The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the 10th set, students use pi to figure out how much of the Sun’s disk will be covered by the Moon during an eclipse and whether it’s a total or annular eclipse.
On Oct. 14, 2023, a solar eclipse will be visible across North and South America, as the Moon passes between Earth and the Sun, blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. Depending on those distances, the Sun's disk area might be fully or only partially blocked during a solar eclipse. In Eclipsing Enigma, students get a sneak peek at what to expect in October by using pi to determine how much of the Sun’s disk will be eclipsed by the Moon and whether to expect a total or annular eclipse.
A solar eclipse occurs when the Moon passes between Earth and the Sun, fully or partially blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. During a total eclipse, the distances are such that the Moon covers all of the Sun's disk area. When the Moon is farther from Earth during an eclipse, it leaves a glowing ring of sunlight shining around the Moon, resulting in an annular eclipse.
On Oct. 14, 2023, a solar eclipse will be visible across North and South America. The Sun, with a radius of 695,700 km, will be 148,523,036 km from Earth. The Moon, with a radius of 1,737 km, will be 388,901 km from Earth.
What percentage of the Sun’s disk area will be obscured by the Moon?
Will the eclipse be an annular eclipse or total eclipse?
Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
NASA Pi Day Challenge
In this challenge, students can use pi to solve some of the same problems faced by NASA scientists and engineers.
Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos with NASA.
National Council of Teachers of Mathematics: Notice and Wonder
Creative brainstorming through noticing and wondering encourages student participation, engagement, and students' understanding of the NASA Pi Day Challenge.
Blogs and Features
How Many Decimals of Pi Do We Really Need?
While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.
Slideshow: 18 Ways NASA Uses Pi
Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
Related Lessons for Educators
Modeling an Asteroid
Lead a discussion about asteroids and their physical properties, then have students mold their own asteroids out of clay.
Time 30 min to 1 hour
Math Rocks: A Lesson in Asteroid Dynamics
Students use math to investigate a real-life asteroid impact.
Time 30 min to 1 hour
Related Activities for Students
What's That Space Rock?
Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.
Infographic: Planet Pi
This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.
Recursos en español
18 Maneras en Que la NASA Usa Pi
Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.