Question

7Okn4. Tidal Forces: A comet of mass m and radius R approaches the Sun with a trajectory described by C ( L/Gm2 Mn)-4 x 10° km, and eccentricity e-0.967. Will the comet break apart by tidal forces, or retun another day? (m -2 x 10 kg, R 10 km, MN-2 x 10" kg) Points (20) m! eliptcal trajectory 34 Roche Limit 5). Binary Star System: Consider a planetary system as pictured (not to scale), with the stars in a circular orbit. Note and use the symbols, M, m, 0, R., d, d, and d. As is often the case m << M* and here R, is also << d, so we can assume that the planet does not significantly change the motion of the stars. Mo a) Write the gravitational force between the stars and the planet and show that it is approximately: F 2GM*m/d+2GM*m R./ d(cos 2 ot- 1/4), where e - 8-dot is the constant rotational speed of the stars about their CM and ineludes the condition that at t-0 the stars and planet were on a line. This requires a 2" order Taylor series expansion retaining the two lowest order terms in 1/ d. b) The first term in a) is the force if all the mass of the stars was concentrated at the CM. Explain why the correction adds to or subtracts from this term for the specific cases of cos 0-0 and 1. (draw a diagram for each case and discuss the reason). stars c) Answer qualitatively: Will all orbits close? Will the perigee precess? How will orbits differ from the Kepler 2-body solutions? Points (10,5,5=20) CM Planst Mer T-e d2 m dR 2dRCas di el

Answer 1

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