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\noindent {\bf PHYSICS 1020}
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{\Large \bf Homework set 1\\}

{\large 8 January 1997\\}
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\begin{description}
\item[{\bf [1.4]}]
Describe an unaided-eye observation you could make to disprove the theory that
the planets orbit Earth in a simple uniform circular motion.\\
Answer:\\
Follow the motion of a planet by recording  its position relative to the stars.
The change of direction of this motion (``retrograde motion'') would provide
evidence that the orbit is not on a circle centered on Earth. 
%Another observation would be to record the brightness.
\item[{\bf [1.6]}]
In seeking an explanation of retrograde motion, why didn't the Greeks just allow
the planets to change their speed and direction of motion as the planets moved
along circular paths around Earth, instead of resorting to circles within
circles?\\

Answer:\\
Assuming that planets simply changed their speeds and direction along a circular
path would be an ``ad hoc assumption'' to describe apparently irregular motion;
a theory based on such an assumption would have no underlying pattern, and thus
would not have any predictive power. The Greeks and scientists after them looked
for an underlying regular pattern  that would explain the apparently irregular
observed motion.

\item[{\bf [1.8]}]
Use Copernicus' theory to predict whether Mars goes through moonlike phases.
Do we ever see a ``new Mars''?\\

Answer:\\
 From Copernicus' theory (See figure 1.15), Mars  appears ``full''  when we see
all of  that side of Mars which is illuminated by the Sun. 
This happens when it is
 farthest from Earth (directly on the far side of the Sun), and also when it is
 closest to Earth. At other times, Mars will appear less than full, but there
 would never be a ``new Mars'', or even a ``crescent Mars''.
So, Mars goes through partial phases, but   does not show all the phases that 
the Moon shows.

\item[{\bf [1.11]}] Would Kepler's theory have agreed with the data available in
Ptolemy's time? In Copernicus' time?\\

Answer:\\
It was only the presision of Tycho Brahe's data on planetary motion that allowed
Kepler to realize that there was disagreement between the observations and the
positions of the planets expected from Copernicus' model. Since the observation
data available at the time of Ptolemaeus, as well as that of Copernicus were
much less precise than those available to Kepler, his theory would also have
agreed with those less precise data.
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\item[{\bf [1.23]}] Since there are some 100 billion stars in a typical galaxy
and since there are at least 100 billion galaxies in the known parts of the
universe, how many stars are there in all? Write out this number.\\

Answer:\\
One billion = $10^9$, so 100 billions = $10^9 \times 10^2 = 10^{11}$;
100 billions times 100 billions = $10^{11} \times 10^{11} = 10^{22}$,
i.e. a one followed by 22 zeroes:\\
(10 000 000 000 000 000 000 000)

\item[{\bf [1.24]}] The 1 million galaxies shown  in fig.1.29 represent only a
tiny fraction of the 100 billion galaxies in the known part of the universe. How
tiny? Write your answer as a decimal number.\\

Answer:\\
The fraction is one million divided by 100 billion =
$${10^6\over 10^{11}} = 10^{-5} = {1\over 10^5} = {1\over 100000} = 0.00001$$
 
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