A planet orbits a star in an elliptical orbit. At its perihelion, the planet's speed is $v_p$ and its distance from the star is $r_p$. At its aphelion, the planet's speed is $v_a$ and its distance from the star is $r_a$. Which of the following expressions correctly relates these quantities?

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto \frac{1}{r^3}$, but still remaining a central force. Then

S-I: The moon moves around the earth in a circular orbit and the earth moves around the sun in elliptical orbit then. S-II: The sun's attraction on the earth and moon are external force acting on the centre of mass of the system

Assertion: Gravitational force between two particles is negligibly small compared to the electrical force. Reason: The electrical force is experienced by charged particles only.

A satellite of the sun is in circular orbit around the sun, midway between the sun and the earth. Then

Hubble's law is related with

(A): The angular velocity of a planets orbiting around the sun increases when they are nearest to the sun. (R): The angular momentum of body is proportional to angular velocity.

Two planets revolve round the sun with frequencies $N_1$ and $N_2$ revolutions per year. If their average orbital radii be $R_1$ and $R_2$ respectively, then $R_1 / R_2$ is equal to:

A particle is moving with uniform speed along the circumference of a circle of radius $R\,$ under the action of a central fictitious force $F$ which is inversely proportional to ${R^3}$. Its time period of revolution will be given by

The minimum time period an artificial satellite can have around the earth is approximately

A satellite $A$ of mass $m$ is revolving round the earth at a height ' $r$ ' from the centre. Another satellite $B$ of mass $2 m$ is revolving at a height $2 r$. The ratio of their time periods will be