- Prove planets orbit in a 2D plane. - Prove some geometric facts about ellipses. - Prove that a planet that is in orbit obeys the equation sin(theta) = 1 / sqrt(-pr^2 + qr), where p and q are constants that depend on the planet's energy and angular momentum and p is greater than zero. - Prove that a curve is an ellipse if and only if its r-theta equation is of the form sin(theta) = 1 / sqrt(-pr^2 + qr), where p and q are constants that depend on the size and shape of the ellipse and p is greater than zero.