Question

A planet of mass M is in an elliptical orbit around the sun with time period T.The semi major axis and semi minor axis are equal to a and b respectively.the angular momentum of planet is?

Answer 1

Explanation:

angular momentum of the planet=mv

v=r omega

omega=2π/T

r=ab

angular momentum of the planet=M(2π/T)ab

Answer 2

Given that,

Mass of planet = M

Mass of sun = M'

Semi major axis = a

Semi minor axis = b

Time period = T

We need to calculate the angular velocity

Using formula of gravitational force

$F=\dfrac{GMM'}{a^2}$

$\dfrac{Mv^2}{a}=\dfrac{GMM'}{a^2}$

We know that,

$\omega=\dfrac{v}{r}$

Here, r = a

$M\omega^2a=\dfrac{GMM'}{a^2}$

$\omega^2=\dfrac{GM'}{a^3}$

We need to calculate the angular momentum of planet

Using formula of angular momentum

$L=I\omega$

Put the value into the formula

$L=Ma^2\times\dfrac{GM'}{a^3}$

$L=\dfrac{GMM'}{a}$

Hence, The angular momentum of planet is $\dfrac{GMM'}{a}$