Python programming:

Use the leapfrog method to calculate the orbit of the Earth around the Sun. The equations of motion for the position r = (x,y) of the planet in its orbital plane (in vector form) are dar GM dt2 where G = 6.6738 x 10-11 m kg-15-2 is Newton's gravitational constant and M = 1.9891 1030 kg is the mass of the Sun. The orbit of the Earth is not perfectly circular, the planet being sometimes closer to and sometimes further from the Sun. When it is at its closest point, or perihelion, it is moving precisely tangentially (i.e., perpendicular to the line between itself and the Sun) and it has distance 1.4710 x 1011 m from the Sun and linear velocity 3.0287 x 10-ms-1. Write a program to calculate the orbit of the Earth using the leapfrog method with a time- step of h = 1 hour. Make a plot of the orbit, showing several complete revolutions about the Sun. The orbit should be very slightly, but visibly, non-circular. Use the leapfrog method to calculate the orbit of the Earth around the Sun. The equations of motion for the position r = (x,y) of the planet in its orbital plane (in vector form) are dar GM dt2 where G = 6.6738 x 10-11 m kg-15-2 is Newton's gravitational constant and M = 1.9891 1030 kg is the mass of the Sun. The orbit of the Earth is not perfectly circular, the planet being sometimes closer to and sometimes further from the Sun. When it is at its closest point, or perihelion, it is moving precisely tangentially (i.e., perpendicular to the line between itself and the Sun) and it has distance 1.4710 x 1011 m from the Sun and linear velocity 3.0287 x 10-ms-1. Write a program to calculate the orbit of the Earth using the leapfrog method with a time- step of h = 1 hour. Make a plot of the orbit, showing several complete revolutions about the Sun. The orbit should be very slightly, but visibly, non-circular