Mathematics 317T2 Assignment3 - Mathematics 317...

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Mathematics 317 Assignment #3: due Wednesday, January 27, 2010 1. Neptune’s period is 164.8 years. Show that it is about 30 times as far from the sun as earth is. 2. Suppose a particle has an elliptical orbit under a force per unit mass 2 / r μ , i.e., toward the centre of force, i.e., , 3 r r r μ - = & & where r ( t ) is the distance from the particle to the centre of force and t is time. If the particle is measured to have a speed 0 v at a distance 0 r from the centre of force at time 0 t , show that the period of the particle’s
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Unformatted text preview: motion is given by . 2 2 2 / 3 2- -π v r 3. When deriving Kepler’s laws from Newton’s Law of Gravitation, i.e., , 3 r r r A m-= & & it was shown that ε r L r-= =-× ector constant v r A & and that the angular momentum vector given by r r L & × = m is also a constant vector. It was also shown the total energy of the system =-⋅ r A m r r & & 2 1 constant = E. Show that 2 2 2 2 1 mA E L + = ε where . , L ε = = L...
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