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 …………… $A$

The distance of a planet from the sun is $5$ times the distance between the earth and the sun. The time period of the planet is

The earth moves around the Sun in an elliptical orbit as shown in figure.The ratio $OA/OB = x$ . The ratio of the speed of the earth at $B$ to that at $A$ is nearly

Two satellites are launched at a distance $R$ from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed $v_0$ and enters a circular orbit. The second satellite, however, is launched at a speed $\frac {1}{2}v_0$ .  What is the minimum distance between the second satellite and the planet over the course of its orbit?

India's Mangalyan was sent to the Mars by launching it into a transfer orbit $EOM$ around the sun . It leaves the earth at $E$ and meets Mars at $M$ . If the semi-major axis of Earth's orbit is $a_e = 1.5 \times 10^{11}\, m$, that of Mars orbit $a_m= 2.28 \times 10^{11}\, m$, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to …….. $days$.