Remote sensing satellites move in an orbit that is at an average height of about $500 \,km$ from the surface of the earth. The camera onboard one such satellite has a screen of area $A$ on which the images captured by it are formed. If the focal length of the camera lens is $50 \,cm$, then the terrestrial area that can be observed from the satellite is close to …………… $A$

If the distance of the earth from Sun is $1.5 \times 10^6\,km$. Then the distance of an imaginary planet from Sun, if its period of revolution is $2.83$ years is $………….\times 10^6\,km$

Every planet revolves around the sun in an elliptical orbit :

$A.$ The force acting on a planet is inversely proportional to square of distance from sun.

$B.$ Force acting on planet is inversely proportional to product of the masses of the planet and the sun

$C.$ The centripetal force acting on the planet is directed away from the sun.

$D.$ The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below :

The fig. shows the motion of a planet around the un in an elliptical orbit with sun at the  focus. The shaded areas can be assumed to be equal. If $t_1$ and $t_2$ represent the  time taken for the planet to move from $A$ to $B$ and $C$ to $D$ respectively, then

A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is ${R_0}$ and mass of the earth M, the angular momentum about the centre of the earth is