Question

Show that Kepler's second law follows from the law of conservation of angular momentum.​

Answer 1

When planets roared around the sun the only force between them is gravitational force now if we calculate the net torque on the planets

.T = r X F = 0

hence T = 0 or dLl/dt = 0 or L = constant

now L = constant L/2m = constant

hence Areal velocity = constant

this explainayion works if ur prep for NEET

if that comes in a board exam then I should I consult a board level book I'll send u pic and edit the answer when I find the hook I used

Answer 2

Explanation:

Consider a small wedge of the orbit traced out in time dt:

So the area of the wedge is

And the rate at which area is swept out on the orbit is

Now, remember(?) the definition of Angular Momentum:

Inserting this previous equation , we get

"Equal areas in equal times" means the rate at which area is swept out on the orbit (dA/dt) is constant.