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Lab 5 Exercise #19
Evidence of the Earth’s
Revolution
Evidence of the Earth’s Revolution
In Lab 4 Exercise 20, you used the Doppler
effect to calculate the rotational period of the
Sun.
The Doppler effect also occurs when the Earth
approaches a light source (blueshifting) or
recedes from it (redshifting).
At one point during the course of a year, the
Earth approaches the star, Arcturus.
Six months later, the Earth is receding from it.
Evidence of the Earth’s Revolution
You will use the
spectrum of light
received from
Arcturus and the
Doppler effect to
provide evidence
of the Earth’s
revolution
around the Sun.
Evidence of the Earth’s Revolution
On July 1, 1939 and January 19, 1940 the
light from Arcturus was analyzed with a
spectroscope.
The spectra are shown in Figure 19-2,
columns a and b.
Column a shows light received from
Arcturus as Earth receded from it.
Evidence of the Earth’s Revolution
You’ll notice in column a that there are a
few dark lines.
These dark lines are absorption lines
caused by the light passing through the
iron in Arcturus’s atmosphere.
Above column a and below column b
you’ll notice a few bright emission lines.
Evidence of the Earth’s Revolution
These bright emission lines are created by
heating an iron filament and allowing it to
glow.
When that light from the heated iron
filament is passed through a spectroscope
the wavelengths of light seen should
correspond to the exact same wavelengths
of light absorbed by the iron atmosphere
of Arcturus.
Evidence of the Earth’s Revolution
This means that all the emission lines
seen should line up with all the absorption
lines seen in columns a and b (since they
are the same wavelength).
With a little observation, you can see that
they don’t and the reason is that the light
in column a has been redshifted because
the Earth is receding from Arcturus.
Evidence of the Earth’s Revolution
Six months later, column b was produced
from the light from Arcturus.
Again, it can be seen that these lines don’t
line up.
This is because the Earth was
approaching Arcturus at that time.
This means the light in column b is now
blueshifted.
Evidence of the Earth’s Revolution
The amount of the shift seen columns a and b
depends on the relative velocity of the moving
Earth.
We must first quantify the amount of shift seen
in columns a and b.
Draw a straight vertical line connecting the
emission lines above column a with the iron
absorption lines seen in column a and column b
Do this for three sets of iron lines.
Evidence of the Earth’s Revolution
As these lines pass through column a and
column b, you’ll notice that they don’t pass
directly through the dark lines seen there.
Measure the distance that the drawn line
misses the dark lines seen in columns a and
b.
Measure the distance to the closest 0.1
millimeter and record your distance Δx in
table form on a sheet of loose leaf paper.
These distances represent the tilts
Evidence of the Earth’s Revolution
In order to convert your Δx’s into Δλ’s, we’ll
need to calculate a conversion factor just as
you did in Lab 4.
Using Figure 19-2, measure the distance in
millimeters between any two adjacent
emission iron lines.
Then divide the difference in the wavelengths
of the two lines (see Fig. 19-3 for these
values in Angstroms) by the distance you
measured
Evidence of the Earth’s Revolution
Repeat for two more sets of lines .
Then find the average of these three
conversion factors in angstroms/millimeter
(Å/mm).
Record your work in calculating the
conversion factor on a sheet of loose leaf
paper.
Evidence of the Earth’s Revolution
Now go back and change your measured
tilts from millimeters to Angstroms by
multiplying your tilts by the conversion
factor you just calculated.
Evidence of the Earth’s Revolution
Use the Doppler equation to solve for the
velocity of the moving Earth.
v = c  / 
where c = speed of light
= 300,000 kilometers / second
= 3 * 105 kilometers / second
 = Doppler shift in Angstroms
Evidence of the Earth’s Revolution
 = wavelength (in Angstroms from Fig. 19-3)
of the iron lines chosen when drawing your
straight line connecting the lines above column
a with the lines below column b.
You’ll need to calculate v for each of the three
iron lines.
This represents the velocity in kilometers per
second of Earth in motion around the Sun.
Evidence of the Earth’s Revolution
Since we now know the velocity, v, of the
moving Earth and…
we know the time, t, involved in one
revolution..31,557,600 seconds in one
year..
then we can use velocity =distance/time
to find the distance Earth travels around
the Sun in one year..
Evidence of the Earth’s Revolution
or rearranged, distance = velocity * time
This distance describes the length of the
(almost) circular path of the Earth around the
Sun.
Circumference of a circle is 2  R
Divide your answer by 2  to get the orbiting
radius of the Earth, R, which should equal 1
Astronomical Unit (A.U.).
The definition of 1 A.U. is in your textbook.
Evidence of the Earth’s Revolution
To get full credit for this lab, turn in all
your work in a very neat, tabulated form
including the spectra from the lab manual.
You will have to make an effort to
organize and label your information.
Please be sure to include the correct units
on all your work.
…
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