CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Kepler's Law

A planet of m...

Question

A planet of mass $m$ moves in an elliptical orbit around an unknown star of mass $M$ such that its maximum and minimum distance from the star are equal to $r_{1}$ and $r_{2}$ respectively. The angular momentum of the planet relative to the centre of the star is:

A

m \sqrt{\frac{2 G M r_{1} r_{2}}{r_{1} + r_{2}}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

m \sqrt{\frac{2 G M (r_{1} + r_{2})}{r_{1} r_{2}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\sqrt{\frac{2 G M m r_{1}}{(r_{1} + r_{2}) r_{2}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $m \sqrt{\frac{2 G M r_{1} r_{2}}{r_{1} + r_{2}}}$
From law of conservation of angular momentum
$m v_{1} r_{1} = m v_{2} r_{2}$
$\Rightarrow v_{2} = \frac{v_{1} r_{1}}{r_{2}} \to (1)$
From law of conservation of total mechanical energy
$\frac{- G M m}{r_{1}} + \frac{1}{2} m v_{1}^{2} = \frac{- G M m}{r_{2}} + \frac{1}{2} m v_{2}^{2} \to (2)$
From equation (1) and (2)
$v_{1} = \sqrt{\frac{2 G m r_{2}}{(r_{1} + r_{2}) r_{1}}}$
Angular momentum
$L = m v_{1} r_{1} = m \sqrt{\frac{2 G M r_{1} r_{2}}{r_{1} + r_{2}}}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A planet of mass m moves around the Sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the Sun are

r_{1}

r_{2}

, respectively. Find the relation between the time period of the planet in terms of

r_{1}

r_{2}

Q. A planet of mass

m

moves in an elliptical path around the Sun so that its maximum and minimum distance from the sun are equal to

r_{1}

r_{2}

respectively. Find the angular momentum of this planet relative to the center of the sun. Mass of the sun is

M

.

Q. A planet of mass

m

moves along an ellipse around the sun so that its maximum and minimum distance from the sun are equal to

r_{1}

r_{2}

respectively. Find the angular momentum of this planet relative to the centre of the sun.

Q. A planet of mass

m

, moves along an ellipse around the sun, so that its maximum and minimum distance from the sun are equal to

r_{1}

r_{2}

, respectively. Find the angular momentum of this planet, relative to the centre of the sun.

Q. A planet of mass

m

moves along an ellipse around the Sun so that its maximum and minimum distances from the Sun are equal to

r_{1}

r_{2}

respectively. Find the angular momentum

M

of this planet relative to the centre of the Sun.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Kepler's Law

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon