derieve derivation of kepler second law of areas ?
Answers
Derivation of 2nd Law
For a central force acting on a body in orbit, there will be no net torque on the body, as the force will be parallel to the radius. Since the net torque is zero, the body will have a constant angular momentum. Therefore:
L = r x mv
L = rmv
where r is the radius of the orbit, m is the mass of the body, and v is the velocity. (for this we will assume the simple case of a circular orbit, but for non-circular, all we need to use is the tangential velocity in the following.)
The area A swept out in a time t will be A = (1/2)r(vt). (For infinitely small time t, this true.)
Combining these two equations, we can say
A = (1/2)(L/m)t
A/t = L/2m
L/2m is a constant, since the mass and angular momentum are constant, so that area per time is a constant. The planet would sweep out equal areas in equal times.