Chapter 24

What type of main sequence star is most likely to become a black hole?

An O-type star

According to the general theory of relativity, the presence of mass:

Causes a curvature (or warping) of spacetime

Which of the following objects do many astronomers believe is a black hole?

Cygnus X-1

When astronauts aboard the International Space Station (ISS) in space let go of an orange, it just floats there. Why is that?

The ISS is falling around the Earth, and in free fall, things feel no weight

Einstein suggested that a portion of the regular change (advance) in the perihelion of the planet Mercury could be explained by:

A distortion in spacetime caused by the gravity of the Sun

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

Deep inside a black hole (and hidden from our view) is the compressed center, where all the "stuff" of the star goes. Astronomer call this central point:

A singularity

When a light wave leaves a region of strong gravity, compared to the same wave leaving a spaceship in empty space, the wave in strong gravity will have:

All of these

Astronomers have concluded that growing supermassive black holes (which have millions of times the Sun's mass or more) is pretty unlikely at our location in the Milky Way Galaxy. Where in the Milky Way do they think such a supermassive black hole does exist?

At the center of the Milky Way Galaxy, where matter is more crowded

When Einstein proposed his General Theory of Relativity, he suggested some pretty strange ideas about space, time, and gravity. How did scientists in 1919 show that Einstein's theory described the behavior of the real world and wasn't just a crazy hypothesis?

By observing starlight coming close to the Sun during an eclipse

When one member of a binary star system is a black hole, and astronomers detect flickering x-rays coming from the system, where are these x-rays usually coming from?

From a disk of material around the black hole (material that has been pulled from the companion star and is falling toward the black hole)

The astronomer who first worked out the mathematical description of black hole event horizons was:

Karl Schwarzschild

To predict whether a star will ultimately become a black hole, what is the key property of the star we should look at?

Mass

Wearing a very accurate watch, you volunteer to go on a mission to a black hole in a spaceship that has powerful rockets. You are able to orbit the black hole and stay a little distance outside of the event horizon. Compared to watches on Earth, your watch near the black hole will run:

More slowly

The radius of a black hole's event horizon is given by the formula R=2GMc2. You may need to look up the values of the constants G and c, as well as well as the mass of the Sun in Appendix E of our textbook in order to complete this problem. Calculate the radius of a black hole that has the 1.1 times the mass of our Sun. Give your final answer in km. (Note that this is only a theoretical calculation. This would not be enough mass to become a black hole.) Calculate the event horizon radius in km of a black hole that has 11 times the mass of the Sun. (This is a more realistic mass for a black hole that forms at the end of a star's life). Suppose a black hole has somehow swallowed the mass of a typical globular cluster, which is 105 times the mass of the Sun. What would the radius in km of the event horizon of that black hole be? Calculate the radius of the event horizon of the black hole in the center of the Milky Way Galaxy in km. This black hole has a mass of 4 million (4 × 106) times the mass of the Sun. Let's see how the value you calculated in part (d) compares to the size (semi-major axis) of the Earth's orbit (1.49 × 108 km). What is the ratio of the value you got to the semi-major axis of our orbit? Suppose we could take the Earth and compress it until it becomes a black hole. How big would the radius of the event horizon be for that black hole in km?

Radius = 3.263 Radius = 32.63 Radius = 296600 Radius = 1.186E+7 R/aEarth = 0.07963 Radius = 8.854E-6

The first example of a black hole that was found by astronomers, Cygnus X-1, is now known to have a mass of 14.8 times the mass of the sun. The radius of a black hole's event horizon is given by the formula R=2GMc2-- where G is the universal constant of gravity, and c is the speed of light. What is the radius of its event horizon in km? The companion star of the black hole in the Cygnus X-1 system is an average distance of 2.8 × 107 km from the black hole. How many times further is that than the radius of the event horizon itself? Using just Newton's ideas of gravity, what would the escape velocity from the black hole in Cygnus X-1 be at a distance of 40 km from its center. The escape velocity is the square root of 2GMr . Be careful with your units and give your answer in meters per second.

Radius = 43.87 d/R = 638200 Escape velocity = 3.142E+8

In 1959, Pound and Rebka did an experiment to test the prediction of Einstein's theory of general relativity about the relationship between the pace of time and the strength of gravity. When two identical atomic clocks, one on the ground floor and one on the top floor, were compared:

The clock on the ground floor ran a tiny bit slower

The equivalence principle (principle of equivalence) says that:

The effects of gravity are equivalent to the effects of acceleration

Once a black hole forms, the size of its event horizon is determined by:

The mass inside the event horizon

Which of the following statements about the way the mass of a white dwarf affects spacetime is correct?

The white dwarf mass will curve spacetime; light has to follow that curvature