Calculating Geostationary Orbit for a 700kg Meterological Satellite

[josephcollins]

Hi people, could someone please help with these:

On 19th June 1981, an experimental meterological satellite of mass m=700kg, was placed in a geostationary orbit using the launch vehicle Ariane.
Calculate:

i. The radius of the geostationary orbit given that the period of revolution of the satellite is 23h 56m.

ii. The linear speed of such a satellite.

iii.The energy required to move the satellite from the surface of the Earth into the geostationary orbit.

Thanks a lot

 

[Tide]

What have you done so far with the problems?

 

[josephcollins]

I used Kepler's law that the cube of the radius of the Earth is proportional to the time of orbit's square, I hope this will work, knowing g=9.8Nkg-1, the mass of the satellite 700kg, the orbit period 86160s and the radius of the Earth 6.37 *10^6. I got an answer of 4.2 *10^7 m. Can someone verify this please?

Then for part 2 I used the formula v=(g*R^2/r)^1/2 with r as the radius of the orbit and R as the radius of the Earth, g equals 9.8Nkg-1. I got 3072.3 ms-1, is this correct?

To put this satellite in orbit I used Ek=(mv^2)/2 to get 3.3*10^9 J.

I'd be grateful if you could check these values. Cheers

 

[Tide]

For the second part, if you know the radius of the orbit then you know the distance it travels in 1 day (circumference of the circle) so just divide by the number of seconds to get the speed. You can use this to check your answer!

To put the satellite into orbit you also should consider the work done against gravity to lift the satellite. You might also want to consider the initial kinetic energy of the satellite before launch due to the rotation of the Earth.