Problem Set
Receiver Riddle: 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 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.
Materials
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
Receiver Riddle
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
Receiver Riddle
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?
› Learn more about Deep Space Optical Communications
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
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Pi in the Sky Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 4-12
Time Varies
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NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy collection for students.
Grades 4-12
Time Varies
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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.
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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.
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10 Ways to Celebrate Pi Day With NASA on March 14
Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.
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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.
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Downloads
Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:
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