help! exam tomorrow! :S

[Sarahisme]

hey could i please get some help or preferably answers to this question...

i will post my answers but i don't know how long it will take me to figure them out...anyways heres the question:

 

A geosynchronous satellite is one which maintains a fixed position above the earths surface, ie its orbital period has duration 24 hours.

 

 

a) At what height above the Earth’s surface do you have to position a satellite so that it is in a geosynchronous orbit? (8 marks)

 

b) Write down an expression for the energy required to position a satellite of mass m a distance d above the Earth’s surface. (6 marks)

 

 

The space shuttle lifts a 500kg satellite to an orbit that is 1000 km above the Earth’s surface.

 

c) How much more energy is required to position this satellite in a geosynchronous orbit?

 

 

thanks guys

 

Sarah

[Sarahisme]

for a) i get

 

~5400km

[swansont]

hey could i please get some help or preferably answers to this question...

i will post my answers but i don't know how long it will take me to figure them out...anyways heres the question:

 

A geosynchronous satellite is one which maintains a fixed position above the earths surface' date=' ie its orbital period has duration 24 hours.

 

 

a) At what height above the Earth’s surface do you have to position a satellite so that it is in a geosynchronous orbit? (8 marks)

 

b) Write down an expression for the energy required to position a satellite of mass m a distance d above the Earth’s surface. (6 marks)

 

 

The space shuttle lifts a 500kg satellite to an orbit that is 1000 km above the Earth’s surface.

 

c) How much more energy is required to position this satellite in a geosynchronous orbit?

 

 

thanks guys

 

Sarah[/quote']

 

 

Geosynchronous means the period is 24 hours, which you get from 2*pi*r/v

 

In a circular orbit, you know that F = mv²/r (centripetal force)

 

Since the force is gravity, you also know F = GMm/r²

 

Set the forces equal, and use the information about v from the period. 5400 km is too small.

 

For the energy use PE = - GMm/r, where the reference is 0 PE at infinite distance. Solve for the various values of r, and take the appropriate differences.

[Sarahisme]

yeah thats what i did for part a) but my answer was abit strange i thought ? :S

[parkinho]

Have you worked out the answer yet Sarah? I have just worked it out roughly to be approx 35600km.

 

Good luck with your exam

 

Andy