An asteroid is three times as far from the Sun at aphelion than at perihelion. At perihelion the orbital speed of the asteroid is 25 km/s. What is the orbital speed of the asteroid at aphelion?
If a is the semi-major axis and e is the eccentricity of the orbit of the asteroid,
Aphelion/perihelion = 3 = (a(1+e))/(a(1-e)) = (1+e)/(1-e).
solving for e, e =
Speed at perihelion = (speed when distance from Sun is a)(1+e)=25 km/s..
So, speed when distance from Sun is a = 25/(1+e)= 50/3 km/s. .
Now, speed at aphelion = (speed when distance from Sun is a)