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
Trending nowThis is a popular solution!
Chapter 7 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- 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.)arrow_forwardMuch of the mass of our Milky Way galaxy is concentrated in a central sphere of radius r = 2 kpc, where pc is the abbreviation for the unit parsec; 1 pc = 3.26 ly. Assume the Sun is in a circular orbit of radius r = 8.0 kpc around the central sphere of the Milky Way. The Suns orbital speed is approximately 220 km/s; assume the central sphere is at rest. a. Estimate the mass in the inner Milky Way. Report your answer in kilograms and in solar masses. b. What is the escape speed of the Milky Way? c. CHECK and THINK: Do you believe that stars in the Milky Way have been observed to have speeds of 500 km/s? Explain.arrow_forwardSince 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?arrow_forward
- Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.arrow_forwardTwo black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?arrow_forward(a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?arrow_forward
- What is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?arrow_forwardAstronomical observations of our milky way galaxy indicate that it has a mass of about 8x1011 solar masses. A star orbiting near the galaxy's periphery is 5.6x104 light years from its center. a.) What should be the orbital period (in years) of that star be? b.) If its period is 6.4x107 years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the center of some galaxies.arrow_forwardThe Small Magellanic Cloud is a dwarf galay orbiting the Milky Way at a distance of 50 kiloparsecs from its center, on a circular orbit. It is moving at a velocity. rolative to the Milky Way, of 207 km/s. What is the mass of the Milky Way, in units of solar masses, inside the Cloud's orbit? B !! 245 If'a quasar emits 10^(10) times the Sun's luminosity, converting 10% of the mass of the material it eats into radiation, how many stars (ach of the Sun's mans) must it consume per year?arrow_forward
- Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star. c. Find the mass of the black hole.arrow_forwardThe Schwarzschild radius RBH for an object of mass M is defined as (See image.) where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. 1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass? 2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass? 3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?arrow_forwardA number of gas giant planets orbiting other stars at distances less than 1 A.U. have been discovered. Because of their proximity to their parent stars, and their compositional similarity to Jupiter, they have been labeled “Hot Jupiters”. The orbital radius of one of these planets is 0.06 A.U. with average orbital speed 600 km/sec. What is the length of this planet’s year in Earth (solar) days? Estimate the mass, M, of its parent star in terms of the mass of the sun (M) using Newton’s first form of Kepler’s 3rd Law. Calculate the star’s luminosity, L, in terms of the luminosity of the sun (L☉), Note: (LL=MM4where L ~ 4 × 1026 W ). The radius of this planet is 1.5 times the radius of Jupiter. Assuming its equilibrium temperature is the temperature at which the planet radiates as much energy as it receives from its star, estimate the temperature of the planet. The value of the planet’s albedo is 0.8. (NOTE: The intensity of the star’s radiant power at a distance d from the star is…arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning