Python programming. Please show your work.

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 li of closest approach that a planet makes to the Sun, also called its perihelion, and its linear velocity vi 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 l2 and velocity v2 of the planet at its most distant point, or aphelion, satisfy 1202 = l101. 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 E = zmu? - GMM, 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 mkg-1s-2 is Newton's gravitational constant. Given that energy must be conserved, show that v2 is the smaller root of the quadratic equation 2GM) = 0. Vili Once we have v2 we can calculate l2 using the relation l2 = k1v1/v2. co - 201 02 (07 - 26M) = 0. b) Given the values of vi, l1, and l2, other parameters of the orbit are given by simple formulas can that be derived from Kepler's laws and the fact that the orbit is an ellipse: Semi-major axis: a = }(li + f2), Semi-minor axis: b= Vlqla, Orbital period: T = 27a l101' Orbital eccentricity: lz-li e=stli Write a program that asks the user to enter the distance to the Sun and velocity at perihe- lion, then calculates and prints the quantities l2, v2, T, and e. c) Test your program by having it calculate the properties of the orbits of the Earth (for which ly = 1.4710 x 1011 m and v1 = 3.0287 x 104 ms-1) and Halley's comet (l1 = 8.7830 x 1010 m and v1 = 5.4529 x 104 ms-1). Among other things, you should find that the orbital period of the Earth is one year and that of Halley's comet is about 76 years