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:

Kepler's second law regarding constancy of the areal velocity of a planet is a consequence of the law of conservation of:

1. Energy

2. Linear momentum

3. Angular momentum

4. Mass

The distance of neptune and saturn from sun are nearly ${10}^{13}$ and ${10}^{12}$ meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

(1) $\sqrt{10}$                                               

(2) 100

(3) $10\sqrt{10}$                                             

(4) $1/\sqrt{10}$ 

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

(1)4T                                                   

(2)$\frac{T}{4}$

(3)8T                                                   

(4)$\frac{T}{8}$