The Sun rotates about the center of the Milky Way Galaxyat a distance of about 3

Question

The Sun rotates about the center of the Milky Way Galaxyat a distance of about 30,000 light years from the center (1 yr =9.5 x 10^15 m). If it takes about 200 million years to make onerotation, estimate the mass of our galaxy. Assume that the massdistribution of our galaxy is concentrated mostly in a centraluniform sphere. If all the stars had about the mass of our Sun (2 x10^30 kg), how many stars would there be in our galaxy? * Use Kepler's laws and the period of the Moon (27.4 d) todetermine the period of an artificial satelite orbiting very nearthe Earth's surface. * The asteroid Icarus, though only a few hundred metersacross, orbits the Sun like the other planets. Its period is about410 d. What is its mean distance from the sun? The Sun rotates about the center of the Milky Way Galaxyat a distance of about 30,000 light years from the center (1 yr =9.5 x 10^15 m). If it takes about 200 million years to make onerotation, estimate the mass of our galaxy. Assume that the massdistribution of our galaxy is concentrated mostly in a centraluniform sphere. If all the stars had about the mass of our Sun (2 x10^30 kg), how many stars would there be in our galaxy? * Use Kepler's laws and the period of the Moon (27.4 d) todetermine the period of an artificial satelite orbiting very nearthe Earth's surface. * The asteroid Icarus, though only a few hundred metersacross, orbits the Sun like the other planets. Its period is about410 d. What is its mean distance from the sun?

Explanation / Answer

Sun's period T = 200 million years and Sun's orbit radius r =30,000 light years So sun's orbital speed (assuming circular path) v = 2r/T (donot forget to convert all units to MKS before you do anycalculation). The gravitational attraction of the Milky Way mass on the Sunprovides the centripetal force. So GMm/r2 = mv2/r Here M is Milky Way mass, m is Sun's mass, and G is universalgravitational constant. Since you know the values of everythingelse, you should be able to compute M. Then divide M by averagestar mass (assumed to be the same as sun's mass m) to get thenumber of stars in Milky Way. Second part: To get the period of an artificial satellite nearearth, use kepler's law T2 ~ a3 (T = period of satellite, a =semi-major axis which is the same as orbital radius for circularpath) Since this is a proportionality relation, you can take the ratio of2 equations (one for satellite and one for the moon) to get Tsatellite/Tmoon)2 =(asatellite/amoon)3 You know Tmoon. asatellite is the same as theradius of earth (because it is a low altitude satellite). Look upamoon in the textbook. Then you can computeTsatellite. 3rd part: Since Icarus revolves around the sun (like earth), youcan use kepler's law again but this time you have to compare itwith earth's motion. So Ticarus/Tearth)2 =(aicarus/aearth)3 Knowing everything else, you can compute aicarus. Hope this helps!

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