Final answer:
The speed at aphelion can be calculated using the equation for conservation of angular momentum. Angular momentum is constant throughout the orbit, so the product of the mass, velocity, and distance from the Sun must remain the same.
Step-by-step explanation:
The speed at aphelion can be calculated using the equation for conservation of angular momentum. Angular momentum is constant throughout the orbit, so the product of the mass, velocity, and distance from the Sun must remain the same. We can set up the equation as follows:
(mass * velocity at perihelion * perihelion distance) = (mass * velocity at aphelion * aphelion distance)
Plugging in the values, we get:
(mass * 55 km/s * 0.586 AU) = (mass * velocity at aphelion * aphelion distance)
Since mass cancels out in the equation, we are left with:
55 km/s * 0.586 AU = velocity at aphelion * aphelion distance
Simplifying the equation gives:
0.586 km = velocity at aphelion * aphelion distance
Dividing both sides of the equation by the aphelion distance gives:
velocity at aphelion = 0.586 km/aphelion distance
Therefore, we need to know the aphelion distance in order to determine the speed at aphelion.