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 $(r)$. If so,the correct relation for areal velocity is:

Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

Which of the following orbits is a possible orbit for a planet?

Earth's orbit is an ellipse with eccentricity $e = 0.0167$. Thus,the Earth's distance from the Sun and its speed as it moves around the Sun vary from day to day. This means that the length of the solar day is not constant throughout the year. Assume that the Earth's spin axis is normal to its orbital plane and find the length of the shortest and the longest day. $A$ day should be taken from noon to noon. Does this explain the variation in the length of the day during the year?

$A$ satellite is launched into a circular orbit of radius $R$ around the Earth. $A$ second satellite is launched into an orbit of radius $1.02 R$. The period of the second satellite is larger than the first one by approximately ........ $\%$

If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii,velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively,then