Question

the distance between sun and a planet is r the angular momentum of planet around the sun in circular orbit is proportional to​

Answer 1

Answer:

The ‘angular momentum of a planet’ which around the sun in the orbit which is circular in shape is directly proportional to the inverse of the radius.

Explanation:

• Angular momentum L of a planet is $\mathrm{L} \propto r^{1 / 2}$
• L the angular momentum of a planet is equal to the product of its mass (m) of the planet, rotational speed (v) of the planet, and radius (r) between the sun and the planet. L = mvr.
• The centripetal force of the planet $\mathrm{F}_{\mathrm{e}}=\mathrm{mv}^{2} / \mathrm{r}$ and the gravitational force on the planet exerted by the sun is $\mathrm{F}_{\mathrm{g}}=\mathrm{GMm} / \mathrm{r}^{2}$ with G being gravitational constant and M being solar mass.  

Since the angular momentum is conserved,  

                      $\mathrm{L}=(m \sqrt{G M}) \mathrm{r}^{1 / 2}$

                             $\mathrm{L} \propto r^{\frac{1}{2}}$