Question

An exoplanet is in an elliptical orbit around a distant star. At its closest approach, the exoplanet is 0.540 AU from the star and has a speed of 54.0 km/s. When the exoplanet is at its farthest distance from the star of 41.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 ✕ 1011 m. You may assume that other planets and smaller objects in the star system exert negligible forces on the exoplanet.)

Answer 1

Answer:

0.71121 km/s

Explanation:

$v_1$ = Velocity of planet initially = 54 km/s

$r_1$ = Distance from star = 0.54 AU

$v_2$ = Final velocity of planet

$r_2$ = Final distance from star = 41 AU

As the angular momentum of the system is conserved

$mv_1r_1=mv_2r_2\\\Rightarrow v_1r_1=v_2r_2\\\Rightarrow v_2=\frac{v_1r_1}{r_2}\\\Rightarrow v_2=\frac{54\times 0.54}{41}\\\Rightarrow v_2=0.71121\ km/s$

When the exoplanet is at its farthest distance from the star the speed is 0.71121 km/s.