Home > Astronomy > Components of the Solar System

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?

Answer 1

Hailey Alvarez

#25/3 km/s#

If e is the asteroid's orbital eccentricity and a is its semi-major axis, then

Aphelion/perihelion = 3 = (a(1+e))/(a(1-e)) = (1+e)/(1-e). solving for e, e = #1/2#

Speed at perihelion is equal to (speed at which the Sun is at distance a)(1+e) = 25 km/s.

Hence, velocity at a distance from the sun is equal to 25/(1+e) = 50/3 km/s.

Now, speed at aphelion = (speed when distance from Sun is a)#(1-e)=(50/3) (1/2)=25/3# km/s..

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Levi Anderson

At aphelion, the asteroid's orbital speed is about 12.5 km/s.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.