NEET Physics Gravitation MCQs

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?

A planet of mass $m$ moves in an elliptical orbit around a star of mass $M$. At its closest approach (periapsis), the distance between the planet and the star is $r_p$ and its speed is $v_p$. At its farthest distance (apoapsis), the distance is $r_a$. What is the planet's speed at apoapsis?

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

Which of Kepler's laws explains why comets speed up significantly as they approach the Sun?

Kepler's First Law states that planets move in elliptical orbits with the Sun at one focus. What is at the other focus?

A satellite moves in elliptical orbit about a planet. The maximum and minimum velocities of satellites are $3 imes {10^4}{\rm{m}}{{\rm{s}}^{ - 1}}\,and\,{\rm{\;}}1 imes {10^3}{\rm{m}}{{\rm{s}}^{ - 1}}{\rm{\;}}$ respectively. What is the minimum distance of satellite from planet, if maximum distance is $4 imes {10^4}\;{\rm{km}}?$

The earth revolves about the sun in an elliptical orbit with mean radius $9.3 imes {10^7}m$ in a period of 1 year. Assuming that there are no outside influences

In an elliptical orbit under gravitational force, in general

A planet moving along an elliptical orbit is closest to the sun at a distance ${r_1}$ and farthest away at a distance of ${r_2}$. If ${v_1}\,and\,{v_2}$ are the linear velocities at these points respectively. Then the ratio $\frac{{{v_1}}}{{{v_2}}}$ is

If $a$ and $b$ are the nearest and farthest distances of a planet form the sun and the planet is revolving in a elliptical orbit, then square of the time period of revolution of planet is directly proportional to