A comet travels around the Sun in an elongated ellipse

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

A comet travels around the Sun in an elongated ellipse. Its closest distance from the Sun (perihelion) is

r_p = 0.8\,\text{AU}

and its speed at perihelion is

v_p = 50\,\text{km\,s}^{-1}

. Assume

1\,\text{AU}=1.5\times10^{11}\,\text{m}

. (a) Calculate the speed of the comet at aphelion if the farthest distance is

r_a = 5.0\,\text{AU}

. (b) Compute the areal velocity of the comet at perihelion. (c) How much time will the comet take to sweep an area of

1.0\times10^{22}\,\text{m}^2

when it is near perihelion?