Astronomy Unit 8

Ranking Task: Time Dilation Part A: Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Imagine that you watch the other spaceship as its clock ticks off one second. Rank the figures according to how much time you would say passes (on your own ship) while the other ship's clock ticks off one second, from the shortest to the longest amount of time.

-Speed = 0.7c -Speed = 0.75c -Speed = 0.8c -Speed = 0.85c

Ranking Task: Time Dilation Part B: The four figures below are the same as those in Part A. This time, imagine that the passengers on the other spaceship are watching your clock as its ticks off one second. Rank the figures according to how much time the passengers (on the other ship) would say passes (on their ship) while they watch your clock tick off one second, from the shortest to the longest amount of time.

-Speed = 0.7c -Speed = 0.75c -Speed = 0.8c -Speed = 0.85c

Ranking Task: Length Contraction Part A: Each figure below shows a spaceship moving past your spaceship ("YOU") at the indicated speed. Assume that all the spaceships have equal length when at rest and that you watch the other spaceship as its clock ticks off one second. Rank the figures based on the length that you would measure for the other spaceship (in its direction of motion), from shortest to longest.

-Speed = 0.85c -Speed = 0.8c -Speed = 0.75c -Speed = 0.7c

Ranking Task: Length Contraction Part B: The four figures below are the same as those in Part A. This time, rank the figures based on your length as measured by the passenger in the other spaceship, from shortest to longest.

-Speed = 0.85c -Speed = 0.8c -Speed = 0.75c -Speed =0.7c

Ranking Task: The Size of the Milky Way Galaxy Part A: Listed following are several locations in the Milky Way Galaxy. Rank these locations based on their distance from the center of the Milky Way Galaxy, from farthest to closest.

-a globular cluster in the outskirts of the halo -a cloud of gas and dust in the outskirts of the disk -our solar system -the edge of the central bulge

Ranking Task: The Size of Planets, Stars, and Stellar Remnants Part B: Listed following are several astronomical objects. Rank these objects based on their mass, from largest to smallest. (Be sure to notice that the main-sequence star here has a different spectral type from the one in Part A.)

-a typical black hole (formed in a supernova) -a typical neutron star -a one-solar-mass white dwarf -main-sequence of spectral type M -Jupiter -the Moon

Ranking Task: The Size of the Milky Way Galaxy Part B: Imagine a photon of light traveling the different paths in the Milky Way described in the following list. Rank the paths based on how much time the photon takes to complete each journey, from longest to shortest.

-across the diameter of the galactic halo -across the diameter of the galactic disk -from the Sun to the center of the galaxy -across the diameter of the central bulge -through the disk from top to bottom

Ranking Task: The Size of Planets, Stars, and Stellar Remnants Part A: Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.)

-main-sequence star of a spectral type A -Jupiter -a one-solar-mass white dwarf -the Moon -a two-solar-mass neutron star -the event horizon of a two-solar-mass black hole

Ranking Task: Understanding Gravitational Lensing Part A: The figures below show several different astronomical objects. Rank the objects based on the amount that spacetime is curved (relative to flat spacetime) very near the surface (or event horizon) of each of the objects, from least to greatest.

-red giant -main-sequence star -white dwarf -neutron star -black hole

Ranking Task: Understanding Gravitational Lensing Part B: The figures below show the same astronomical objects as shown in Part A. Rank the objects based on the amount that each would deflect the path of a photon of light from a very distant galaxy (as viewed from Earth), assuming the photon passes very near the surface (or event horizon) of each object, from smallest to largest.

-red giant -main-sequence star -white dwarf -neutron star -black hole

Ranking Task: Understanding Curved Spacetime Part C: The figures below show several different astronomical objects. Rank the objects based on the amount that spacetime is curved (relative to flat spacetime) very near the surface (or event horizon) of the objects, from least to greatest.

-red giant -the Sun -white dwarf -black hole

Ranking Task: Understanding Curved Spacetime Part D: The figures below show several different astronomical objects. Rank the objects based on the acceleration a spaceship would have as it passed very near the surface (or event horizon) of each object, from smallest to largest.

-red giant -the Sun -white dwarf -black hole

Ranking Task: The Size of Planets, Stars, and Stellar Remnants Part C: Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest.

-the singularity of a black hole -a typical neutron star -a one-solar-mass white dwarf -a main-sequence star

Ranking Task: Understanding Curved Spacetime Part A: The figures below show several different astronomical objects. Rank the objects based on the strength of the gravitational force that would be felt by a spacecraft traveling at a distance of 10 AU from the center of each of the objects, from weakest to strongest. If the gravitational force is equal for two (or more) cases, show this equality by dragging one figure on top of the other(s).

All are the same.

Ranking Task: Understanding Curved Spacetime Part B: The figures below show several different astronomical objects. Rank the objects based on the amount that spacetime is curved (relative to flat spacetime) at a distance of 10 AU from the center of each of the objects, from least to greatest. If two (or more) cases are equal, show this equality by dragging one figure on top of the other(s).

All are the same.

Ranking Task: Length Contraction Part C: We can summarize the results of Parts A and B as follows: When another spaceship is moving by you (at constant velocity), you will measure the spaceship to be shorter than its rest length, while passengers on that ship will measure your length to be shorter. Imagine that you and the passengers on the other ship are arguing (by radio) about who really is the one that has become shorter. To settle the argument, you agree to meet up on Mars and put the two spaceships next to each other to see which one is really shorter. What will you find when you meet up on Mars?

Both spaceships are the same length.

Sorting Task: The Bizarre Stellar Graveyard Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death.

White dwarf: -in a binary system, it can explode as a supernova -has a mass no greater than 1.4 MSun -supported by electron degeneracy pressure -typically about the size (diameter) of Earth Neutron star: -sometimes appears as a pulsar -usually has a very strong magnetic field Black hole: -viewed from afar, time stops at its event horizon -size defined by its Schwarzchild radius

Ranking Task: Time Dilation Part C: Consider again the spaceships from Parts A and B. Suppose that, at rest, both you and a passenger on the other spaceship have the same heart rate of 60 beats per minute. How will you and the passenger on the other spaceship observe each other's heart rates as you pass by in your spaceships?

You would observe that the passenger in the other spaceship has a slower heart rate than you do, and she would observe that you have a slower heart rate than hers.

Sorting Task: Effects of Relativity Imagine that you are located on Earth while a spaceship travels from Earth to the star Vega at constant velocity of 0.8c. The following items describe quantities that, according to Einstein's special theory of relativity, would be either larger (or longer), smaller (or shorter), or the same as their rest values. (Note that by "rest value," we mean the value you would find if both you and the spaceship were at rest on Earth.) Match each item to the correct category.

larger/longer than rest value: -one second on a spaceship clock as seen by you -mass of the spaceship as measured by you -your mass as measured by spaceship passengers -one second on your clock as seen by spaceship passengers smaller/shorter than rest value: -distance from Earth to Vega as measured by spaceship passengers -length (in the direction of motion) of the spaceship as measured by you same as rest value: -speed of the spaceship's headlight beam as measured by you