The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become ......... $hours$

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

An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is  ........ $days$

Mean solar day is the time interval between two successive noon when sun passes through zenith point (meridian). Sidereal day is the time interval between two successive transit of a distant star through the zenith point (meridian). By drawing appropriate diagram showing the earth's spin and orbital motion, show that mean solar day is $4\,\min$ longer than the sidereal day. In other words, distant stars would rise $4\,\min$ early every successive day

Consider a planet moving around a star in an elliptical orbit with period $T$. The area of the elliptical orbit is proportional to ...........