Orbital velocity of the earth using stellar spectra
In this exercise you will find the orbital velocity of the Earth by measuring the Doppler shift in
the spectrum of the star Arcturus. Among the very brightest of stars, shining with a soft orange
light, Arcturus lights northern spring skies. While orbiting the Sun, the Earth moves towards the
Arcturus half of its orbital period and it moves away from the star rest of the period as shown in
figure. When the Earth is moving towards and away from the star, the observed light is
respectively blue-shifted and red-shifted
Earth moving away
Arcturus
Earth moving towards
The photocopied figure (taken from SKY AND TELESCOPE) below displays two spectrograms
of the star Arcturus taken six months apart. The top and the bottom spectrograms are of a
reference light source at rest with respect to the telescope. Corresponding to each of the reference
lines is a dark line in the star spectrum, displaced slightly to the right (red-shifted) in , and to
the left (blue-shifted) in
Select line 1 and measure the displacement of it in and to tength of millimeters. One way to
do it is to use a straight edge to connect matching reference lines as shown in the figure on the
lower right corner on the next page. The shift are shown by filled rectagles (red in a and blue in
b) in the figure.Measure the shifts with a scale estimating to tength a tength of millimeter. A
magnifying glass would be handy. Try to be as accurate as possible. The measurements give the
shift Al in mm for the line. Draw a table similar to one shown below and note down the
measurements. Repeat the process for lines 1, 3, 5, and 7 and enter into the table.
line original shift A?» shift AX _ A_/1
110 WaVe1ength spectrum spectrum spectrum spectrum 10
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