Home
Class 12
PHYSICS
A planet of mass m moves along an ellips...

A planet of mass m moves along an ellipse around the sum of mass M so that its maximum and minimum distances from sum are a and b respectively. Prove that the angular momentum L of this planet relative to the centre of the sun is `L=msqrt((2GMab)/((a+b)))`

Text Solution

AI Generated Solution

To prove that the angular momentum \( L \) of a planet of mass \( m \) moving in an elliptical orbit around the sun of mass \( M \) is given by the expression \[ L = m \sqrt{\frac{2GMab}{a+b}}, \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    ALLEN|Exercise Exercise 1 (Check your Grasp)|28 Videos

  • GRAVITATION

    ALLEN|Exercise Exercise 2 (Brain Teasers)|27 Videos

  • GEOMETRICAL OPTICS

    ALLEN|Exercise subjective|14 Videos

  • KINEMATICS-2D

    ALLEN|Exercise Exercise (O-2)|46 Videos

Similar Questions

Explore conceptually related problems

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 and r_2 respectively. Find the angular momentum M of this planet relative to the centre of the Sun.

A planet of mass m revolves in elliptical orbit around the sun of mass M so that its maximum and minimum distance from the sun equal to r_(a) and r_(p) respectively. Find the angular momentum of this planet relative to the sun.

A planet of small mass m moves around the sun of mass M along an elliptrical orbit such that its minimum and maximum distance from sun are r and R respectively. Its period of revolution will be:

A satellite of mass m orbits around the Earth of mas M in an elliptical orbit of semi - major and semi - minor axes 2a and a respectively. The angular momentum of the satellite about the centre of the Earth is

A planet of mass m moves around the Sun of mass Min an elliptical orbit. The maximum and minimum distance of the planet from the Sun are r_(1) and r_(2) , respectively. Find the relation between the time period of the planet in terms of r_(1) and r_(2) .

A planet of mass m is moving in an elliptical orbit about the sun (mass of sun = M). The maximum and minimum distances of the planet from the sun are r_(1) and r_(2) respectively. The period of revolution of the planet wil be proportional to :

A hypothetical planet of mass m is moving along an elliptical path around sun of mass M_s under the influence of its gravitational pull. If the major axis is 2R, find the speed of the planet when it is at a distance of R from the sun.

Speed of a planet in an ellioptical orbit with semimajor axis a about sun of mass M at a distance r from sun is

A satellite of mass m moving around the earth of mass m in a circular orbit of radius R has angular momentum L. The rate of the area swept by the line joining the centre of the earth and satellite is

A particle of-mass m moves along a circular path of radius r with velocity v. What is its instantaneous angular momentum about a point on the plane of the orbit at a distance x from the centre of the axis of rotation.