1) What is the distance between the perihelion and the aphelion?
70 + 46 = 116 million miles
2) What is the distance from the center of Mercury’s elliptical orbit and the Sun?
The major axis is 116 million miles
This = 2a
So
2a = 116
a = 58
This is the distance from the center of the ellipse to one endpoint on the major axis
And c = the distance from the center of its elliptical orbit to the Sun = 58 - 46 = 12 million miles
3) Write the equation of the elliptical orbit of Mercury, where the major axis runs horizontally. Allow a and b to be measured in millions of miles. Use the origin as the center of the ellipse.
b = sqrt [ 58^2 - 12^2] = sqrt (3220)
b^2 = 3220
a^2 = 58^2 = 3364
The equation is
x^2 y^2
____ + ____ = 1
3364 3220
4) Eccentricity = c/a = 12 / 58 ≈ .207
5) The closer to 0 the eccentrcity is, the more circular the ellipse....the nearer to 1, the more elongated
Thus.....the elliptical path here is somewhat circular
Here's a graph : https://www.desmos.com/calculator/cj4ey4e2gx