** Purpose:**
Use the Doppler shift of a stellar spectrum to determine the velocity of the
Earth as it revolves around the sun and to determine the length of 1
Astronomical Unit (AU)

** References:** Activities
in Astronomy p. 113-117

** Procedure:** See
Activities in Astronomy p. 114-116

** Data: **In spectra a), we observe a small red shift, while spectra b) exhibits a large blue shift. This tells us that Arcturus must be moving
towards us (see Appendix A).

** **

** **

** Calculations: **To convert the above values to angstrom units, we need to determine
the dispersion. This is done using the
formula:

_{}

This gives us an Average shift in Spectrum A) of 0.205 A and an average shift in Spectrum B) of .369 A.

We
can now calculate the relative velocity between the Earth an Arcturus on both ^{st} 1939^{th} 1940

_{} , Where c is the speed
of light in Km/s.

Now, by solving the system of equations:

_{}

we can calculate the orbital velocity of the Earth. This value is approximately 5.85 Km/s. Solving this system also gives is the velocity of Arcturus with respect to the sun. Arcturus is approaching at about 20.5 Km/s.

Now, by assuming that the orbit of the Earth around the sun is circular, we can estimate it’s distance from the sun using the formula:

_{}, where P is the period of rotation in
seconds. This gives the length of
1 AU as being _{} Km.

_{}

__Results__:

** Conclusion: **The experimental uncertainty in this experiment is enormous. An acceptable error of .4 mm in the initial
calculations explodes to a final uncertainty of

The value achieved for 1 AU is within the values permitted by the experimental uncertainty. Better results could be achieved if finer techniques were used to perform the initial measurements.

__Discussion Questions__:

- In general, the Earth is approaching those stars that display a pronounced red or blue shift. Some examples include Betelgeuse shines red and Regel shines blue.

2.

- Yes, stars that are not directly approached or receded from can be used. However, the phase shifts will be less well defined and the velocity of the Earth must be altered so that only the velocity of the Earth in the direction of the star is used.

4.

5.