### Astronomy 321 First Homework Assignment

1. The transit of Venus is again occurring this year (last one
occurred in the late 19th century). Using this event, it is possible
to determine the distance from the sun. This was first done by Jeremiah
Horrocks (should you need to google this).
This transit allows for the angular size of the dark spot (i.e. Venus)
to be measured in a way that is more accurate than other ways.

So, let EV be the distance between Earth and Venus and SV be the distance
between the Sun and Venus.

EV + SV = 1 (by definition).

The angular size of Venus, as seen from the Earth is dV/EV (where dV is
the physical diameter of Venus). This angular size is in units of radians.

The angular size of Venus as seen by the Sun is dV/SV.

From Kepler's third law, by measuring the orbital period of Venus we know
its distance to the sun, relative to the earth. Thus.

EV = 0.27 and SV = 0.73.

Suppose that the angular size of Venus measured during this transit is
75 arc-seconds.

Calculate the distance to the Sun by assuming that the Earth and Venus
have the same physical diameter (i.e. 12,600 km). Note the correct value
is 150 million kilometers -- you won't quite get this using the numbers
above.

2. The acceleration on a body in circular orbit is:

a = v^{2}/R
where v is the circular (orbital) velocity and R is the radius of
the orbit. From this, calculate the mass of the Sun in grams (you
should get 2 x 10^{33} grams.

3. The solar constant, the amount of energy that is received by the earth
at the top of our atmosphere is 1.4 x 10^{6} ergs cm^{-2} sec^{-1}, Calculate the total luminosity of the sun (you should get
4x10^{33} ergs/sec).

4. Calculate the energy lifetime of the Sun under the following three
scenarios:

** Chemical Energy ** Assume the sun is entirely hydrogen. Suppose
there is some weird chemical reaction occurring in this hydrogen in which
there is 1 eV (electron Volt) of energy available per atom to be released.
** Gravitational Contraction ** The total amount of energy that is
available via gravitational collapse is (we may prove this later):

GM^{2}/2R
M and R are the mass and radius of the sun.

** Nuclear Reactions ** Assume that only 10% of the sun's mass is
participating in nuclear fusion and that the efficiency per reaction is 0.007
(we will prove this later in class).

5. Using the
Parallax Simulation make an HR diagram for the two catalogs labeled
__ 30 Bright Stars __ stars and __ 20 Near Stars __. In this case, the
term brightest means the highest apparent flux, that is the stars that
appear to be the brightest in the night time sky.

Explain why these two diagrams are so different and which one of the two
samples is likely to be the most representative. Be sure you submit this
work through the publish to global view interface in the simulation.