Measuring the Distance from The Earth to The Sun
Introduction
Methods
Angular Diameter:
A heliostat was used to measure how long it takes for the sun to move a length of its own diameter. A heliostat is a series of mirrors that reflects the light of the sun into the lab classroom and onto a table (Figure 2). Once lined up with the sun, tracking can be used so that the heliostat follows the sun, or it can be turned off so that it remains stationary. With the sun's light projected on the table we can measure how long it takes with the time recorded as shown in Figure 3. To take these measurements, the outline of the sun's reflection is sketched onto paper so it is clear when the sun has travelled the length of its diameter, so we know when to start and stop the time (Figure 4). This experiment was repeated for a total of three trials and the average of the trials was calculated. These results are summarized in Table 1.Figure 2: The heliostat uses mirrors to project the light from the sun inside the classroom [1].
Rotational Period:
The sunspots can be measured by reflecting the light from the sun into the classroom using the heliostat. The sunspots are visible from the reflection so they can be marked on a sheet of paper and observed over the course of a few hours/days. This was not possible for our lab group because there were too many clouds so the heliostat could not be used consistently enough to measure the path of the sunspots. Therefore, we used archived data (Figure 10) [5]. We measured the time it took for a certain sunspot to move across the sun by overlaying a grid that helped us measure the movement (Figure 11). We repeated this experiment for a total of three trials. Knowing how far the sunspots move over a certain amount of time, we can determine how long it would take for the sunspots to move 360 degrees which is the period of rotation (Table 2a and Table 2b).
Figure 10: Sunspots move across the sun overtime (Archived data [5]).
Analysis
The useful values that we have found so far are:
Acknowledgements
I would like to thank Allyson Bieryla for instructing my groups first two lab classes when we measured angular diameter and used the heliostat and spectrograph. I would like to thank Jea Adams for instructing our last lab class where we completed the rotational velocity python calculations. I would like to thank my fellow lab members including Callie Garcia, Larom Segev, Max Christopher, Mekhi Moore, Nyle Garg, Owen Bae, and Tovi Sonnenberg for participating in lab class with me.
Sources
[1] Gupta, S.: Sky is the limit, https://news.harvard.edu/gazette/story/2016/07/sky-is-the-limit/.
[2] LESIA, P.O.-: Solar spectrum, http://bass2000.obspm.fr/solar_spect.php.
[3] Doppler effect, https://www.britannica.com/science/Doppler-effect.
[4] Harvard University, https://astrolab.fas.harvard.edu/AU_Ay16.html.
[5] Solar and heliospheric observatory homepage, https://soho.nascom.nasa.gov/home.html.
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