Two satellites $P$ and $Q$ go round a planet in circular orbits having radii $3R$ and $R$ respectively. If the speed of satellite $P$ is $2V$,what will be the speed of satellite $Q$?

Two satellites $A$ and $B$ go round a planet $P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3V$,the speed of the satellite $B$ will be ........ $V$.

Spaceman Fred's spaceship (which has negligible mass) is in an elliptical orbit about Planet Bob. The minimum distance between the spaceship and the planet is $R$; the maximum distance between the spaceship and the planet is $2R$. At the point of maximum distance,Spaceman Fred is traveling at speed $v_0$. He then fires his thrusters so that he enters a circular orbit of radius $2R$. What is his new speed?

Assertion $(A):$ An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason $(R):$ An object moving around the earth under the influence of earth's gravitational force is in a state of 'free fall'.

Three equal mass satellites $A, B,$ and $C$ are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are $L_A, L_B$,and $L_C$. Which of the following statements is correct?

The period of moon's rotation around the earth is nearly $29$ days. If moon's mass were $2$ fold, its present value and all other things remained unchanged, the period of moon's rotation would be nearly ......... $days$.