a. I do not agree. The formula for the gravitational potential energy is
U = -GMm/r
The change in gravitational energy equals the initial kinetic energy provided.
Hence, this gives
(mv^2)/2 = - (GMm)/(r+h) + (GMm)/r
b. The centripetal force on the satellite is provided by the gravitational force.
Hence;
mRω^2 = (GMm)/(R^2)
Simplifying gives indeed
T = 2pi \sqrt{R^3/(GM)}
And here, R = r + h
And the T that you got is in seconds, not m/s
And one assumption here is that the Earth is not rotating on itself then. Because otherwise, you'll have another value, lower or higher depending whether it is rotating in the same direction as the Earth or rotating in the opposite direction.
__________________
Jerry (Got my results!) It is easier to protect your feet with slippers than to cover the earth with carpet.
No one can go back and change a bad beginning; but anyone can start now and create a successful ending.
If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying? |