Physics 310 – Cosmology
Homework Set E
1. The table at right shows those spectral lines of hydrogen that are in the range 400-700
nm (left column) and the observed spectral lines of a distant star (right column).
a) One possibility is that the first observed spectral
Reference
Observed
line is a blue-shifted version of the first reference
656.28
nm
526.58
nm
line. If this were the case, then other lines on the
486.13 nm 470.16 nm
right would have the same ratio 0/. Convince
434.05 nm 444.30 nm
yourself that that this is not the case, in other
410.17 nm 430.04 nm
words, the other spectral lines don’t match up.
421.27 nm
b) Another possibility is that the first observed
415.45 nm
spectral line is a red-shifted version of the second
reference line. If this is the case, then other lines on the right would have the
same ratio 0/. Convince yourself that that this is the case, in other words, the
other spectral lines do match up.
c) Find the red-shift z and the velocity vr of the star.
2. In this problem you will attempt to predict the average temperature of the Earth, in
Kelvin. This will involve several unrealistic assumptions.
a) What is the brightness of the Sun at the Earth, in terms of the distance d and the
Sun’s luminosity L ?
b) The Earth’s cross-sectional area, the area that absorbs sunlight, is the area of a
circle (not a sphere) of radius R . Find a formula for the total power absorbed by
the Earth, assuming the Earth is perfectly black (all light that hits it is absorbed).
c) Assume the Earth is a perfect black body radiating at temperature T . It emits
light from its full surface area (the surface of a sphere). Assuming the power
absorbed equals the power emitted, find a formula for the temperature T . The
radius of the Earth should cancel out.
d) Substitute the actual value of the solar luminosity L and the distance d and
estimate the temperature of the Earth. It should be the correct order of magnitude
(but not exactly right).