If the earth is at one-fourth of its present distance from the sun, the duration of the year will be
Half the present year
One-eighth the present year
One-fourth the present year
One-sixth the present year
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 .......... $\min$
If $r$ denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to
Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $I_{A}$ and $I_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?
The orbital speed of Jupiter is
The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas $A$ and $B$ are also shown in the figure which can be assumed to be equal. If ${t_1}$ and ${t_2}$ represent the time for the planet to move from $a$ to $b$ and $d$ to $c$ respectively, then