Question

Although the orbit of earth around the sun is elliptical, it closely resembles a circle. the orbit can be modeled by x^2+y^2=8649, where the sun is at the origin and and each unit of the coordinate plane represents 1 million miles. in other words, 8649 in the equation represents 8649 million miles. How far does Earth travel in one year as it makes one complete orbit? (hint: find the circumference of the circular orbit.)

Answer 1

No, 8649 represents miles squared, but in any case\[x^{2} + y^{2} = r^{2}\]is what you want, giving\[r=93\]and\[circumference = 2\pi r\approx584.3\]

Answer 2

Thanks so much! Wow I was really over thinking that.