This homework consists of two computational problems (with a few parts) and one short
discussion-type question. For this and future homeworks, you may want to consult Appendices
A, B and C for math refreshers, formulas, and constants. Appendix C is particularly useful on
how to convert from one set of units to another set of units. For example, for a quantitative
question, you must get all parameters in the same set of units. One option is to have distances in
centimeters (cm), mass in grams (g), and time in seconds (s) —called CGS units. The so-called
English units of feet, pounds and seconds are rarely used in science courses in the USA or
elsewhere.
In our textbook, most often the system of units used is meters (m) for distances, with masses in
kilograms (kg), and time in seconds (s) — called MKS units. See Appendix C.3 for
conversion of units and C.4 for a full discussion of MKS units. Astronomers also use Light
years (Ly) and the Astronomical Unit (AU) for distances. These are the distance light travels in
one year, and the average distance between the Sun and the Earth, respectively. Obviously, they
can also be expressed in kilometers, as specified in various parts of the textbook. Appendix A
gives numerical values.
Appendices E and F give all needed values about planets and stars.
For computational questions, show all work, not just answer. For the discussion question, please
submit text in type, i.e., not hand-written.
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The first two questions are related to lecture material dealing with the time and space aspects of
the Universe—from every-day notions of distances (D), speeds and time to cosmic expansion.
(1) Driving Around The Solar System. (50 points, 10 points for a, b, c, d and e). Driving
in Boston is always illegal at 100 kilometers/hour (=62 miles/hour). But suppose you
could drive at that speed unaffected by gravity or by a cosmic police force.
(a) How long would it take you to drive around the Earth’s equator (yeah, there’s water,
but make believe it’s all land)?
(b) How about from the Earth to the Sun?
(c) And from the Sun to Pluto?
(d) Finally, from our Solar System to the closest star (Proxima Centauri)?
(e) Do any of these travel times exceed the age of the Earth? Express you answer in a
percent of the age of the Earth.
***Use Average values for distances, as given in Tables E.1 and E.2 and Table F1. *****
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(2) Changing the Age of Universe (20 points)
Hubble’s Law (page 613 of textbook) is V = Ho x d
where V is the velocity of separation (in km/sec) between a galaxy observed at distance d (in
Millions of light years, Mly) and our Milky Way galaxy.
The standard equation that relates distance (d), velocity (V) and time (T) is d = V x T.
The Hubble equation can be converted to this type of equation by solving for distance
d = V x (1/Ho).
Thus, (1/Ho) has the units of time—-and gives the amount of time that the Universe has been
expanding — The Age of the Universe (T). These relationships are shown in the textbook in
Math Insight Boxes 20.3 and 20.4 on pages 613 and617, respectively.
The accepted value of the Hubble Constant is 22 km/sec/Mly that leads to a specific age.
What would the age of the universe be if the Hubble Constant was 33 km/sec/Mly?
The last question is a discussion question:
(3) Cosmology and Philosophy (30 points). One hundred years ago, many scientists
believed that the universe was infinite and eternal, with no beginning and no end. When
Einstein first developed his general theory of relativity, he found that it predicted that the
universe should be either expanding or contracting, but not static. He felt so strongly in
an eternal and unchanging universe that he modified his equations to eliminate evolution.
When Hubble’s results became accept, Einstein called the “fix” of his equations “My
Greatest Blunder!”
Why do you think Einstein, as well as other scientists of his generation, assumed that the
universe had no beginning? You might want to think about the nature of evidence and
drawing conclusions from it. You might want to think about the role of authority. Or you
might want to consider philosophical impacts…or other aspects of the issue.
NOTE: We are not looking for a multi-page essay! In a concise paragraph, or at most two
short paragraphs (typed), give your thoughtful answer as “a nugget of knowledge!”
