Tuesday, November 03, 2009

Astronomy Homework

Just for fun--the current homework assignment for my Astronomy class. (It is for freshmen non-science-majors.)

1. Which one of the following statements is NOT a consequence of the postulates of special relativity?
A) The wavelength emitted from a source moving with respect to an observer is different from the wavelength measured by an observer who is moving along with the source.

B) A clock moving with respect to an observer ticks more slowly than when measured by an observer who is moving along with the clock.

C) The length of an object moving with respect to an observer is shorter than it is when measured by a different observer moving along with the object.

D) The mass of an object moving with respect to an observer is larger than the mass measured by a different observer who is at rest with respect to the object.

2. Einstein's theory of special relativity contains some very strange ideas such as time dilation (moving clocks run slow), length contraction (moving lengths are shorter), and lack of absolute simultaneity. What is the basis of these ideas?
A) The speed of light is the same for all observers in all reference frames.

B) New technologies allow more precise measurements of length and time than had been possible in Newton's era, and the theory had to be reworked to fit this new evidence.

C) The ether (the medium that supports the passage of light) proved to be denser than originally thought.

D) The fabric of spacetime is dominated by black holes.

3. According to general relativity, why does Earth orbit the Sun?
A) Space around the Sun is curved, and Earth follows a geodesic in this curved space.

B) Matter contains quarks, and Earth and the Sun attract each other with the “color force” between their quarks.

C) The Sun exerts a gravitational force on Earth across empty space.

D) Earth and the Sun are continually exchanging photons of light in a way that holds Earth in orbit.

4. A black hole is so named because
A) no light can escape from it due to its powerful gravitational field.

B) it emits no visible light because it is so cold, less than 100 K.

C) the gravitational field is so high that the wavelength of its emitted light is gravitationally redshifted to radio wavelengths.

D) it is colder that the rest of the universe; that is, its effective temperature is less than 3 K.

5. What is a singularity?
A) point of infinite density

B) tunnel into another universe

C) point at the Schwarzschild radius of a black hole

D) particle-antiparticle pair

6. The Schwarzschild radius is
A) the distance from the center of a black hole to the point at which the escape velocity becomes equal to the speed of light.

B) the distance to which gas is ejected in a planetary nebula.

C) half the diameter of a neutron star.

D) half the diameter of the singularity in a black hole.

7. What is the ergoregion of a Kerr black hole?
A) region outside the event horizon where objects cannot remain at rest without falling into the black hole

B) region inside the event horizon where virtual particles are created from the vacuum of space

C) inner part of the accretion disk where X rays are generated

D) region between the event horizon and the singularity from which nothing can escape

8. What appears to happen to a clock as it approaches and reaches the event horizon around a black hole when viewed by a remote observer?
A) Time appears to slow down and stop.

B) Time appears to pass at a much faster rate, becoming infinitely fast at the event horizon.

C) Time speeds up because of the intensified gravitational field.

D) Time ticks uniformly since nothing changes the progress of time.

9. What mechanism in the vicinity of a star gives us a hint of the presence of a black hole as a companion to the star?
A) Gas from the star, falling in toward a black hole, is compressed to very high densities and temperatures so that it emits an intense and rapidly fluctuating flux of X rays.

B) The star periodically disappears from the viewpoint of Earth during its eclipses by the black hole as the two objects orbit each other.

C) The space near the star darkens, indicating that the black hole prevents the light from distant objects from reaching Earth.

D) The light from the companion star shows extreme redshift because of the gravitational field of the black hole.

10. Gamma-ray bursters are great distances from Earth, yet Earth receives tremendous amounts of energy from them. Explain.
A) The energy is released along jets rather than uniformly in all directions. If Earth is in the path of one of these jets, we see a gamma-ray burster.

B) A gamma-ray burster represents the explosion of an entire galaxy.

C) Gamma-ray bursters are supermassive stars, equivalent to 100,000 ordinary supernovae.

D) The gamma radiation from a burster is released in all directions, but then it is focused in the direction of the Earth by gravitational lensing.

11. If nothing can ever leave a black hole, can the mass of a black hole ever decrease?
A) yes, if particle-antiparticle pairs are created outside the event horizon out of gravitational energy from the black hole and one particle enters the event horizon while the other escapes

B) yes, if antiparticles enter a black hole and annihilate with matter already inside the black hole

C) yes, if the matter inside the black hole is radioactive (e.g., uranium), allowing their decay products—alpha particles, electrons, and gamma rays—to constantly leave the black hole

D) no

12. (Extra Credit) Through whom is the only path to salvation?
A) Jesus Christ

B) Bill Buckner

C) Joe the Plumber

D) Angry Al Gore

(Okay, the last question is not really on the assignment, so don't notify my dean. Just wanted to wake you up.)

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