Two planets P1 and P2 orbit a star S in elliptical orbits with semi-major axes a1 and a2 respectively, where a1 > a2. If T1 and T2 are their respective periods, and at some point both planets are simultaneously at their respective aphelia, after how many periods of P1 will they simultaneously be at their respective aphelia again?

Assertion: When a planet moves in elliptical orbit around sun, its angular momentum about sun remains conserved.Reason: Total energy of the planet remains conserved

A satellite is in a low, circular orbit around Earth. A small, impulsive retro-rocket burn is executed, reducing the satellite's speed by a small amount $\Delta v$. Which of the following best describes the resulting orbit immediately after the burn?

When a satellite moves around the earth in a certain orbit, the quantity which remains constant is:

The distance of planet Jupiter from the sun is 5.2 times that of the earth. Find the period of revolution of Jupiter around the sun.

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)?

The rotation of the earth about its axis speeds up such that a man on the equator becomes weightless. In such a situation, what would be the duration of one day?

What is the radius of the circular orbit of a stationary satellite which remains motionless with respect to earth's surface?

The ratio of gravitational force and electrostatic repulsive force between two electrons is approximately (gravitational constant $=6.7 imes 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2,$ mass of an electron $=9.1 imes 10^{-31} \mathrm{~kg},$ charge on an electron $=1.6 imes 10^{-19} \mathrm{C}$)

Assertion: If the radius of the earth's orbit around the sun were twice its present value, the number of days in a year would be 1,032 days.

Reason: According to Kepler's law of periods, $T^2 \propto r^3$

A satellite orbits just above a planet's surface with period $P$. The planet has density $\rho$ and the gravitational constant is $G$. What quantity is represented by $\frac{3\pi}{G\rho}$?