A planet revolves around a star in an elliptical orbit. At what point in its orbit is the planet's speed maximum?

Consider the following statements and select the correct statement(s). (i) Gravitational force may be attractive or repulsive. (ii) Gravitational force between two particles is independent of presence of other particles. (iii) Gravitational force is a short-range force.

The period of revolution of a planet around a star is 8 years. What is the semi-major axis of its orbit in astronomical units (AU)?

Kepler's law states that, square of the time period of any planet moving around the sun in an elliptical orbit of semi-major axis $(R)$ is directly proportional to

If the angular momentum of a planet of mass m, moving around sun in a circular orbit is $L$ about the centre of the sun, its areal velocity is

Two satellites $S_1$ and $S_2$ are revolving around a planet in coplanar circular orbits of radius $r_1$ and $r_2$ in the same direction, respectively. Their respective periods of revolution are $1 \mathrm{~h}$ and $8 \mathrm{~h}$. The radius of orbit of satellite $S_1$ is equal to $10^4 \mathrm{~km}$. What will be their relative speed (in $\mathrm{km} / \mathrm{h}$ ) when they are closest?

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

A comet revolves around the Sun in an elliptical orbit. When it is closest to the sun at distance ${d}$, then its corresponding kinetic energy is ${k}_0$. If it is farthest from the sun at distance $3 {~d}$ then the corresponding kinetic energy will be

Assertion: Comets move around the Sun in elliptical orbits. The gravitational force on the comet due to Sun is not normal to the comet? Velocity but the work done by the gravitational force over every complete orbit of the comet is zero. Reason: Gravitational force is a non-conservative force.

Two spherical bodies, each of mass $50 \mathrm{~kg}$, are placed at a separation of $20 \mathrm{~cm}$. Equal charges are placed on the bodies and it is found that the force of Coulomb repulsion equals the gravitational attraction in magnitude. Find the magnitude of the charge placed on either body.

The mean radius of the orbit of a satellite is 4 times as great as that of a parking orbit of the earth. Then its period of revolution around the earth is