Problem Set
Signal Solution: 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 eighth set, students use the mathematical constant pi to compare the signal strength between traditional radio wave communication and the Deep Space Optical Communication system.
Materials
Background
NASA uses radio signals to communicate with spacecraft across the solar system and in interstellar space. As more and more data flows between Earth and these distant spacecraft, NASA needs new technologies to improve how quickly data can be received. One such technology in development is Deep Space Optical Communications, which will use nearinfrared light instead of radio waves to transmit data. Nearinfrared light, with its higher frequency than radio waves, allows for more data to be transmitted per second. In Signal Solution, students can compare the efficiency of optical communication with radio communication, using pi to crunch the numbers.
Procedures
As more and more data are collected and transmitted through space, NASA needs new technologies to communicate faster and more efficiently with its spacecraft. One such technology is called Deep Space Optical Communications, or DSOC, which uses nearinfrared light instead of radio waves to transmit a signal. This allows us to use a higher frequency (shorter wavelength), so more data can be transmitted per second.
The twin Voyager spacecraft launched in 1977 use a 12.5 Watt transmitter paired with a parabolic reflector that creates a circular radio signal with a diameter roughly 0.5 degrees wide. A DSOC system would use a 4 Watt transmitter on a flight laser transceiver, producing a light signal with a diameter of 0.0009 degrees.
If Voyager and a DSOCequipped spacecraft were both placed 124 AU from Earth (1 AU = 150,000,000 km) what fraction of each original wattage would be received by a 70m antenna back on Earth?
By what factor is DSOC more effective?
Assessment
Extensions
Pi Day Resources

Pi in the Sky Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 412
Time Varies

NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 412
Time Varies

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.

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.

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.

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.

Mobile & Web Backgrounds
Can't get enough pi? Download this year's NASA Pi Day Challenge graphics as mobile phone and web meeting backgrounds:

Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.
Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.
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