Problem Set

Eclipsing Enigma: A ‘Pi in the Sky’ Math Challenge

Overview

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.

Materials

Pi in the Sky 10: Eclipsing Enigma worksheet – download PDF (for best results, download and print from Adobe Reader)

Pi in the Sky 10: Eclipsing Enigma answer key – download PDF (also available as a text-only doc)

Background

A composite of four images of the sun, each being covered by progressively more of the sun. The final image shows the sun eclipsed by the moon with a ring of light showing behind the moon that is too small to cover the entire disk of the sun.

This image sequence shows an annular solar eclipse from May 2012. The bottom right frame illustrates the distinctive ring, or "annulus," of such eclipses. A similar eclipse will be visible from North and South America on Oct. 14, 2023. Credits: Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons | + Expand image

Eclipsing Enigma

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.

Teachable Moments: 10 Years of NASA's Pi Day Challenge

Learn more about pi, the history of Pi Day, and the science behind the 2023 NASA Pi Day Challenge.

Procedures

Eclipsing Enigma

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?

› Learn more about the 2023 solar eclipse