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:
                     

When a planet revolves around the sun in an elliptical orbit, then which of the following remains constant?

In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity \((\omega)\) and the distance of the planet from the sun \((r)\). The correct relation for areal velocity is:
1. \(\frac{dA}{dt}\propto \omega r\)
2. \(\frac{dA}{dt}\propto \omega^2 r\)
3. \(\frac{dA}{dt}\propto \omega r^2\)
4. \(\frac{dA}{dt}\propto \sqrt{\omega r}\)

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

If two planets are at mean distances \(d_1\) and \(d_2\) from the sun and their frequencies are \(n_1\) and \(n_2\) respectively, then:
1. \(n^2_1d^2_1= n_2d^2_2\)
2. \(n^2_2d^3_2= n^2_1d^3_1\)
3. \(n_1d^2_1= n_2d^2_2\)
4. \(n^2_1d_1= n^2_2d_2\)

The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is: 

The kinetic energies of a planet in an elliptical orbit around the Sun, at positions \(A,B~\text{and}~C\) are \(K_A, K_B~\text{and}~K_C\) respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\), as shown in the figure. Then:

1. \(K_A <K_B< K_C\)
2. \(K_A >K_B> K_C\)
3. \(K_B <K_A< K_C\)
4. \(K_B >K_A> K_C\)

If \(R\) represents the orbital radius of a planet and \(T\) its orbital period, which of the following graphs correctly depicts the relationship between \(R\) and \(T\) for a planet revolving around the Sun?

1.		2.
3.		4.

A planet moves around the Sun \(S\) in an elliptical orbit, as shown in the figure. If its distances from the Sun at points \(A\) and \(B\) are \(r_1\)​ and \(r_2\)​ respectively, what is the ratio of its linear momentum at \(A\) to that at \(B\)?