Question

The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 224,000,000 km at perihelion and 232,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis. ...?

Answer 1

`a= (224,000,000+232,000,000)/(2) =228,000,000 \\e=228,000,000-224,000,000=4,000,000 \\e^2=a^2-b^2 \\b^2=a^2-e^2=228,000,000^2-4,000,000^2=228^2*10^(12)-4^2* 10^(12) \\b^2=(228^2-4^2)*10^(12)=51,968* 10^(12) \\b^2=5.1968*10^(16) \\ \\ (x^2)/(5.1984* 10^(16)) + (y^2)/(5.1968*10^(16)) =1`