Question

The Earth's orbit around the sun is elliptical, with the center of the sun at one focus. The length of the major axis is 186 million miles and the two foci are 3.2 million miles apart. What is the length of the minor axis of the ellipse?

Answer 1

By my calculation, the length of the minor axis is 185.9931182. I got this number by using the formula for calculating the focal length of an ellipse, which is \[a ^{2}-b ^{2}=c ^{2}\]. Rearranging this formula to make use of my known data (that A=186 and C=1.6 [remember, the focal length will be HALF of the distance between the foci]) I get \[186^{2}-b ^{2}=1.6^{2}\]. Solving for b, I get \[\sqrt{186^{2}-1.6^{2}}\], which is approximately 185.9931182.