Solving Satellite Orbits: Geostationary Radius & Speed

[Jack16]

Hi People I had problems solvin this question could you please help me,

The question:

On 19th June 1981,an experimental meteorological satellite of mass m=700 kg,was placed in a geostationary orbit usingthe launch vehicle Ariane.

Calculate:

a) the radius of geostationary orbit given that the period of revolution of the satellite is 23 h 56 m

b)the linear speed of such a satellite

 

[Doc Al]

Treat the orbit as an example of circular motion. What's the force pulling the satellite in a circle? Apply what you should know about centripetal acceleration.

Show your work if you need more help.

 

[M98Ranger]

in its orbit

Hi there,

I'd be happy to help you with this question. Let's break it down step by step.

a) To calculate the radius of a geostationary orbit, we can use Kepler's Third Law: T^2 = (4π^2/GM)*r^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the central body (Earth in this case), and r is the radius of the orbit. We can rearrange this equation to solve for r:

r = (GMT^2/4π^2)^(1/3)

Plugging in the values given in the question, we get:

r = [(6.67 x 10^-11 Nm^2/kg^2)(5.98 x 10^24 kg)(23 h 56 m)^2]/(4π^2)^(1/3)

= 4.22 x 10^7 meters

Therefore, the radius of the geostationary orbit is approximately 42,200 kilometers.

b) To calculate the linear speed of the satellite, we can use the formula v = 2πr/T, where v is the linear speed, r is the radius of the orbit, and T is the period of revolution. Plugging in the values from part a, we get:

v = (2π)(4.22 x 10^7 meters)/(23 h 56 m)

= 3.07 km/s

So the linear speed of the satellite in its geostationary orbit is approximately 3.07 kilometers per second.

I hope this helps! Let me know if you have any further questions or need clarification on any of the steps. Good luck!