homework 6
There are a few ways to estimate the diameter of Sgr A*. Which one of them results in the smallest radius measurement? 1.Radio measurements of its accretion disk from the Very Long 2.Baseline Array show that the diameter of Sgr A* can be no larger than about 0.3 AU. 3. Calculating the Schwarzchild radius of Sgr A* shows that the radius of the black hole is about 1.18 x 1010 m. The closest approach of a star to Sgr A* is about 1.96 x 10^-3 lightyears. Recall that there are about 1.5 x 1011 m in 1 AU, and about 9.5 x 1015 m in 1 lightyear. Hint: Explain why the method yielding the smallest result has to yield the smallest result.
Calculating the Schwarzchild radius
Which of the following statements are true?
Newton's Law of Gravity correctly describes the Earth having an elliptical orbit, Einstein's General Theory of Relativity correctly describes the Earth having an elliptical orbit, Einstein's General Theory of Relativity correctly describes the path that light follows being curved in a gravitational field
If the Sun could suddenly collapse to a black hole, how would the period of Earth's orbit differ from what it is now?
The period would stay the same, as the "black hole Sun" would have no effects on the orbit
Which wavelength ranges are most useful for imaging the supermassive black hole Sgr A* at Galactic center? Hint: Which part of the black hole structure does each wavelength range give info about?
X-rays, Infrared, Radio
According to the general theory of relativity, light and other radiation coming from a white dwarf or a neutron star should (and experiments show that it does) exhibit
a gravitational redshift
From which of the following will a wave of light show the greatest gravitational redshift:
a white dwarf
According to the General Theory of Relativity: Matter tells spacetime how to _________ ; spacetime tells matter how to ________ (This is actually a quote from John Wheeler, a famous physicist.)
curve, move
To show that SgrA*, the bright radio source at Galactic center, is a black hole, astronomers need to measure both its mass and its diameter. How did they do this, and what were the results? They measured the mass using the orbital periods and orbital radii of stars , measured using infrared light. By applying ________ , we can calculate a mass of about _________ . The most precise diameter estimate comes from __________ , measured using ___________ light. The diameter is a few light-seconds across, which is about the size of Mercury's orbit around the Sun. So much mass in such a small space makes it most likely that this object is a black hole.
the orbital periods and orbital radii of stars, infrared, Kepler's third law, 4.6 million solar masses, the size of the accretion disk, radio, light-minutes
Which of these is a good description of the event horizon of a black hole?
the region around a black hole whose radius is equal to the Schwarzchild Radius, the place where the warping of spacetime around a collapsed star becomes so great that all straight lines pointing outward actually become curved paths bringing you back in, the place around the black hole where the speed you need to escape becomes greater than the speed of light
