If $A$ is the areal velocity of a planet of mass $M,$ then its angular momentum is:

The figure shows the elliptical orbit of a planet $m$ about the sun ${S}.$ The shaded area $SCD$ is twice the shaded area $SAB.$ If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B,$ then:
                     

Let the speed of the planet at the perihelion $P$ in figure shown below be $v_{_P}$ and the Sun-planet distance $\mathrm{SP}$ be $r_{_P}.$ Relation between $(r_{_P},~v_{_P})$ to the corresponding quantities at the aphelion $(r_{_A},~v_{_A})$ is:

Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?

Two planets orbit a star in circular paths with radii $R$ and $4R,$ respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is $T,$ what is the minimum time after which the star and the planets will again be aligned in a straight line?