Question

The night before your birthday in 2007 you set up your telescope on a nearby mountaintop. It was a clear night, and you had a stroke of luck: At 12:30 A.M. you spotted a new comet. After repeating the observation on successive nights, you were able to calculate its solar system coordinates p_0 = (x_0, y_0, z_0) and its velocity vector v_0 = (v_x0, v_y0, v_z0) on that first night. Using this information, determine the following:

1. the comet's perihelion (point nearest the sun) and aphelion (point farthest from the sun),

2. the comet's velocity at perihelion and at aphelion,

3. the comet's period of revolution around the sun,

4. and the comet's next two dates of perihelion passage.

Using units of length in AU and time in earth years, the equations of motion of your comet are given in (4). For your personal comet, begin with random initial position and velocity vectors with the same order of magnitude as those of Halley's comet. Repeat the random selection of initial position and velocity vectors, if necessary, until you get a plausible eccentric orbit that ranges well outside the earth's orbit (as most real comets do).

Answer 1