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
2. The acceleration on a body in circular orbit is:
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 1033 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 106 ergs cm-2 sec-1, Calculate the total luminosity of the sun (you should get 4x1033 ergs/sec).
4. Calculate the energy lifetime of the Sun under the following three scenarios:
Gravitational Contraction The total amount of energy that is available via gravitational collapse is (we may prove this later):
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.