The two stars Sirius A and Sirius B orbit their commoncenter of mass. Sirius A has a mass of 4.12 × 1030kg andSirius B has a mass of 2.04 × 1030kg. Assuming theyeach have circular orbits and they stay 2.99 × 1012mapart, what is the radius of the orbit of Sirius A?
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The two stars Sirius A and Sirius B orbit their common
center of mass. Sirius A has a mass of 4.12 × 1030kg and
Sirius B has a mass of 2.04 × 1030kg. Assuming they
each have circular orbits and they stay 2.99 × 1012m
apart, what is the radius of the orbit of Sirius A?
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- A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)Problem 6. (Palen, et. al., 2nd ed., Problem 49) Sirius and its companion orbit around a common center of mass with a period of 50 years. The mass of Sirius is 2.02 times the mass of the Sun. a) If the orbital velocity of the companion is 2.07 times greater than that of Sirius, what is the mass of the companion? b) What is the semimajor axis of the orbit?
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