The earth is about 150 million kilometers from the sun. The orbit around the sun is not a perfect circle, but is approximately a circle. If the orbit of the earth around the sun were circular, what would be the equation if the origin of the coordinate system were placed at the sun?
The equation of a circle is : (y-k)² + (x-h)² = R², since the center of this circle has its origin in the "center" of the sun, then h=0 and k= 0 and the equation becomes:
y²+x² = [150 x 10⁶]² y² + x² = 150² x 10¹² = 22,500x10¹² or y²+x² = 22.5 x 10¹⁵
