The preihelion is the smallest distance from a planet to the sun, and aphelion is the greatest distance. The sun is one of the two foci. For the Earth, the perihelion is 147.1 million km and the aphelion is 152.1 million km. These two distances help identify the location of the sun on the major axis of Earth's elliptical orbit.
Assume that the major axis of Earth is on the x-axis.
a. Find an equation of the Earth's orbit about the sun.
b. With the given information, estimate Earth's speed around the sun in milers per hour.
So I'm thinking half the total distance of the aphelion and perihelion would give half the major axis. ($\frac{147.1+152.1}{2}=149.6$) My problem is how would I find the length of the minor axis?
$$\frac{x^2}{149.6^2}+\frac{y^2}{?}=1$$ Thanks for any help!
Best Answer
You are given $a-f$ and $f+f+a-f=a+f$, from which you get $a$ and $f$ and then $b$ from $f=\sqrt{a^2-b^2}$.