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?

Statement-1: A planet is moving around the sun in an elliptical orbit. Then from aphelion point to perihelion point the speed of the planet continuously increases.Statement-2: According to Kepler's second law, the areal velocity of the line joining planet to the sun is constant.

(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.

The planet Venus orbits the Sun with a mean orbital radius of $1.076 imes 10^{11} \mathrm{~m}$. The mass of the Sun is $1.99 imes 10^{30} \mathrm{~kg}$. Using Newton's version of Kepler's third law, calculate the orbital period of Venus.

$1 \mathrm{~kg}$ sugar have maximum mass

One planet is orbiting around the sun, At a point $P$ it is at minimum distance $d_1$ from the sun and at that time speed is $v_1$. If at a another point $Q$ it is at maximum distance $d_2$ from the sun then at this point the speed of planet will be

A satellite orbits just above Earth's surface with period $T$. If Earth's density is $d$ and $G$ is the gravitational constant, what does $\frac{3\pi}{Gd}$ represent?

The planet Saturn revolves around the sun with a time period of 27 years. The ratio of orbital radii of Saturn to that of earth is (orbital radius of earth $= 1.5 imes {10^{11}}m$ )

The planet Neptune travels around the sun with a period of 165 years. Show that the radius of its orbit is approximately 30 times that of earth's orbit, both being considered as circular.

Assertion: Gravitational force between two masses in air is $F.$ If they are immersed in water, force will remain $F.$ Reason: Gravitational force does not depend on the medium between the masses.

Consider a binary star system of star $A$ and star $B$ with masses ${m_A}$ and ${m_B}$ revolving in a circular orbit of radii ${r_A}$ and ${r_B}$ respectively. If ${T_A}$ and ${T_B}$ are the time period of star $A$ and star $B$ respectively, then