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Statement of a problem № 3333

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When a comet is at a distance 1.75 AU from the sun, it is moving with velocity u = 30 km/s and its velocity vector is at an angle of 30° relative to its radius vector r centred on the sun (see Fig. 5.7). What is the angular momentum per unit mass of the comet about the sun? The closest distance from the sun that the comet reaches is 0.39 AU. What is the speed of the comet at this point? Is the comet's orbit bound or unbound? (1 AU = 1.5x10^11 m, mass of the sun = 2x10^30 kg)

Solution:
When a comet is at a distance 1.75 AU from the sun, it is moving with velocity u

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