Education and Career Forum

can you show the mathematical derivation of the law of periods...could u please explain to me

dA/dt=L/2m

dA=L/2m*dt
intregrating 0 to T and A=PI*a*b
e^2=1-a^2/b^2

so A=PI*a*root(1-e^2)
LT/Am=pi*a*root(1-e^2).............(1)

L=Vtan.R
VtanR IS tanential component of V
R=ea+a
putting in EQ1 AND GET EQ 2............3
NOW WE NOW THAT
Fnet=mVtan^2/R=GMm/R^2\......4

FROM 3 AND 4 WE FIND THE RESULT