3. The dynamics of a comet is governed by the gravitational force between the comet and the Sun, f-GMmr/r3, where G = 6.67 x 10-11 Nm2/kg2 is the gravitational constant, M = 1.99 x 1030 kg is the mass of the Sun, m is the mass of the comet, r is the position vector of the comet measured from the Sun, and r is the magnitude of r. Write a program to study the motion of Halley's comet that has an aphelion (the farthest point from the Sun) distance of 5.28 x 1012 m and an aphelion velocity of 9.12 x 10² m/s. What are the proper choices of the time and length units for the problem? Discuss the error generated by the program in each period of Halley's comet.

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