Earth Satellites

Satellites $A \text{and }B$ are orbiting around the earth in orbits of ratio $R \text{and} 4R$, respectively. The ratio of their areal velocities is

A satellite is launched into a circular orbit $1600 \mathrm{km}$ above the surface of the earth. Find the period of revolution in nearest integer (in hours) if the radius of the earth is $R=6400 \mathrm{km}$ and the acceleration due to gravity is (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and ${\pi }^2=10$). 

A satellite moves around the earth in a circular orbit of radius $r$ making one revolution per day. A second satellite moving in a circular orbit, moves around the earth once in $8$ days. The radius of the orbit of the second satellite is

Which of the following quantities does not depend upon the orbital radius of a satellite?
($R=$ radius of orbit)

The period of a satellite in a circular orbit around a planet is independent of

Two identical satellites are orbiting at distances $R$ and $7R$  from the surface of the earth, $R$ being the radius of the earth. The ratio of their

The orbital velocity of a body close to the earth's surface is

The period of revolution of planet $A$ round the sun is $8$ times that of $B$. The distance of $A$ from the sun is how many times greater than that of $B$ from the sun?

Kepler's law states that square of the time period of any planet about the sun is directly proportional to

What would have been the duration of the year if the distance between the earth and the sun were half the present distance?

The radii of orbits of two satellites revolving around the earth are in the ratio $3:8$. Compare their (i) critical speeds (ii) period of revolution.

The distances of two planets from the sun are ${10}^{13} \mathrm{m} \mathrm{and} {10}^{12} \mathrm{m}$ respectively. Find the ratio of time periods and orbital speeds of the two planets.

Define binding energy and obtain an expression for binding energy of a satellite revolving in a circular orbit around the earth.

Define critical velocity of a satellite and write an expression for it.

Show that the square of the period of revolution of a satellite is directly proportional to the cube of the orbital radius.

The ratio of the kinetic energies of two stars $\left(K_m/K_M\right)$ are:

The ratio of the angular momentum of the two stars about their common centre of mass $\left(L_m/L_M\right)$ is:

Satellite is an object which revolves around the _____.

An astronaut inside an earth satellite experiences weightlessness. Then, choose correct statements from the following options.

An unmanned satellite $A$ and a spacecraft $B$ are orbiting around the earth in the same circular orbit as shown. The spacecraft is ahead of the satellite by some time. Let us consider that some technical problem has arisen in the satellite and the astronaut from $B$ has made it correct. For this to be done, docking of two ( $A$ and $B$) is required (in layman terms connecting $A$ and $B$). To achieve this, the rockets of $A$ have been fired in forward direction and docking takes place as shown in the figure below:

Take mass of the earth $=5.98\times {10}^{24} \mathrm{k}\mathrm{g}$
Radius of the earth $=6400 \mathrm{k}\mathrm{m}$
Orbital radius $=9600 \mathrm{k}\mathrm{m}$
Mass of satellite $A=320 \mathrm{k}\mathrm{g}$
Mass of spacecraft $=3200 \mathrm{k}\mathrm{g}$
Assume that initially spacecraft $B$ leads satellite $A$ by $100 \mathrm{s}$, i.e., $A$ arrives at any particular position after $100 \mathrm{s}$ of $B\text{'}\mathrm{s}$ arrival. Based on the above information answer the following question.

To dock $A$ and $B$ in the above-described situation, one can use the rocket system of either one, i.e., either of $A$ or of $B$. To accomplish docking in the minimum possible time, which of the following is the best way?