Question

How do i do this?

According to Kepler's Laws, planets have elliptical orbits, with the sun at one of the foci. The farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets to the sun is 4.4 billion kilometers. Find the equation of the orbit of Pluto.

Answer 1

thank you!

Answer 2

Make those distances billions of km, not miles. The equation stays the same

Answer 3

Let us center the ellipse at (0,0) with the major axis along the x axis. The semimajor axis is a = (7.4 + 4.4)/2 = 5.9 . We will call that "a" in the general equation
x^2/a^2 = y^2/b^2 = 1
(x, y, a & b are in billions of miles).

The minor axis b is given by
b^2 = a^2 - c^2, where c is the distance of either focus from the middle, which in this case is 5.9 - 4.4 = 1.5. That means b^2 = 32.56; b = 5.71

The orbit equation is
(x/5.9)^2 + (y/5.71)^2 = 1