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?