Question

The equation that models Saturn's elliptical orbit around the sun is....
,

Answer 1

Answer: 1.5131 billion mi.

Answer 2

1.5131 billion mi.

Explanation:

The general equation of the ellipse with center (h,k) is

`((x-h)^(2))/(a^(2)) + ((y-k)^(2))/(b^(2)) =1`

Here the equation of ellipse is given as

`((x+0.0831)^2)/(2.0449)+ (y^(2))/(2.0380) =1 \\`

Therefore, the center of the given ellipse is (-0.0831,0)

The focus is (0,0)

a is the radius along major axis

Here a= √2.0449 =1.43

The distance between focus and center of the given ellipse = 0.0831

Since the farthest distance between Saturn and the Sun is required, we have to add up the radius of the ellipse along the major axis and the distance between the focus and center.

Distance between sun and saturn = 1.43 + 0.0831 = 1.5131

∴ The farthest distance between the Sun and saturn is 1.5131 billion miles.