# 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?

Apr 24, 2016

$\frac{25}{3} k \frac{m}{s}$

#### Explanation:

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 = $\frac{1}{2}$

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)$\left(1 - e\right) = \left(\frac{50}{3}\right) \left(\frac{1}{2}\right) = \frac{25}{3}$ km/s..