Astronomy Math Problem

Question

Pluto travels in a path that is not circular. Pluto's farthest distance from the Sun is 4539 million miles, and its coset distance is 2756 million miles. Write a equation that can be solved to find the minimum and maximum distances from the Sun to Pluto.

Answer 1

Mai,

 

Do you mean equations such as

 

r_a = a(1 + e)

r_p = a(1 - e)

 

where r_a = maximum distance, r_p = minimum distance, a = semimajor axis of orbit, e = eccentricity?

 

If so, then just solve 2 equations in 2 unknowns to get a and e from

 

4539 x 10⁶ = a(1 + e)

2756 x 10⁶ = a(1 - e)

 

After you solve for a and e, then substitute into the 2 equations and you will have expressions for r_a and r_p in terms of a and e:

 

r_a = a(1 + e)
r_p = a(1 - e)

 

Can you work the problem from here?

 

Knowing a and e also lets you obtain other properties of the elliptical orbit.