 30 000km but I still don't know what to do with it? Help!
 
  • #4
The 30,000 km is the radius.

If they had meant in addition to the radius it would have said above the surface.
 
  • #5
Good point, I'm reading too fast...

~Lyuokdea
 
  • #6
But the formula you are trying to use is not exactly correct.

Kepplers 3rd Law is:T = 2π√(r³/GM )
 
  • #7
Hi,

Thanks for replying. Unfortunately were not given that equation at this stage and so the answer needs to be worked out some other way, which is the confusing bit!

all were given is the above equation and for kepplers laws K = T^2/a^2 which I don't think is any help??
 
  • #8
You can derive it easily enough.

You know centripetal force. You know gravitational force.

They balance for orbit.

GM*m/r² = m*v²/r = m*ω²r

ω² = (2π/T)² = GM/r³

T² = (2π)² *r³ /GM

Anything look familiar?
 
  • #9
Hi,

Thanks very much for replying. I kind of get it but to ask a really stupid question what do I use for GM. I only have gravity and radius of the earth? I'm not given the mass or told to look it up?

Cheers,
Claire
 
  • #11
Hi,

Thanks very much for all your help and for including the link, I get it now, finally!

Sorry for the delay in replying, I've been really busy lately with Christmas preparations and unexpected visitors popping into spread their Christmas cheer - Joy! Bah humbug!

Best wishes,
Claire
 

1. What is a period orbit around Earth?

A period orbit around Earth is a circular orbit in which a satellite or other object takes a consistent amount of time to complete one full revolution around the Earth. This is also known as a synchronous orbit, as the object's period is synchronized with the Earth's rotation.

2. How long does it take for an object to complete one period orbit around Earth?

The amount of time it takes for an object to complete one period orbit around Earth depends on the altitude of the orbit. For a low Earth orbit, it can take about 90 minutes, while for a geostationary orbit, it takes 24 hours to complete one orbit.

3. What factors affect the period of an orbit around Earth?

The main factor that affects the period of an orbit around Earth is the altitude of the orbit. The higher the altitude, the longer the period of the orbit. Other factors that can affect the period include the mass and size of the Earth, as well as the shape and eccentricity of the orbit.

4. How does a period orbit around Earth benefit communication and weather satellites?

A period orbit around Earth is beneficial for communication and weather satellites because it allows them to maintain a consistent position relative to the Earth's surface. This allows for continuous communication coverage and accurate monitoring of weather patterns.

5. Are all satellites in period orbits around Earth?

No, not all satellites are in period orbits around Earth. Some satellites are in elliptical or polar orbits, depending on their specific purpose and mission objectives. However, many communication and weather satellites are placed in period orbits to optimize their performance and capabilities.

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