The orbit of a planet around the sun is not circular It is a

The orbit of a planet around the sun is not circular; It is an ellipse with the sun at one focus. The alphelion of a planet is the greatest distance from the sun and the perihelion is its shortest distance. The mean distance of a planet from the sun is the length of the semimajor axis of the elliptical orbit. The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the sun is 897.5 million miles. Find the aphelion of Pluto. What is the mean distance of pluto from the sun? Write an equation to represent the orbit of Pluto around the sun.

Solution

distance from Pluto to origin (a):

4551 + 897.5 = 5448.5 million miles.
aphelion = 5448.5+897.5 = 6346 million miles.
b = (5448.5)^2 - (897.5)^2 = (5374.07)^2
mean distance = (5448.5+5374.07)/2 =

5411.29 million miles.

x^2/(5448.5)^2 + y^2/(5374.07)^2 = 1