Using Backyard Astronomy to Verify Kepler’s Laws

by Patrick James and Nolan Williams

Kepler’s first law implies that the Moon’s orbit is an ellipse with the Earth at one of the foci. By observing the moon over a month’s time we can plot its orbit and then use this data to analyze the shape of the orbit. We used a Vixen astronomical telescope equipped with a Meade MA 12mm illuminated reticle to observe the moon each day of its orbit to prove that the moon follows Kepler’s First Law. The location where we made measurements and observations of the moon was from a residential driveway because of the clear visibility of the night sky and the convenience of the location.

In order to gather data, we first had to locate the moon in the sky with the telescope. Once located, we used the focus of the telescope to make sure the image of the moon was clear. Then we positioned the scale of the reticle over the widest point of the moon and took the measurement of the moon’s diameter. We repeated this process two more times, thus yielding three independent measurements for each night. Next, we averaged the three in order to give a more accurate measurement for the night.

On the first night of making observations, the moon was at apogee and was in the western sky. Using the reticle, we measured its apparent diameter to be about 51 mm. Over the next several days, the moon’s diameter increased slowly from about 51mm to 53mm. The moon’s orientation in the night sky changed from the West to the South. After a week of being unable to take measurements during spring break, we found the moon’s diameter had increased from 53mm to 58mm. The moon was still in the southern sky at night, but a few days later it was only visible in the morning.

On April 4, 2012, the moon reached perigee. and its diameter was about 59mm and it was sitting in the southwestern sky. After another few days, the moon’s diameter slowly decreased from 59mm to 57mm. Unfortunately, there was a period of time where the moon wasn’t visible due to the weather; however, this did not skew the data. On the last day of observations (April 25, 2012), the moon was at apogee and its diameter was once again 51mm, but was in the eastern sky instead of the western sky.

From the observations, we could see that the moon’s apparent diameter changed from a minimum of 51mm to a maximum of 59mm (and then back to 51mm). We plugged the data into an observation spreadsheet, which would take the diameter measured on the reticle and convert it to the actual diameter of the moon based on the focal length of the telescope. The spreadsheet then converted the diameter into the position coordinates of the moon and then graphed these coordinates. This gave us a plot of the orbit of the moon. I was then able to fit an ellipse to the plot of orbit of the moon and show that the orbit is elliptical.

After a month of observing, we were able to successfully prove Kepler’s First Law. The best fit line to the plot of the orbit was an ellipse, thus showing that planetary orbits are not circular, but elliptical as Johannes Kepler stated hundreds of years ago (amazing!). Although we were successful in our task, there are various possible sources of error. One of the sources of error could be human error. The measurements we took were all taken by looking at a scale imposed on the moon by very inexperienced observers. This could have resulted in some inaccurate measurements, but by using multiple measurements by multiple people each night, this error was hopefully reduced. Also, there were several days throughout the month where it was impossible to collect data due to bad weather. This could have affected the plot of the orbit; however, because we only missed a few days of observing, we can assume the error to be negligible. Overall, this was an awesome experience, it was amazing to be able to analyze and observe such huge objects and forces in motion!

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