$A$ comet (assumed to be in an elliptical orbit around the sun) is at a distance of $0.4 \, AU$ from the sun at the perihelion. If the time period of the comet is $125 \, yr$,the aphelion distance is ........... $AU$ ($AU$: Astronomical Unit).

The time period of a satellite revolving around earth in a given orbit is $7 \, hours$. If the radius of orbit is increased to three times its previous value,then the approximate new time period of the satellite will be ...... $hours$.

$Assertion$ : For the planets orbiting around the sun,angular speed,linear speed and $K.E.$ change with time,but angular momentum remains constant.
$Reason$ : No torque is acting on the rotating planet. So its angular momentum is constant.

The figure shows the elliptical path $abcd$ of a planet around the sun $S$ such that the area of triangle $csa$ is $\frac{1}{4}$ of the area of the ellipse. With $db$ as the major axis and $ca$ as a chord perpendicular to the major axis,if $t_1$ is the time taken for the planet to travel along the path $abc$ and $t_2$ is the time taken for the path $cda$,then:

Which graph best represents the variation of radius $r$ of a circular orbit of a satellite against its time period $T$?

According to Kepler, the period of revolution of a planet $(T)$ and its mean distance from the sun $(r)$ are related by the equation: