Astronomy final exam question: why universe has no center?

Astronomy 210 Final Exam, spring semester 2014
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

?: Why does the universe have no center?
im: According to the big bang theory everything in the universe is moving away from each other, therefore there is no one "center."
cr: If the big bang theory is correct, the universe does have a center. We just don't know where it is, and it may not be within the observable universe.

Discuss which answer is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

[*] Adapted from https://answers.yahoo.com/question/index?qid=1006041908256.

Solution and grading rubric:

• p = 20/20:
  Correct. Hubble's law is (1) that the recession velocity of galaxies is proportional to distance, evidence is that there is a greater redshift of absorption lines for distant galaxies compared to nearby galaxies. This corresponds to the expansion of space between galaxies, such that (2) each galaxy seems to be center of expansion as observed from their position. May use analogies as not-like-an-explosion, raisin bread, enlargement of between-spaces, etc.
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. One of the two points (1)-(2) correct, other is problematic/incomplete.
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Both points (1)-(2) problematic/incomplete, or one point correct while other is missing.
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit. Discusses factors other than relevant to Hubble's law, redshifts/recession velocities, expansion of space, big bang, etc.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Section 30674
Exam code: finaln0oN
p: 3 students
r: 4 students
t: 15 students
v: 1 student
x: 1 student
y: 0 students
z: 0 students

Section 30676
Exam code: finals0N6
p: 6 students
r: 4 students
t: 10 students
v: 6 students
x: 2 students
y: 3 students
z: 3 students

A sample "p" response (from student 4380):

Astronomy midterm question: big bang expansion, not explosion?

Astronomy 210 Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board(*) was asked and answered:

strange questioner: Big bang: explosion or expansion? Most...sources say big bang as explosion, some others say it is wrong to say explosion and it's only expansion.
green meklar: It is more like an expansion [than an explosion].

Discuss why this answer is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

*Adapted from: http://answers.yahoo.com/question/index?qid=20120820231957AAhZq7N.

Solution and grading rubric:

• p = 20/20:
  Correct. Discusses (a) Hubble's law (recession velocity of galaxies is proportional to distance), (b) evidence for Hubble's law (greater redshift of absorption lines for distant galaxies compared to nearby galaxies), and (c) relates this to the expansion of space, as opposed to an explosion (where the velocity of particles is inversely proportional to the distance from the center of the explosion, and also has a unique center).
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Discusses two of the three (a)-(c) points in (p).
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Discussion of only one of the three points (a)-(c) in (p) is complete.
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on evidence of the earlier stages in the history of the universe, with little or no substantive discussion of Hubble's law.
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Section 70158
Exam code: midterm02s0Ur
p: 4 students
r: 11 students
t: 10 students
v: 6 students
x: 2 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02NuF7
p: 7 students
r: 9 students
t: 9 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1105):
Another sample "p" response (from student 2344):

Astronomy midterm question: you at where big bang started?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board[*] was asked and answered:

sai: We know that [the] big bang created everything we know today, but if it formed the universe where did the big bang take place?!
Dude: Right where [you] are standing.

Discuss why this answer is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

[*]Source: http://answers.yahoo.com/question/index?qid=20100926113402AAQcp5I.

Solution and grading rubric:

• p = 20/20:
  Correct. Understands that (a) Hubble's law is that the recession velocity of galaxies is proportional to distance (greater redshift of absorption lines for distant galaxies compared to nearby galaxies), corresponding to the expansion of space between galaxies, and (b) extrapolating time backwards means that the distance between everything was zero, thus any location can be said to be where the big bang took place (or may instead argue for no unique center of expansion for expanding-space-between-galaxies universe).
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. One of the two points (a)-(b) is correct, other is problematic.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Only one of the two points (a)-(b) correct, other is missing, or both are problematic.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on evidence of the earlier stages in the history of the universe, with little or no substantive discussion of Hubble's law, such as everything was created by the big bang, therefore everything can be said to be where the big bang took place.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70158
Exam code: midterm02s3Ar
p: 4 students
r: 11 students
t: 9 students
v: 7 students
x: 3 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02n1cT
p: 7 students
r: 7 students
t: 7 students
v: 4 students
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 1027):
A sample "v" response (from student 1177):
Another sample "v" response (from student 8436), still showing the astronomy love:

Astronomy midterm question: exploding big bang?

Astronomy 210 Midterm 2, spring semester 2011
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board [*] was asked and answered:

nema: What is [the] big bang theory...?
Wobzter: First all matter and energy was stored [in] a ball the size of a fist...and exploded. Then all matter and energy spread out, and moved away from the place of the fist...

Discuss why this answer is incorrect, and how you know this. Explain using observations and evidence related to the Hubble law.

[*] Source: http://answers.yahoo.com/question/index?qid=20100117025456AAzBY3X.

Solution and grading rubric:

• p = 20/20:
  Correct. Discusses Hubble's law (recession velocity of galaxies is proportional to distance) and evidence (greater redshift of absorption lines for distant galaxies compared to nearby galaxies), and uses this to contradict one or both: (a) no unique center, (b) expansion is not like an explosion (where speeds would decrease with increasing distance).
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Hubble's law discussion is problematic or
  incomplete, but least understands that as a consequence there must be no unique center, and/or expansion cannot be like an explosion.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on other aspects of the universe, with little or no substantive discussion of Hubble's law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
Exam code: midterm02N3n4
p: 8 students
r: 7 students
t: 15 students
v: 15 students
x: 1 student
y: 0 students
z: 0 students

Section 30676
Exam code: midterm02Sys7
p: 4 students
r: 5 students
t: 14 students
v: 12 students
x: 15 students
y: 0 students
z: 0 students

A sample "p" response (from student 4200):
Another sample "p" response (from student 2364):

Astronomy quiz question: galaxy recession

Astronomy 210 Quiz 6, Spring Semester 2011
Cuesta College, San Luis Obispo, CA

Observations that distant galaxies __________ is evidence that they are moving away from the Milky Way.
(A) are getting dimmer.
(B) are getting smaller in size.
(C) have redshifted absorption lines.
(D) appear much younger than the Milky Way.

Correct answer: (A)

Absorption lines that are shifted towards slightly longer values ("redshifted") indicate that its source is moving away.

Section 30676
Exam code: quiz06SoR3
(A) : 13 students
(B) : 6 students
(C) : 20 students
(D) : 0 students

"Success level": 56% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.64

Astronomy midterm question: big bang not like an explosion?

Astronomy 210 Midterm 2, fall semester 2010
Cuesta College, San Luis Obispo, CA

[20 points.] Consider the following statement regarding the big bang:

"The big bang did not explode into space like a bomb exploding..."
--Sujoy Desai, Uniphase: A Solution to Albert Einstein's "The Unified Field Theory," iUniverse, Bloomington, IN, 2003, p. 10.

Discuss why this statement is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

Solution and grading rubric:

• p = 20/20:
  Correct. Hubble's law is that the recession velocity of galaxies is proportional to distance, evidence is that there is a greater redshift of absorption lines for distant galaxies compared to nearby galaxies. This is in opposition to an explosion, where the velocity of particles is inversely proportional to the distance from the center of the explosion. (Or may use Hubble's law to argue that there is no unique center to the expansion of space, in opposition to an explosion, which does have a unique center.)
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Discusses how Hubble's law expansion is not like an explosion, but does not explicitly discuss absorption line redshift evidence for Hubble's law.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Describes how an explosion is not like the actual expansion of the universe, but Hubble's law discussion is problematic or incomplete.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on evidence of the earlier stages in the history of the universe, with little or no substantive discussion of Hubble's law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70158
p: 8 students
r: 14 students
t: 7 students
v: 7 students
x: 9 students
y: 0 students
z: 1 student

A sample "p" response (from student 1122):
Another sample "p" response (from student 1021):
A sample "x" response (from student 4146):
A sample "x" response (from student 4130), tossing in a "bing bang [sic]" reference:
A sample "x" response (from student 7183), with a personal message:

Astronomy midterm question: no center for universe?

Astronomy 210 Midterm 2, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board (http://answers.yahoo.com/question/index?qid=20100905145749AAyQLJr) was asked and answered:

Bell: What is at the center of the universe?

Stimpy: The universe is not defined to have [a] center. Wherever you are in the universe you will always appear to be in the center.

Discuss why this answer is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

Solution and grading rubric:

• p = 20/20:
  Correct. Hubble's law is that the recession velocity of galaxies is proportional to distance, evidence is that there is a greater redshift of absorption lines for distant galaxies compared to nearby galaxies. This corresponds to the expansion of space between galaxies, such that each galaxy seems to be center of expansion as observed from their position. May use analogies as not-like-an-explosion, raisin bread, enlargement of between-spaces, etc.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Discusses how Hubble's law expansion will be observed identically for all viewpoints, but does not explicitly discuss absorption line redshift evidence for Hubble's law.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Describes how Hubble's law expansion will be observed identically for all viewpoints, but Hubble's law discussion is problematic or incomplete.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on evidence of the earlier stages in the history of the universe, with little or no substantive discussion of Hubble's law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  y = 2/20: Irrelevant discussion/effectively blank.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70160
p: 11 students
r: 10 students
t: 11 students
v: 5 students
x: 3 students
y: 1 student
z: 0 students

A sample "r" response (from student 2421):

Astronomy quiz question: no center of universe expansion

Astronomy 210 Quiz 6, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

__________ is evidence that the universe has no center of expansion.
(A) Matter and antimatter annihilate to convert into energy.
(B) Galaxy redshifts are proportional to galaxy distances.
(C) The finite speed of light.
(D) The night sky is dark, and not blindingly bright.

Correct answer: (B)

The Hubble law indicates that space is expanding, such that galaxies which are stationary within this expanding space will appear to recede faster from an observer the more distant they are. Since this would be true for any observer at any location in this expanding space universe, such that the expansion would not have a center.

Section 70158
(A) : 1 student
(B) : 38 students
(C) : 5 students
(D) : 1 student

"Success level": 86% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.22

Astronomy midterm question: centers of the universe

Astronomy 210 Midterm 2, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Consider the following comment:

"The Universe has as many different centers as there are living beings in it. Each of us is a center of the Universe..."
—Aleksander Isaevich Solzhenitsyn, The Gulag Archipelago: 1918-1956, Harper & Row Publishers, 1985, p. 3.

Discuss why observers in different galaxies would each think that they are the center of expansion for the universe. Explain using Hubble's law.

Solution and grading rubric:

• p = 20/20:
  Correct. Explains how Hubble's law (recession velocity is proportional to distance) corresponds to the expansion of space between galaxies, such that each galaxy seems to be center of expansion as observed from their position. May use analogies as not-like-an-explosion, raisin bread, enlargement of between-spaces, etc.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Typically Hubble's law discussion is missing or problematic.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70158
p: 16 students
r: 11 students
t: 20 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8260):

Another sample "p" response (from student 1989):

A sample "t" response (from student 1781), with no explicit discussion of Hubble's law, but still capturing the essence of the relativeness of galaxies receding from all observers::

A sample "v" response (from student 2522), appealing to a version of the Copernican principle:

Astronomy midterm question: expansion, not explosion

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Discuss why the expansion of the universe is not like an explosion, using observations and evidence related to the Hubble law in your explanation.

Solution and grading rubric:

• p = 20/20:
  Correct. Hubble's law is that the recession velocity of galaxies is proportional to distance, evidence is that there is a greater redshift of absorption lines for distant galaxies compared to nearby galaxies. (Also there is no unique center to this expansion of space.) This is in opposition to an explosion, where the velocity of particles is inversely proportional to the distance from the center of the explosion.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Describes how an explosion is not like the actual expansion of the universe, but Hubble's law discussion is problematic or incomplete.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on other aspects of explosions, with little or no substantive discussion of Hubble's law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
p: 9 students
r: 5 students
t: 10 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A similar version of this question was asked as a multiple-choice question in Spring 2009.

