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OverviewIn the sixth installment of the "Pi in the Sky" illustrated problem set, students use the mathematical constant pi to solve real-world science and engineering problems. Students will use pi to determine the size of a Mars dust storm, estimate the water content of a rain cloud, gauge how much Jupiter's Great Red Spot has shrunk and calculate the strength of a laser used to explode ice samples.
In late spring of 2018, a dust storm began on Mars and eventually covered nearly the entire planet in a cloud of dust. Darkness fell across Mars’ surface, blocking sunlight used by the solar-powered Opportunity rover to charge its batteries. At its height, the storm covered all but the peak of Olympus Mons, the largest known volcano in the solar system. In the Deadly Dust challenge, students must use pi to calculate what percentage of the Red Planet was covered by the dust storm.
The Terra satellite uses the nine cameras on its Multi-Angle Imaging SpectroRadiometer, or MISR, instrument to provide scientists with unique views of Earth, returning data about atmospheric particles, land-surface features and clouds. Estimating the amount of water in a cloud and the potential for rainfall is serious business. Knowing how much rain may fall in a given area can help residents and first responders prepare for emergencies like flooding and mudslides. In Cloud Computing, students can use their knowledge of pi and geometric shapes to estimate the amount of water contained in a cloud.
Jupiter’s Great Red Spot, a giant storm that has been fascinating observers since the early 19th century, is shrinking. The storm has been continuously observed since the 1830s, but measurements from spacecraft like Voyager, the Hubble Space Telescope and Juno indicate the storm is getting smaller. How much smaller? In Storm Spotter, students can determine the answer to that very question faced by scientists.
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/Churyumov-Gerasimenko. 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.
In the summer of 2018, a large dust storm enshrouded Mars, blocking visibility over a large portion of the planet. The thick dust covered almost all of the Mars surface, blocking the vital sunlight that NASA’s solar-powered Opportunity rover needed to survive. In fact, the storm was so intense and lasted for so long that Opportunity, which had spent 14.5 years traveling around the Red Planet, never managed to regain consciousness and the mission had to come to an end.
During the height of the storm, only the upper caldera of one of the solar system’s largest volcanos, Olympus Mons, peeked out above the dust cloud. The diameter of Olympus Mons’ caldera is approximately 70 km.
What percent of the Mars surface was covered in dust at that time?
The MISR instrument on NASA’s Terra satellite has nine cameras that view Earth from different angles to study features on the surface and in the atmosphere in 3D. One of MISR’s tasks is to collect measurements of clouds, which are full of liquid water or ice. Scientists can use the measurements to estimate how much water is in a cloud. Imagine MISR flies over a cloud that from directly overhead looks like a circle, 10 km across. From the side, it looks like a soup can, indicating it’s roughly the shape of a right cylinder.
Given that the cloud’s top and height measure 16 km combined, calculate the approximate volume of the cloud in cubic kilometers.
Given the liquid water content of a typical puffy cumulus cloud, calculate the total amount of water in the cloud.
If all the water in the cloud fell as rain, how many Olympic size swimming pools could it fill?
Cumulus cloud liquid water content = 500,000 kg/km3
Olympic swimming pool volume = 2,500 m3
Water density = 1,000 kg/m3
Jupiter’s well known Great Red Spot is shrinking and someday may disappear entirely. Continuously observed since the 1830s, this massive storm was once more than three times the diameter of Earth.
When the twin Voyager spacecraft flew by Jupiter in 1979, they sent back images of the Great Red Spot. At that time, the storm measured 24,700 km wide by 13,300 km tall. When scientists measured the storm again in 2018, using images from the Hubble Space Telescope, their estimates were 16,500 km wide by 11,400 km tall.
Given these measurements, how does the current width of the Great Red Spot compare to the diameter of Earth?
By what percent did the area of the Great Red Spot shrink from 1979 to 2018? The formula for the area of an ellipse is πab.
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 πw2/2, 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/cm2?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/cm2 to explode?
Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Slideshow: NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Pi Day: What’s Going ’Round
Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
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.
The Sky and Dichotomous Key
Students learn about cloud types to be able to predict inclement weather. They will then identify areas in the school affected by severe weather and develop a solution to ease the impacts of rain, wind, heat or sun.
Time 30 mins - 1 hr
Precipitation Towers: Modeling Weather Data
This lesson uses stacking cubes as a way to graph precipitation data, comparing the precipitation averages and seasonal patterns for several locations.
Time 30 mins - 1 hr
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.
Time < 30 mins
Comet on a Stick
Students build their own comet models using craft materials.
Time 30 mins - 1 hr
Modeling the Water Budget
Students use a spreadsheet model to understand droughts and the movement of water in the water cycle.
Time 30 min - 1 hr
Make a Cloud Mobile - NASA SpacePlace
This mobile of feathery clouds will twist and turn in a gentle breeze. It even includes rain clouds with sparkling showers!
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!
Facts and Figures
- Comet 67P/ Churyumov-Gerasimenko
- What is a Laser? – NASA SpacePlace
- What Is the Water Cycle? – Climate Kids