If the active core of a galaxy contains a black hole of 106 Me, what will the orbital period be for matter orbiting the black hole at a distance of 0.23 AU? GM Hint: Use the formula for circular velocity, V. = V hr
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A: mass of black hole, M=106 MΘ=106*2*1030=2*1036 Kg radius of orbit,r=0.33 Au=0.33*1.5*1011=0.495*1011…
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A: The expression for the orbital period, T=2πrv =2πrGMr =2πr32GM
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- For a circular velocity profile of the type (r) = ar¹ ar1/9, where a is a constant and r is the radial distance from the centre of a spiral galaxy, find the ratio (r)/(r), where (r) is the epicyclic frequency and 2(r) is the angular velocity. Enter your answer to 2 decimal places.In the reading, you were told that there were roughly 10,000 galaxies in the image of the Hubble Ultra Deep Field alone. The image is roughly 10 square arcminutes and there are roughly 1.5*10^8 square arcminutes composing the entire sky. With that in mind and assuming that the Hubble Ultra Deep Field represents an average part of the sky, roughly how many galaxies may exist in the observable universe? (Please include commas for every factor of 1,000; for example 2,343,567,890)The Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass. 250 km s-1. Using Kepler's 3rd Law,
- If astronomers find they have made a mistake and our Solar System is actually 7,350 pc rather than 8,300 pc from the center of the Milky Way Galaxy, but the orbital velocity of the Sun is still 225 km/s, what is the minimum mass (in solar masses, MSun) of the Galaxy within the orbit of the Sun?An 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)The Universe is approximately 13.8 Billion years old. What is the volume of the visible universe in m3?
- A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen- tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe dark matter exists. Let's work out why! Assuming that each star in a given galaxy has a circular orbit, we know that the accelera- tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and equal to v?/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected relationship between ve and r due to the stellar halo (p(r) xr-3.5) does not produce a flat rotation curve. (b) Show that a p(r) ∞ r¯² density profile successfully produces a flat ro- tation curve and must therefore be the general profile that dark matter follows in our galaxy.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…what is the difference between an E0 galaxy and an E1 galaxy?