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 11th set, students use pi to calculate the position of Earth in its orbit as a signal is sent from a spacecraft in deep space.

Background

This animation shows how DSOC's laser signals are sent between the Psyche spacecraft and ground stations on Earth - first as a pointing reference to ensure accurate aiming of the narrow laser signal and then as a data transmission to the receiving station. Credit: NASA/JPL-Caltech/ASU| Watch on YouTube

In December 2023, NASA tested a new way to communicate with distant spacecraft using technology called Deep Space Optical Communications, or DSOC. From 19,000,000 miles (30,199,000 km) away, the Psyche spacecraft beamed a high-definition video encoded in a near-infrared laser to Earth. The video, showing a cat named Taters chasing a laser, traveled at the speed of light, where it was received at Caltech’s Palomar Observatory. Because of the great distance the laser had to travel, the team needed to aim the transmission at where Earth would be when the signal arrived. In Receiver Riddle, use pi to determine where along Earth's orbit the team needed to aim the laser so that it could be received at the Observatory at the correct moment.

Procedures

In December 2023, NASA transmitted the first ultra-high-definition video from deep space using new technology known as Deep Space Optical Communications, or DSOC. DSOC uses an infrared laser to transmit data at a much higher rate than current radio transmitters. The 15-second video, featuring a cat chasing a laser, was beamed to Earth from the Psyche spacecraft at a rate faster than many terrestrial internet connections.

DSOC’s transmission had to travel 30,199,000 km to reach Earth. Even traveling at the speed of light, that takes a long time! And all that time, Earth was still moving along its orbit. That meant that the team needed to aim the laser transmission at where Earth would be when the signal arrived.

Given this, how many kilometers ahead along Earth’s orbit did the team need to aim the laser?

Image credit: NASA/JPL-Caltech | + Expand image

Assessment

Image credit: NASA/JPL-Caltech | + Expand image

Extensions

Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge