Passage
Black holes have played an important part in astrophysics for the last half-century. A black hole is a region of space where the force of gravity is especially strong and gravitational potential energy U is very large. Analogous to the electrostatic potential energy associated with electrical charges, U is defined as the work required to move an object of mass m from an infinite distance to a point at radial distance r within the gravitational field of a second mass M as given by
Equation 1where G is the gravitational constant. Near a black hole, the gravitational potential energy can become so negative that not even light has enough energy to escape the black hole's gravity.Escape velocity can be determined by launching an object of mass m with velocity v to an infinite radial distance from the surface of a central mass M (eg, a star or a planet) with radius R. For a black hole to exist, the escape velocity must be equal to the speed of light.Scientists have thoroughly studied the physics of black holes. Stars near the center of our galaxy have been observed to orbit an extremely massive, invisible object (millions of times more massive than our Sun) that is almost certainly a black hole. The orbital angular velocity ω of a star is defined as
ω=360°⋅fEquation 2where f is the frequency of rotation in hertz (Hz) . Likewise, black holes are not merely static masses but are often observed to rotate about their own axis. The interaction between the rotation of a black hole and matter falling into the hole is suspected to form powerful beams (jets) of ionized matter that project away from the black hole along its axis of rotation. Nevertheless, many aspects of how these jets are formed remains a mystery. Black holes will remain a fruitful area for research far into the future.
-A star orbiting a supermassive black hole makes two approximately circular revolutions around the black hole every 20 hours. What is the approximate angular velocity of the star?

Question

Passage
Black holes have played an important part in astrophysics for the last half-century. A black hole is a region of space where the force of gravity is especially strong and gravitational potential energy U is very large. Analogous to the electrostatic potential energy associated with electrical charges, U is defined as the work required to move an object of mass m from an infinite distance to a point at radial distance r within the gravitational field of a second mass M as given by

Equation 1where G is the gravitational constant. Near a black hole, the gravitational potential energy can become so negative that not even light has enough energy to escape the black hole's gravity.Escape velocity can be determined by launching an object of mass m with velocity v to an infinite radial distance from the surface of a central mass M (eg, a star or a planet) with radius R. For a black hole to exist, the escape velocity must be equal to the speed of light.Scientists have thoroughly studied the physics of black holes. Stars near the center of our galaxy have been observed to orbit an extremely massive, invisible object (millions of times more massive than our Sun) that is almost certainly a black hole. The orbital angular velocity ω of a star is defined as

ω=360°⋅fEquation 2where f is the frequency of rotation in hertz (Hz) . Likewise, black holes are not merely static masses but are often observed to rotate about their own axis. The interaction between the rotation of a black hole and matter falling into the hole is suspected to form powerful beams (jets) of ionized matter that project away from the black hole along its axis of rotation. Nevertheless, many aspects of how these jets are formed remains a mystery. Black holes will remain a fruitful area for research far into the future.
-A star orbiting a supermassive black hole makes two approximately circular revolutions around the black hole every 20 hours. What is the approximate angular velocity of the star?

Quizplus · Accepted Answer

11ecba2d_132c_f1fe_a3bf_152830a14ed6_MD0008_00 Periodic motion occurs when an object moves in a cyclical fashion, returning to the same location after a certain period of time. Classic examples of periodic motion are the oscillatory behavior of a clock pendulum, or a mass located on the end of a perturbed spring. Periodic motion is modeled in terms of wave motion, where the time required to complete one cycle of motion is defined as the period (T). The frequency (f) of oscillations per interval of time, which is often expressed in units of cycles per second (hertz), is the inverse of the period: 11ecba2d_132c_f1ff_a3bf_d1794917b420_MD0008_00 The orbital motion of a mass around a central body is also periodic. In this question, a star orbiting around a supermassive black hole completes two revolutions in 20 hours. Consequently, T within this system is equal to 10 hours. Using this period to calculate the frequency and converting the units from hours to seconds yields: 11ecba2d_132d_1910_a3bf_c9974a7cebc9_MD0008_00 11ecba2d_132d_1911_a3bf_a71b3c579533_MD0008_00 f=1 cycle10 hours⋅1 hour60 min⋅1 min60 s=136,000cyclesecond=136,000 Hz Using the period (expressed in seconds) determined from one complete orbital cycle, Equation 2 may be used to determine the angular velocity of the orbit: 11ecba2d_132d_1912_a3bf_81e3d9c74d84_MD0008_00 11ecba2d_132d_1913_a3bf_39fa94d31de9_MD0008_00 11ecba2d_132d_1914_a3bf_55acd54a30bb_MD0008_00 Therefore, the angular velocity of the star orbiting the supermassive black hole is 1.0 × 10⁻² degrees/second (Choice B). Educational objective: Periodic motion describes an object moving in a cyclical fashion in which the same movements recur in regular intervals. The frequency of cyclical motion is the inverse of period, which is the time required to complete one cycle.

Passage Black Holes Have Played an Important Part in Astrophysics for for the Last