Illustration of Jupiter, clouds, a laser pointing at ice and mars partially covered by a dust storm

This activity is related to a Teachable Moment from March 8, 2019. See "NASA Rocket Science? It's Easy As Pi"

Explore more on the Teachable Moments Blog

Overview

In 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. The answers will be revealed on March 15!

Materials

Background

Flat map of Mars with dust moving across it and covering the surface

This set of images from NASA’s Mars Reconnaissance Orbiter (MRO) shows a giant dust storm building up on Mars in 2018, with rovers on the surface indicated as icons. Image credit: NASA/JPL-Caltech/MSSS | › Full image and caption

3D image of Hurricane Florence

This 3D image from the MISR instrument on NASA's Terra satellite shows Hurricane Florence as it approached the eastern coast of the United States on Sept. 13, 2018. Image credit: NASA/GSFC/LaRC/JPL-Caltech, MISR Team | › Full image and caption

Animation showing Hubble observations of Jupiter's Great Red Spot, 1992 through 2017

Animation showing Hubble observations of Jupiter's Great Red Spot, 1992 through 2017. Image credit: Z. Levay (STScI)/R. Garner (NASA Goddard) | › Full image and caption

Animated black-and-white image of a jet shooting out from a comet

A short-lived outburst from comet 67P/Churyumov-Gerasimenko was captured by the Rosetta spacecraft on July 29, 2015. Image credit: ESA/Rosetta/MPS | › Full image and caption

Deadly Dust

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.

Cloud Computing

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.

Storm Spotter

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.

Icy Intel

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.

Procedures

Deadly Dust

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?

Illustration of Mars before the dust storm with the view from the rover showing full sun, then a view after the dust storm with the rover's view of the sun blacked out

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

Cloud Computing

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

Illustration of clouds floating over the land with a large cloud in the middle showing an outline of a cylinder and a measurement of 10 km. The terra satellite is flying above with arrays from its nine cameras pointing down at the land.

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

Storm Spotter

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.

Illustration showing Jupiter and its great red spot in 1979 with the Voyager spacecraft flying by on one side. On the other side, Jupiter's great red spot is smaller and an inset shows the Hubble Space Telescope imaging the planet.

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

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 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?
Illustration showing a laser pointed down at ice on one side. On the other side the ice has been exploded and an inset shows molecules, including amino acids.

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

Infographic of all of the Pi in the Sky 6 graphics and problems

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

Assessment

Infographic answer key for all of the Pi in the Sky 6 graphics and problems

Image credit: NASA/JPL-Caltech/Kim Orr | + 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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