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Harvard University

Astronomy Lab and Clay Telescope

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The Measurement of the Astronomical Unit

The goal of this lab is to determine the distance between the Earth and the Sun, referred to as the Astronomical Unit (AU), using a basic understanding of geometry and tools available in the lab. The significance of this measurement cannot be overstated: the AU is the basis of the distance ladder. An incorrect value of the AU would yield errors in parallax measurements to nearby stars and thereby errors in all subsequent distance measurements. Using Kepler's 3rd Law and observations of the sidereal period of the planets in our solar system, astronomers were able to create a scaled model of the solar system in units of the AU. Errors in the AU would thus also result in an under/over-estimation of the size of our local neighborhood. In this lab, you will use the size of the Doppler shift due to the Sun's rotation to determine the rotational speed, and then, using the rotation period and the angular size of the Sun, determine the value of the AU.

There are three steps :

Step 1: Determine the Angular Size of the Sun

The sun appears to move all the way around the Earth (360 degrees) in 24 hours. If we measure how long (minutes and seconds) the Sun takes to move its own diameter along the sundial in our lab, we can measure its angular diameter, in degrees.

In the lab you will see a lens attached to the window. The lens is used to focus the Sun's light and make a sharper image on the easel. This is our "sundial".

Analysis:

Step 2: Determine the Rotational Speed of the Sun

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 a Telluric absorption line, which arises from H2O in the Earth's atmosphere. Because we do not know the orientation of the solar equator, we will take 8 meaurements around the edge in pairs (left, right; top, bottom; top right, bottom left; top left, bottom right).

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.

Step 3: Determine the Rotational Period of the Sun

The motion of the Sun in the sky tells us something about the rotation of the Earth, and the Earth's orbit around the Sun. An important motion of the Sun itself is its rotation about its own axis. This can be measured by using sunspots as tracers of that rotation, as Galileo first did in 1612.

Why is rotation period important? For one thing, it is believed that the solar rotation ultimately causes the creation of sunspots themselves. Other stars (with similar, or cooler, temperature) that rotate more rapidly than the Sun can have more and bigger spots. A primary goal for this section is to determine the period of rotation of the Sun - that is, how many days it takes to rotate once around its own axis.

If we take data over a period of a few days to a few weeks, we can determine how much the sunspots move and determine its apparent motion across the face of the Sun. If we make the assumption that the spots are carried across the Sun by rotation, we can then infer the period with which the Sun rotates.

Analysis:

 

 

Final calculations/results: