- #1

- 15

- 0

## Homework Statement

Two planets are orbiting the sun in elliptical orbits in the same plane. The orbit of planet Q has a semi-major axis of 64.8 AU and eccentricity of 0.445. Planet R has a semi-major axis of 42.5 AU and eccentricity of 0.825. The perihelion point of Planet R's orbit is rotated relative to that of Planet Q by 124 degrees. Determine the closest and greatest distance that Planet R and Q get from each other in AU.

## Homework Equations

P^2 is proportional to a^3

c^2=a^2-b^2 (where b is the semi-minor axis)

c=ae

Circumference (orbital distance) = 2pi*sqrt((a^2+b^2)/2))

## The Attempt at a Solution

P = sqrt*(a^3)

PQ= 277.0661022 yrs

PR= 521.6299378 yrs

cQ = (64.8*0.445) = 28.836 AU

cR = (42.5*0.885) = 35.0625 AU

bQ = sqrt*(64.8^2-28.836^2) = 58.03 AU

bR = 24.02 AU

So I'm not sure that I understand the set up of the orbits but either way I don't know where to go from here. How I understand it is that when both are at their perihelion points, there is an angle of 124 degrees between them where planet R's orbit is rotated from that of Planet Qs so that they aren't perfectly aligned but are still within the same plane (I hope that makes sense). With that I have two side lengths (both of their semi-major axis lengths) and an angle so I can get a distance between them. What next (if that's even a correct start)?