Harvard University Astronomy Lab and Clay Telescope

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The Measurement of the Astronomical Unit

From your own spectral measurements of the Sun's rotation velocity (which we will do in this lab), the period of the Sun's rotation, and the measurement of the Sun's angular diameter, you will be able to measure the Astronomical Unit (AU). This is not an easy measurement in Astronomy but one that can be done from our lab in Cambridge, MA.

The Doppler Shift of the NaD lines

The doppler shift allows us to measure radial velocity. We will make several spectral measures of the NaD lines (at 5889 and 5896 Angstroms) from the East limb of the Sun and then the West limb of the Sun. Then with the CCD (and attached microscope lens) we take careful measurements of the Doppler shifts of these two lines relative to that of an absorption line in between them, which arises from H₂O in the Earth's atmosphere.

Procedure:

• The first step is to carefully align the CCD with the NaD lines. This is a slightly tedious process and your TF will show you the tricks to aligning it painlessly!
  • First, align the CCD with the Sodium lamp. This will give you a chance to adjust the slit width to get the sharpest lines possible without compromising brightness. You will need to take a series of short exposures until you get a non-saturated, sharp image. If you need help refer to the MaximDL help on taking images.
  • When you have everything aligned, remove the lamp and now allow sunlight to shine on the slit! Take a test image to ensure that the table has not been bumped and that you have the right exposure time and slit width. This may need to be adjusted for the Sun's spectrum.
• OK the hard part is over; everything is aligned so don't bump the CCD or lab bench!
  • We don't know the exact orientation of the equator of the Sun since the Sun's rotation axis is tilted due to the Earth's axis tilt and the solar image is "reversed" after it bounces off the mirrors and enters the spectrograph slit so we will take images at 8 locations of the Sun's limb (top, bottom, left, right, top right, top left, bottom right, bottom left). The two (opposite) locations which give the NaD line measurement with the biggest shift will be closest to defining the equator of the Sun!
  • Take 2 spectra (i.e. record the CCD images) at each of the 8 locations on the limb. Take the images in pairs - i.e. N-S (2 exposures for each N and S) and then E-W, etc. Reference the online Solar spectrum and compare with the solar atlas to ensure that you include an H₂O line in your images!! Record the exposure time and image name in table 2 (pdf or docx).

Analysis:

We need to derive the most accurate possible minimum positions of the NaD lines vs. the H₂O telluric line in order to measure what will be a small Doppler shift.

• Open your images (spectra) in MaximDL.
  • Open a line information box and draw a horizontal box (~ 10pixels wide) across the middle of your spectrum. It is VERY important that you start your box from the very left edge of the image and that it spans the entire width of the image. Pull the box from top-left to bottom-right. The data exported will be pixel number (starting with pixel 1 no matter where your box starts) and number of counts/pixel.
  • Click export and save your file accordingly.
  • Do this for all of your spectra.
• You will now have 8 Excel data sheets. Your TF will guide you through entering this data into the Doppler Shift template. There are also instructions on the template to help you as well.
• Once you enter all your data in the template you should have all the information needed to determine a value for the rotational velocity of the Sun. Step through the in calculations in table 3 (pdf or docx) and solve for the AU following the steps on the table!