Write the equation for the period, T, for a reduced mass orbiting system. Show that the equation can be approximated if one mass is significantly larger than the other, e.g. our Sun and an orbiting planet.
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- Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 46.8 km/s, and v, = 59.6 km/s respectively. (a) If the period of the first planet P, is 7.70 years, what is the mass of the star it orbits around? | kg (b) Determine the orbital period of P,. yrPlease solveTwo newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 36.2 km/s and 65.0 km/s. The slower planet's orbital period is 8.33 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years? (a) Number (b) Number i Units Units
- Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 39.5 km/s and 58.5 km/s. The slower planet's orbital period is 6.68 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years? (a) Number i (b) Number i Units Units ◄►Suppose that the gravitational force exerted by the sun on the planets were inverse r-squared, but not proportional to the planet masses. Would Kepler’s third law still be valid in this case?An object of mass m is released from rest a distance R above the surface of a planet of mass M and radius R. Derive an expression for the speed with which it hits the planet’s surface v.
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