Abstract

Solar energy is the primary source of energy used to warm our planet. As changes occur in the amount of sunlight we get, there are also changes in the air temperature, clouds, and wind (University of California Museum of Paleotology, 2024). A total solar eclipse occurs when the Moon blocks the Sun completely, such as occurred on April 8, 2024, in North America. This created a teachable moment where science teachers could use pi(E) (with “E” referring to energy) to look at lower temperatures as the Moon blocked energy from the Sun. With the aid of NASA scientists and the ARISA Lab Eclipse Soundscape team, research was conducted in Jersey City, New Jersey which experienced 90.02% eclipse cover at 3:25 pm. For this research study, we investigated the changes in air temperature, surface temperature, and cloud cover during the solar eclipse. Results indicated that the temperature decreased significantly; the air temperature changed by 7.6^oC and the surface temperature changed by 4.9^oC.   

1. Background

On Monday, April 8th, 2024, millions of people in North America were unified as they witnessed a rare celestial event—the Great North American Eclipse! This event was the inspiration for this paper. An estimated 31.6 million were living in the path of the eclipse. Also of note, 2024 was “The Year of Heliophysics,” during which the Sun was at its most active point in the 11-year Solar cycle. Coincidently, the eclipse also coincided with the arrival of comet 12P/Pons-Brooks, which was near the Sun on the sky and so bright that some people could see it during Totality. With all this going on, we asked the research question: How does air temperature change compare to surface temperature change during the April 8th, 2024 Total Solar Eclipse as seen in Jersey City? The hypothesis was: as the Sun gets blocked by the Moon, the air temperature will drop by 1.5^oC, whereas the surface temperature will drop by 1^oC.

2. Totality

 First, let’s explore what the term “totality” means in the context of a solar eclipse. According to NASA (2024), totality is when the Moon moves between the Earth and the Sun and has just the right geometry and distance from the Earth to block the disk of the Sun entirely. Anyone located within the 122-mile-wide path of this complete blocking of the Sun on April 8th, 2024 was in the “Path of Totality” that is the Moon’s shadow touching the Earth. Observers near the center of that “Path” saw the Moon completely block the Sun for the longest duration — four minutes! However, everyone in the continental United States saw the Sun blocked by the Moon to some degree.

3. Research Methods

Eclipse Data for a total solar eclipse on April 8th, 2024 in Jersey City, New Jersey, was recorded in Liberty State Park, located near downtown Jersey City. The air temperature was recorded using an alcohol thermometer from Flinn Scientific and the surface temperature was recorded using a TS-FT0423 Wireless Thermo-Hygrometer purchased from Amazon. Cloud coverage was observed in person. The air thermometer was set up on a park bench using a ring stand and the digital surface thermometer was placed on the ground next to the bench. Almost simultaneously, the surface and air temperatures were recorded using the NASA Globe app that was installed on an Android cell phone days prior to the eclipse. Measurements began at 1:25 pm and ended at 5:25 pm. The same data were recorded by hand on paper. From 1:25 pm to 2:55 pm, data was recorded every ten minutes. During this timeframe, some of the birds, like a flock of geese, began running towards the river and leaving the area. From 2:55 pm to 3:55 pm data was recorded every five minutes, with a maximum eclipse at 3:25 pm with 90% coverage. At this point, it was very cold and windy outside with a partly cloudy and overcast sky. Temperature readings were at 11.9 ^oC for the air temperature and the surface temperature was recorded at 15.8 ^oC. Additionally, one could see Jersey City’s partial total eclipse with solar glasses. Photos were taken using a cell phone filter and solar app. From 3:55 pm to 5:25 pm, readings and recordings continued to be documented every ten minutes again until the last recordings. Furthermore, it was observed that in this time range, the air temperature began to cool much more rapidly as compared to the surface temperature, which is reflected in Figure 1.

4. Pi and Its Use in High School Mathematics

Now, onto pi. Pi is a mathematical constant that is often used in K-12 classrooms around the world, but just what is its definition? Pi is approximately equal to 3.14159265359 and is defined as the ratio of the circumference of a circle to its diameter.  Its use in mathematics and construction dates back to 2000 B.C. (with some references stating 4000 B.C.), when the Babylonians used it to calculate the perimeter of a hexagon. In modern times, pi has been very useful with applications in geometry, trigonometry, calculus, physics, and engineering, whereas in the latter two fields, the pi constant is used to study ellipses, circles, motion, and other physics concepts. In middle and high school geometry classes, pi is heavily used in mathematics curricula.

The Connection Between Pi and Solar Eclipses

 So, how can one use 𝜋 to study the eclipse? Teachers can assist students with measuring the approximate size of the Moon’s shadow on Earth as the Moon passes between the Earth and the Sun during a total solar eclipse. First, students must calculate the length of the portion of the Moon’s shadow that is blocked by Earth. Next, students must use that calculation and apply to the properties of similar triangle ratios to solve for r, the radius for the shadow on Earth (NASA, 2017). Finally, students must find the area of the Moon’s shadow by using the shadow’s radius calculated in step three. To see the full instructional lesson, along with materials go to: https://www.jpl.nasa.gov/edu/teach/activity/epic-eclipse-a-pi-in-the-sky-challenge/.

5. Results and Future Research

 The results for eclipse data collected in Jersey City, New Jersey are as follows.

The maximum and minimum temperatures for air temperature were 19.5± 0.5^oC and 11.9± 0.5^oC for a range of 7.6^oC. Maximum and minimum temperatures for surface temperature were 19.8±0.5^oC and 14.9±0.5^oC for a range of 4.9^oC. Air and surface temperatures began to decrease at 2:10 pm, which was 35 minutes after the eclipse began. Air and surface temperature continued to decrease until 3:25 pm, which was 35 minutes after the eclipse max. 

 In conclusion, although there will be solar eclipses around the globe for years to come, this will be the last total solar eclipse for the North American region for the next 20 years. Therefore, in terms of seizing this “teachable moment” in United States history, math, and science teachers could use pi(E) (with “E” referring to energy) to teach about how the orbit of the Moon will cause it to move directly between the Sun and the Earth creating a total eclipse which decreases the energy received by the Earth from the Sun, thus lowering temperatures. In turn, 𝜋 can be used to measure the size of the shadow created by the Moon. Moreover, in terms of innovative, pedagogical didactics in middle and high school classrooms, incorporating the math constant 𝜋 to study the eclipse on April 8th, 2024, and other future eclipses, is a unique way to apply math in a real-world, authentic context, with possibilities for use in another school Pi day activity on 3-14! Empirical studies for the next solar eclipse would involve the following research questions:

1. How does cloud type change as a solar eclipse occurs?

2. By how much does the percent cloud coverage change?