Please write program in python

22:01 Sun Feb 9 @ 50% Not Secure-www-personalumich.edu Exercise 2.6: Planetary orbits 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 of closest approach that a planet makes to the Sun, also called its perihelion, and its linear velocity v 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 12 and velocity 0 of the planet at its most distant point, or aphelion, satisfy (202 = 101. At the same time the total 2.2 | BASIC PROGRAMMING from energy, kinetic plus gravitational, of a planet with velocity v and distance the Sun is given by 22:01 Sun Feb 9 @ 60% Not Secure-www-personalumich.edu 2.2 BASIC PROGRAMMING energy, kinetic plus gravitational, of a planet with velocity v and distance from the Sun is given by E = m-GM where m is the planet's mass, M = 1.9891 x 10kg is the mass of the Sun, and G = 6.6738 x 10-11 mkg-15-?is Newton's gravitational constant. Given that energy must be conserved, show that is the smaller root of the quadratic equa tion 2GM 1 - 076 02-07-26M = 0. Once we have 12 we can calculate 62 using the relation 12 = 6101/02, b) Given the values of 0, 1, and lz, 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: Semi-minor axis: a = b= (1 + (2) 162, Orbital period: T-2nab Orbital eccentricity: er Write a program that asks the user to enter the distance to the Sun and velocity at perihelion, then calculates and prints the quantities 12,02, 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 mand 01 = 3.0287 x 10ms) and Halley's comet ( = 8.7830 x 100 m and = 5.4529 x 10ms). 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. 22:01 Sun Feb 9 @ 50% Not Secure-www-personalumich.edu Exercise 2.6: Planetary orbits 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 of closest approach that a planet makes to the Sun, also called its perihelion, and its linear velocity v 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 12 and velocity 0 of the planet at its most distant point, or aphelion, satisfy (202 = 101. At the same time the total 2.2 | BASIC PROGRAMMING from energy, kinetic plus gravitational, of a planet with velocity v and distance the Sun is given by 22:01 Sun Feb 9 @ 60% Not Secure-www-personalumich.edu 2.2 BASIC PROGRAMMING energy, kinetic plus gravitational, of a planet with velocity v and distance from the Sun is given by E = m-GM where m is the planet's mass, M = 1.9891 x 10kg is the mass of the Sun, and G = 6.6738 x 10-11 mkg-15-?is Newton's gravitational constant. Given that energy must be conserved, show that is the smaller root of the quadratic equa tion 2GM 1 - 076 02-07-26M = 0. Once we have 12 we can calculate 62 using the relation 12 = 6101/02, b) Given the values of 0, 1, and lz, 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: Semi-minor axis: a = b= (1 + (2) 162, Orbital period: T-2nab Orbital eccentricity: er Write a program that asks the user to enter the distance to the Sun and velocity at perihelion, then calculates and prints the quantities 12,02, 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 mand 01 = 3.0287 x 10ms) and Halley's comet ( = 8.7830 x 100 m and = 5.4529 x 10ms). 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