In polar coordinate, the equation of motions for the radial and angular coordinate (r, 0) of E with respect to the Sun,

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In Polar Coordinate The Equation Of Motions For The Radial And Angular Coordinate R 0 Of E With Respect To The Sun 1 (41.03 KiB) Viewed 24 times

In polar coordinate, the equation of motions for the radial and angular coordinate (r, 0) of E with respect to the Sun, are given by +(-). mr a₁ = GM 2.² GM where L = mr² de L = m√√GMa(1 — e²) is a constant of the system, denoting the angular moment of the Earth about the Sun; a = 1.496 × 10¹¹ m (=1 A.U) (semi-major); m = 5.97 × 10²4 kg, mass of Earth; M = 1.987 × 1030 kg, mass of the Sun; G = 6.673 × 10-¹¹Nm²/kg2; e = 0.017 (eccentricity). The dt period is T = 21 At the 'perihelion' position where the Earth is closest to the Sun, the radial velocity v, is 0. 2 The instantaneos position of the Earth, x(t), y(t) at time t is related to r, 0 as per x(t) = r(t) cos 0(t) y(t) = r(t) sin 0(t) where r(t), 0(t) denote that both r and are time-dependent. Use Velocity Verlet algorithm to simulate the motion of the Earth around the Sun for a length of simulation time of 2T. It is up to you whether to present your simulation in the form of a video or just display the simulation on the screen via display.display()