## Problem Set

# Epic Eclipse: A 'Pi in the Sky' Math Challenge

*This activity is related to a Teachable Moment from Aug. 10, 2017. See "Get Students Excited About Science With This Month’s Total Solar Eclipse."*

### 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 set, students use the mathematical constant pi to measure the approximate size of the shadow that will fall on Earth during a total solar eclipse.

### Materials

### Background

In 2017, a unique astronomical event will come to the United States for the first time in nearly 40 years! On August 21, a total solar eclipse will be visible in the continental United States. Starting in Oregon, the shadow of the moon will cross the country at more than 1,000 miles per hour, making its way to the Atlantic Ocean off the coast of South Carolina. Everyone inside the moon’s shadow will witness one of the most impressive sights nature has to offer.

So how big is the shadow? Students can use pi to find out.

### Procedures

When sunlight hits the moon (which has a radius of 1,738 km), a cone-shaped shadow is created. During the total solar eclipse on August 21, 2017, the distance from the center of the Moon to the center of Earth (which has a radius of 6,378 km) will be 372,027 km. On that day, if the Moon’s shadow were not intersected by the surface of Earth, it would extend 377,700 km from the Moon to its vertex. Viewers on Earth who want to witness the eclipse will have to be at a location inside this shadow as it passes over Earth to see the eclipse at totality. What is the approximate surface area of Earth that will be covered by the disc of the Moon’s shadow at any one time during the eclipse?

### Assessment

### Extensions

Pi Day Challenges- Pi in the Sky
- Pi in the Sky 2
- Pi in the Sky 3
- Pi in the Sky 4
- Pi in the Sky Challenge (slideshow for students)

Multimedia

Websites