Respuesta :
It implies that when a planet is closest to the sun it moves more slowly in its orbit. Kepler’s 2nd Law determines the orbital speed of the planet.
Answer:
Kepler's 2nd law : It is also known as law of area as per which the total area swept by the planet with respect to sun per unit time is remain constant. So here we can say that all planets will swept equal area in equal interval of time.
As we know that all planets move in elliptical orbit about the sun. Now when planets move around the sun then torque on the planet due to force of gravitation of sun is zero.
This will show that
[tex]\tau = \frac{dL}{dt}[/tex]
now we know that rate of change in angular momentum is torque
so here if net torque on the planet is zero than its angular momentum must be constant.
now the area swept by the planet in some small interval of time is given as
[tex]dA = \frac{1}{2}r^2d\theta[/tex]
now rate of area is given as
[tex]\frac{dA}{dt} = \frac{1}{2}r^2\frac{d\theta}{dt} = \frac{1}{2}r^2\omega[/tex]
[tex]\frac{dA}{dt} = \frac{mr^2\omega}{2m} = \frac{L}{2m}[/tex]
so we can say that rate of area will be constant for all planets
