How high is the Manned Orbital Lab above the Earth's surface and what is its kinetic & potential energy in orbit?
The Manned Orbital Lab makes 16.0 revolutions per day around the earth and its mass is 400 kg
The satellite completes 16 revolutions around the Earth in one day. The centripetal force acting on the satellite is due to the gravitational force of the Earth. This is equal to G*Me*Ms/r^2. As the satellite is in a constant orbit, it is equal to (Ms)*r*w^2, where r is the radius, w is the angular velocity and Ms is the mass of the satellite.
Equating the two, G*Me*Ms/r^2 = (Ms)r*w^2
The orbital radius of a satellite is given by the relation:
R^3 = [(T^2* G* Me) / (4* pi^2) ]
G*Me = 398600, T = 24*3600/16
=> R^3 = [(24*3600/16)^2* 398600/(4*pi^2)]
=> R = 6652 km
Therefore the satellite is 6652 km from the center of the Earth.
The potential energy of the satellite is G*Me*Ms/r
= 398600*400/6652 = 23968.7 J
The kinetic energy of the satellite is (Potential Energy)/2 = 11984.3 J