The orbit in space of one body around another, such as a planet around the Sun, need not be circular. In general it takes the form of an ellipse, with the body sometimes closer in and sometimes further out. If you are given the distance 21 of closest approach that a planet makes to the Sun, also called its perihelion, and its linear velocity v1 at perihelion, then any other property of the orbit can be calculated from these two as follows a) Kepler's second law tells us that the distance &2 and velocity v2 of the planet at its most distant point, or aphelion, satisfy l202 - L1v1. At the same time the total energy, kinetic plus gravitational, of a planet with velocity v and distance r from the Sun is given by where m is the planet's mass, M-1.9891 x 1030 kg is the mass of the Sun, and G 6.6738 x 10-11 m3 kg 1 s-2 is Newton's gravitational constant. Given that energy must be conserved, show that v2 is the smaller root of the quadratic equation 2 2GM Once we have v2 we can calculate £2 using the relation l2- L1v1/v2.