Problem Set
Icy Intel: 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 set, students use the mathematical constant pi and data from NASA scientists to determine if a laser can explode an ice sample for analysis. The answer will be revealed on March 15!Materials
Background
Scientists studying ices found in space, such as comets, want to understand what they’re made of and how they interact and react with the environment around them. To see what molecules may form in space when a comet comes into contact with solar wind or sunlight, scientists place an ice sample in a vacuum and then expose it to electrons or ultraviolet photons. Scientists have analyzed samples in the lab and detected molecules that were later observed in space on comet 67P/ChuryumovGerasimenko. To analyze the lab samples, an infrared laser is aimed at the ice, causing it to explode. But the ice will explode only if the laser is powerful enough. Scientist use pi to figure out how strong the laser needs to be to explode the sample – and students can do the same when they solve the Icy Intel challenge.
Procedures
Icy Intel
Scientists at JPL study ices found in space to understand what they’re made of and how chemical processes unfold in cold environments. To find out what molecules are produced when sunlight or solar wind hits a comet, scientists place a piece of simulated comet ice in a vacuum to expose it to conditions that exist in space. Then, they aim an infrared laser at the sample to produce a plume that can be analyzed. Scientists have found that when simple molecules are exposed to light or electrons, they can transform into more complex molecules – even ones considered key to life’s formation!
Scientists need to know how much energy is hitting the sample in a given area. This is called “fluence.” Enough of it will explode the ice so the sample can be analyzed. Peak fluence is found by dividing the laser’s total optical pulse energy by πw^{2}/2, where w is the radius of the beam. Using a beam that has a radius of 125.0 µm and a total optical pulse energy of 0.30 mJ, what is the laser’s peak fluence in J/cm^{2}?
If the optics used to aim and focus the laser reduce its energy by 27% before it hits the sample, will this beam be sufficient to examine a sample that needs a peak fluence of 1.0 J/cm^{2} to explode?
Assessment
Extensions
Participate

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

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

Pi Day: What’s Going ’Round
Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
Blogs and Features

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.

Slideshow: 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.
Related Activities

Create a Comet with Dry Ice
Build an icy model of a comet out of dry ice  complete with shooting jets!  as a demonstration for students.
Grades 25
Time < 30 mins

Comet on a Stick
Students build their own comet models using craft materials.
Grades 28
Time 30 mins  1 hr
Multimedia

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.

Game: Comet Quest  NASA SpacePlace
Control a spacecraft and use it to explore an icy comet!