The period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $4R$ is:

$A$ planet is revolving around the Sun in an elliptical orbit as shown in the figure. Which of the following is a correct statement?

$A$ planet of mass $m$ is moving in an elliptical orbit about the sun with time period $T$. If $A$ is the area of the orbit,then its angular momentum is:

$A$ star of mass $M$ (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the centre of mass of the star-planet system is shown below. The radius of the planet's orbit is closest to .......... $AU$ ($1 \, AU =$ Earth-Sun distance).

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:

An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to