A sample "p" response (from student 1959), positing that the galaxies in the universe have all drank the "Haterade":

Another sample "p" response (from student 2902), appealing to the "everyone smelt it, so everyone dealt it" theory:

A sample "p" response (from student 2947) explaining in pictures what word cannot do justice:

Another sample "p" response (from student 5398) using a "no-center" argument:

Astronomy quiz question: expansion, not explosion

Astronomy 210 Quiz 6, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

__________ is evidence that the universe is not expanding like an explosion.
(A) The finite speed of light.
(B) The night sky is dark, and not blindingly bright.
(C) Galaxy redshifts are proportional to galaxy distances.
(D) Matter and antimatter annihilate to convert into energy.

Section 30674
(A) : 5 students
(B) : 3 students
(C) : 19 students
(D) : 3 students

Correct answer: (C)

In an explosion, debris travels slower as it gets farther from the explosion, which is the opposite of what is actually observed, which is Hubble's law (response (C). Response (A) is the cause of lookback time, and response (B) is Olber's explanation of why the universe cannot be infinite in extent.

A similar version of this question was asked on a Final Exam in Spring 2008.

"Difficulty level": 63% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

Astronomy midterm question: no-center universe expansion

Astronomy 210 Midterm 2, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

[20 points.] Discuss why the expansion for the universe has no center, using observations and evidence related to the Hubble law in your explanation.

Solution and grading rubric:

• p = 20/20:
  Correct. Argument involves redshifts (and thus recession velocities) being proportional to distances (i.e., Hubble's law), and how this implies that there is no unique center, any other galaxy would observe a similar Hubble's law. May also invoke no-edge, no-center argument of an non-finite universe.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70160
p: 23 students
r: 3 students
t: 2 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response, discussing Hubble's law (from student 1225):

Another "p" response, discussing "Cosmic Haterade" (from student 7120):

Astronomy final exam question: expansion, not explosion

Astronomy 10 Final Exam, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q12.2

[3.0 points.] Which one of the following statements best explains why the universe is not expanding like an explosion?
(A) The cosmic background radiation is nearly equal in all directions.
(B) Recession velocities of galaxies get faster with increasing distance.
(C) Ages of galaxies get younger with increasing distance.
(D) The cosmic background radiation has a very low temperature.
(E) Brightnesses of galaxies get dimmer with increasing distance.

Correct answer: (B)

In an explosion, debris travels slower as it gets farther from the explosion, which is the opposite of what is actually observed. (Response (B) is Hubble's law.)

Student responses
Section 5166
(A) : 7 students
(B) : 28 students
(C) : 1 student
(D) : 1 student
(E) : 3 students

Section 4160
(A) : 9 students
(B) : 20 students
(C) : 3 students
(D) : 0 students
(E) : 3 students

Astronomy quiz question: Hubble's law

Astronomy 10 Quiz 12, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q12.2

[3.0 points.] Which one of the following statements best describes Hubble's law?
(A) Distant galaxies recede faster than nearby galaxies.
(B) Spacetime becomes more flat over time.
(C) Expansion must be followed by an equal and opposite contraction.
(D) There are equal amounts of dark matter and dark energy in the universe.
(E) The distances to other galaxies are farther away than expected.

Correct answer: (A)

Hubble's law correlates the recession speeds (v) of galaxies to their distances (d) from the Earth, where:

v = H*d.

Response (B) is related to the flatness problem of the cosmic background radiation, which is solved by the inflationary era. Response (C) is a mangled (but apparently convincing) version of Newton's third law: "For every action there must be an equal and opposite reaction." Response (E) is evidence (from type Ia supernovae) that the expansion of the universe is relatively recent.

Student responses
Section 5166
(A) : 36 students
(B) : 1 student
(C) : 6 students
(D) : 4 students
(E) : 2 students

Universe expansion movie

Continued Consistent Expansion (*.mov, 3.7 MB)
Hubblesite.org

Astronomy 10 learning goal Q12.2

This movie is not just a zoom-in shot! Note that as the universe expands, the distances between galaxies increases, while the size of the galaxies remains constant (due to gravitational interactions). This can be illustrated during the movie by covering one of the galaxies with the mouse cursor, and showing that that the size of the galaxy does not change relative to the cursor.