Observations 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?

Observations 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?

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter28: The Evolution And Distribution Of Galaxies

Section: Chapter Questions

Problem 24E: Assume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer...

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If the diameter of the Milky Way Galaxys visible disk, 80,000 ly, is represented in a model by a dinner plate with a diameter of 10 inches, what is the model distance to galaxy M31, 2.6 millionly away? What is the model distance to the Virgo galaxy cluster, 16 Mpc away? (Convert answers to feet.)
Given the ideas presented here about how galaxies form, would you expect to find a giant elliptical galaxy in the Local Group? Why or why not? Is there in fact a giant elliptical in the Local Group?
The first clue that the Galaxy contains a lot of dark matter was the observation that the orbital velocities of stars did not decreases with increasing distance from the center of the Galaxy. Construct a rotation curve for the solar system by using the orbital velocities of the planets, which can be found in Appendix F. How does this curve differ from the rotation curve for the Galaxy? What does it tell you about where most of the mass in the solar system is concentrated?
Once again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.
Can an elliptical galaxy evolve into a spiral? Explain your answer. Can a spiral turn into an elliptical? How?
If the active core of a galaxy contains a black hole of 106 MSun , what will the orbital distance be (in km) for matter orbiting the black hole with an orbital period of 1 hour?
Globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why? (If you would like to learn more about globular clusters, read Section 22.2 of the book, though it is not necessary to answer this question)
When astronomers make maps of the structure of the universe on the largest scales, how do they find the superclusters of galaxies to be arranged?
Assume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer halo but also throughout the bulge and in the disk, where the solar system lives. How much dark matter would you expect there to be inside the solar system? Would you expect that to be easily detectable? Hint: For the radius of the Milky Way’s dark matter halo, use R=300,000 light-years; for the solar system’s radius, use 100 AU; and start by calculating the ratio of the two volumes.
What are the two best ways to measure the distance to a distant, isolated spiral galaxy, and how would it be measured?
Suppose somebody proposed that rather than invoking dark matter to explain the increased orbital velocities of stars beyond the Sun’s orbit, the problem could be solved by assuming that the Milky Way’s central black hole was much more massive. Does simply increasing the assumed mass of the Milky Way’s central supermassive black hole correctly resolve the issue of unexpectedly high orbital velocities in the Galaxy? Why or why not?
One way to calculate the size and shape of the Galaxy is to estimate the distances to faint stars just from their observed apparent brightnesses and to note the distance at which stars are no longer observable. The first astronomers to try this experiment did not know that starlight is dimmed by interstellar dust. Their estimates of the size of the Galaxy were much too small. Explain why.