The 2024 total solar eclipse news cycle has come and gone since April 8th, but I wanted to share my experience viewing the total eclipse from Dallas, TX last month. I went to a local park (on my cousin Josily’s recommendation) in Dallas with my mom, my cousin, her husband, and their 3 year old son, and set up at a picnic table, eclipse glasses and cameras in hand. The day started out partly cloudy and so we were concerned that the eclipse wouldn’t be completely visible given the weather. However, miraculously, the sky cleared up just in time for the total solar eclipse at 1:42 pm.
The total solar eclipse itself was not as dark as I had imagined it would be. It felt like twilight or early evening and nothing at all like night. For an observer using solar eclipse glasses, the eclipse looks more like a bright ring of light surrounding the lunar orb and nothing like the professional high-resolution astrophotography images that have been widely distributed last month showing a wispy solar corona surrounding the moon. I hadn’t brought a light meter with me at the time, but I wanted to find out how dark the solar eclipse was for a location in the path of totality based on actual measurements. One way to do this is to look at data from solar power generation output from a region that had experienced the solar eclipse.
At one of the locations in the path of the totality this year, near St. Louis, Missouri, the Midcontinent Independent System Operator (also known as MISO) which runs the electric high-voltage transmission system in the Midwest U.S. and Manitoba, Canada and parts of the U.S. south, tabulated the metered solar generation output on its system to publish a blog post on April 16th showing that its total system solar PV generation output dropped to about 8% of the typical solar generation maximum output during the total solar eclipse. In addition, MISO found that wind generation dropped 35% over the course of 90 minutes during the total eclipse, while electric demand dropped only slightly by 3.5% and the grid was stable throughout the solar eclipse even with MISO’s 12.4%+ solar, wind, and battery generation mix.
It is also possible to calculate the theoretical solar output drop at a particular location in the path of the total solar eclipse just using trigonometry and the relative apparent size of the moon and sun in the sky. (You can also apply concepts from Einstein’s general theory of relativity to this case, but it doesn’t change the answer very much). Given the relative distances of the sun, moon, and earth, the angular distance of the moon (or sun) in the sky is:
Theta (moon) = distance_moon-earth/diameter_moon * 206264.5 arcsec/rad = 1864 arcsec
Theta (sun) = distance_sun-earth/diameter_sun * 206264.5 arcsec/rad = 1907 arcsec
In addition, if light from the sun bent around the gravitational well of the moon, as predicted by both its wave and particle characteristics from Einstein’s general theory of relativity (see NASA’s calculation for starlight deflection around the sun), the light from the sun (or any star source) would be deflected by the moon’s gravitational well according to the following formula:
Theta = 4GM / (c^2 * R)
Where G is the gravitational constant, M is the mass of the moon, c is the speed of light, and R is the radius of the moon.
In order to calculate the deflection of light around the moon from far away sources (including the sun and stars), imagine that the sun was slightly smaller and exactly equal to the moon in its apparent size (in arcsecs) from Earth. This would be at 97.7% of the sun’s actual size. Since the sun is a sphere (or a circle in two dimensions), the light reduction would be squared or 95.45% of full-sun insolation. Any part of the sun that is less than the moon’s apparent radius in Earth’s sky would be completely blocked by the moon, except for a portion that is deflected by the moon’s gravitational well. Using the equation above, the sunlight deflected by 0.026 arcseconds by the moon’s gravitational well on each side or 0.053 arcsecs in total, compared to the moon’s apparent size of 1864 arcsecs. This deflection, measured in arcsecs should be added to the portion of the sun (also measured in arcsecs) that is uncovered by the moon during the total eclipse.
So according to the model above, total solar output during the solar eclipse should drop to 4.527% (or 4.597% accounting for general relativity) of maximum solar PV generation output. However, MISO saw that solar output dropped less than expected to ~8.0% of maximum solar output. The difference could also due to physics factors I have not included (e.g. small changes in the earth-moon-sun orbit, light from other stars, nighttime city lights) or system-related measurement errors (e.g. perhaps batteries had discharged during the total solar eclipse). Thus, a high-precision light meter or an application of Einstein’s theory of the photoelectric effect, the solar photovoltaic panel, could itself be used in a system to verify Einstein’s general theory of relativity.