Question

Problem 1 Planetary Orbits Consider the two-body problem for a planet-star system. The planet, of mass m, is initially in a circular orbit of radius r and angular speed w about the star, of mass M. (i) What is the gravitational potential energy of the system, U? What is the kinetic energy of the planet, K? What is the total energy of the system, E = K +U? (ii) The star suddenly loses half of its mass, M + M/2. How does the planet's orbit change in this case? Does the planet remain gravitationally bound to the star? (iii) The star's mass suddenly doubles, M + 2M. How does the planet's orbit change in this case? If the mass of the planet is much smaller than the mass of the star, m<M, show that the planet's new orbital period is given by Tnew ~ Told 2 3V3 . = 0.38

Answer 1

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