Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light-years and an orbital speed of about 200 km/s. (b) Observations of stars, as well as theories of the structure of stars, suggest that it is impossible for a single star to have a mass of more than about 50 solar masses. Can this massive object be a single, ordinary star?

Use the results of Example 13.5 (Section 13.3) to calculate the escape speed for a spacecraft (a) from the surface of Mars and (b) from the surface of Jupiter. Use the data in Appendix F. (c) Why is the escape speed for a spacecraft independent of the spacecraft's mass?

In 2005 astronomers announced the discovery of a large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every 27 hours and moving at 30,000 km/s. (c) What is the radius of its event horizon?

In 2005 astronomers announced the discovery of a large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every 27 hours and moving at 30,000 km/s. (b) What is the mass of this black hole, assuming circular orbits? Express your answer in kilograms and as a multiple of our sun's mass.

In 2005 astronomers announced the discovery of a large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every 27 hours and moving at 30,000 km/s. (a) How far are these clumps from the center of the black hole?

Cosmologists have speculated that black holes the size of a proton could have formed during the early days of the Big Bang when the universe began. If we take the diameter of a proton to be 1.0 * 10^-15 m, what would be the mass of a mini black hole?

The Parker Solar Probe, launched in 2018, was the first spacecraft to explore the solar corona, the hot gases and flares that extend outward from the solar surface. The probe is in a highly elliptical orbit that, using the gravity of Venus, will be nudged ever closer to the sun until, in 2025, it reaches a closest approach of 6.9 million kilometers from the center of the sun. Its maximum speed as it whips through the corona will be 192 km/s.(b) The probe's highly elliptical orbit carries it out to a maximum distance of 160 Rₛ with a period of 88 days. What is its slowest speed, in km/s?

Two stars, one twice as massive as the other, are 1.0 light year (ly) apart. One light year is the distance light travels in one year at the speed of light, 3.00 ✕ 10⁸ m/s . The gravitational potential energy of this double-star system is ─8.0 ✕ 10³⁴ J. What is the mass of the lighter star?