Concept explainers
(a)
To calculate:
The Schwarzschild radius of a super massive black hole of mass
Answer to Problem 39Q
Radius of a super massive black hole of mass kilometers =
Radius of a super massive black hole of mass astronomical units =
Explanation of Solution
Given:
Mass of the black hole =
Formula used:
The Schwarzschild radius can be calculated using the following:
Where, G is the gravitational constant, M is mass, c is the
Calculation:
Substitute the values:
Conclusion:
The radius of a supermassive black hole of mass kilometers =
The radius of a supermassive black hole of mass astronomical units =
(b)
To calculate:
The angular diameter in arcseconds of the black hole at a distance of
Answer to Problem 39Q
Angular diameter in arcseconds of the black hole at a distance of
Explanation of Solution
Given:
Distance from Earth to the galactic center =
Formula used:
Calculation:
Conclusion:
Angular diameter in arcseconds of the black hole at a distance of
(c)
To calculate:
The angular diameter in arcseconds of the black hole when seen from a distance of
Whether or not, it will be discernible to the naked eye.
Answer to Problem 39Q
The angular diameter of the black hole at a distance of
Yes, the naked eye can discern the black hole.
Explanation of Solution
Given:
Distance from which the black hole is observed =
The field of view of a naked eye =
Formula used:
Calculation:
As
Conclusion:
Angular diameter of the black hole at a distance of
As
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Chapter 22 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
- The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy’s disk is the distance for which we can measure accurate parallaxes?arrow_forwardConsider the following five kinds of objects: open cluster, giant molecular cloud, globular cluster, group of O and B stars, and planetary nebulae. A. Which occur only in spiral arms? B. Which occur only in the parts of the Galaxy other than the spiral arms? C. Which are thought to be very young? D. Which are thought to be very old? E. Which have the hottest stars?arrow_forwardAn astronomical image shows two objects that have the same apparent magnitude, i.e., the same brightness. However, spectroscopic follow up observations indicate that while one is a star that is within our galaxy, at a distance dgal away, and has the same luminosity as the Sun, the other is a quasar and has 100x the luminosity of the entire Milky Way galaxy. What is the distance to the quasar? (You may assume, for this rough calculation, that the Milky Way has 1011 stars and that they all have the luminosity as the Sun.) Give your response in Mpc. Value: dgal = 49 pcarrow_forward
- The best parallaxes obtained with the Hipparcos satellite have an uncertainty such that we believe measurements as low as 0.005 arc-seconds. What is the farthest distance a star can be to have an accurate distance from Hipparcos? 200 Parsecs The disk of our Galaxy is 100,000 light-years in diameter. Using the results from the previous problem, what fraction of the diameter of the Galaxy's disk is the distance for which we can measure accurate parallaxes? 0.0065 The Gaia satellite has greatly improved precision over Hipparcos, measuring parallaxes that are as small as 0.00025 arcseconds. How many times farther away is Gaia be able to measure distances to than Hipparcos?arrow_forwardAn observational survey of distant galaxies is undertaken that involves measuring their distances using cepheid variables and red-shifts using spectroscopy. Explain how cepheid variables can be used to measure the distances to galaxies. A spectral line is observed whose wavelength in the laboratory is de length of this spectral line observed in each galaxy, Xo, is listed in the table, along with the distance, d, to the galaxy. Determine the red-shift and the recession velocity of each galaxy and tabulate your results by making a copy of the table and filling in the blank spaces. Sketch a Hubble diagram using your results and determine the value of the Hubble constant Ho in units of km s-1 Mpc. 650 nm. The wave- Galaxy 1 652.69 Galaxy 2 Galaxy 3 Galaxy 4 Galaxy 5 653.01 do (nm) d (Mpc) 658.54 662.18 681.63 17 19 54 77 200 v (km s-1)arrow_forwardQuestion 2: apparent magnitude my 1 = 305.9, b = −44.9 and is d=4.5 kpc from the Sun. a.) The integrated light from the Milky Way globular cluster NGC 104 has an 4.03 mag and absolute magnitude My -9.52 mag. It is located at b.) = = Estimate the amount of extinction between the Sun and 47 Tucanae in magnitudes. What does this value of extinction mean for the amount of attenuation by dust between Earth and NGC 104?.arrow_forward
- Suppose a quasar is shining with a luminosity L. What is the approximate minimal mass of the black hole? (If the black hole had a lower mass than this, the pressure in the material would overcome the gravity of the black hole and the material would be blown apart.) Give your answer in solar masses, in scientific notation to one significant figure (no decimal places). Value: L=1×10^12Lsun Suppose the quasar in the previous problem is 10% efficient at turning rest mass into energetic photons, according to Einstein's equation E=mc2. What is the necessary rate of accretion of mass onto this black hole, to sustain its luminosity of 1* 1012 solar luminosities -- i.e. how much mass must be 'fed' to this black hole to keep the AGN shining so brightly? Give your response in units of solar masses of material per year, with one decimal place.arrow_forward(a) Estimate the height (z) above or below the Galactic plane for the globular cluster M13 (1,b = 59°, 40.9°) and the Orion Nebula (1,b = 209°, -19.4°). M13 and the Orion Nebula are 7 kpc and 450 pc away from Earth respectively. (b) To which components of the Galaxy do these objects probably belong? Explain your answers.arrow_forwarda) Calculate the period of the solar system's orbit around the Milky Way. Assume that we are 8.5 kpc from the galactic center and assume that the mass of the Milky Way interior to our orbit is ~ 10¹¹ solar masses. Alpha Centauri is a multiple star system only 1.34 parsecs away. The apparent magnitudes of the two main stars are: a Cen A: my = +0.01; a Cen B: my = +1.33. b) Calculate the ratio of the flux we receive in the V filter from a Cen A to the flux we receive from a Cen B. c) Calculate the absolute magnitude My of a Cen B.arrow_forward
- Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…arrow_forwardObservations of the central region of the galaxy M87 indicate that stars which are 60 light years later from the centre are orbiting the central supermassive black hole at speeds of 730kms^-1. Estimate the lads of the black hole, in solar masses.(You can assume circular motion, e.g. if you get 3 solar masses, type in 3). just wondering what formula I use?arrow_forwardThe HI intensity vs. velocity curve for a disk galaxy has a width W = 400 km s-. This galaxy has a pitch angle of 20°, a bulge-to-total luminosity of 7%, and a mass-to-light of 2.5. What is its absolute B-band magnitude and why?arrow_forward
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