Satellite Motion: Calculate Speed & Time to Orbit Earth

[SS2006]

A satellite orbits the Earth at a height of 200 KM in a cirlce of radius 6570 km. Find the speed of the satellite and the time taken tocomplete one revolution. Assume the Earth's mass is 6.0 X 10 exp 24.
(Hint: The gravitation force provides the centripetal force)

i found Velocity using:
v = square root of gravity constant * m central / r

but they want the time, what can i use
thanks

 

[rocketboy]

try using d = vt
therefore, t = d/v

you found the velocity, and you have the radius of its circular path.

 

[SS2006]

so 6570/7.8
gives 842 seconds i assume? dividign b 60 just gives 14
the answer is 88 minutes

 

[mezarashi]

The d mentioned by rocketboy is the circumference of the orbit, not the radius of orbit.

 

[rocketboy]

The d mentioned by rocketboy is the circumference of the orbit, not the radius of orbit.

yea, sorry for not making that more clear. The 'd' I mentioned above is the total distance covered by the satellite. So if you have the radius of its circular path, then you need to find the circumference of this circle. This circumference is the distance that the satellite has travelled.

Once you have this distance, you can find the time taken using the equation I mentioned above, which you should know from your basic kinematics lessons.

 

[cscott]

Alternatively you could use $$G\frac{m_E}{r^2} = \frac{4\pi^2r}{T}$$