Science fiction meets science fact in this Star Wars inspired Teachable Moment all about ion propulsion and Newton’s Laws.

### In the News

What do "Star Wars," NASA's Dawn spacecraft and Newton's Laws of Motion have in common? An educational lesson that turns science fiction into science fact using spreadsheets – a powerful tool for developing the scientific models addressed in the Next Generation Science Standards. Keep reading to learn more and find out how to get students wielding the force.

### Why It's Important

The TIE (Twin Ion Engine) fighter is a staple of the "Star Wars" universe. Darth Vader flew one in "A New Hope." Poe Dameron piloted one in "The Force Awakens." And many, many Imperial pilots met their fates in them. While the fictional TIE fighters in "Star Wars" flew a long time ago in a galaxy far, far away, ion engines are a reality in this galaxy today – and have a unique connection to NASA’s Jet Propulsion Laboratory.

Launched in 1998, the first spacecraft to use an ion engine was Deep Space 1, which flew by asteroid 9969 Braille and comet Borrelly. Fueled by the success of Deep Space 1, engineers at JPL set forth to develop the next spacecraft that would use ion propulsion. This mission, called Dawn, would take ion-powered spacecraft to the next level by allowing Dawn to go into orbit twice – around the two largest objects in the asteroid belt: Vesta and Ceres.

### How It Works

Ion engines rely on two principles that Isaac Newton first described in 1687. First, a positively charged atom (ion) is pushed out of the engine at a high velocity. Newton’s Third Law of Motion states that for every action there is an equal and opposite reaction, so then a small force pushes back on the spacecraft in the opposite direction – forward! According to Newton’s Second Law of Motion, there is a relationship between the force (F) exerted on an object, its mass (m) and its acceleration (a). The equation F=ma describes that relationship and tells us that the small force applied to the spacecraft by the exiting atom provides a small amount of acceleration to the spacecraft. Push enough atoms out, and you'll get enough acceleration to really speed things up.

### Why is It Important?

Compared with traditional chemical rockets, ion propulsion is faster, cheaper and safer:

• Faster: Spacecraft powered by ion engines can reach speeds of up to 90,000 meters per second (more than 201,000 mph!)
• Cheaper: When it comes to fuel efficiency, ion engines can reach more than 90 percent fuel efficiency, while chemical rockets are only about 35 percent efficient.
• Safer: Ion thrusters are fueled by inert gases. Most of them use xenon, which is a non-toxic, chemically inert (no risk of exploding), odorless, tasteless and colorless gas.

These properties make ion propulsion a very attractive solution when engineers are designing spacecraft. While not every spacecraft can use ion propulsion – some need greater rates of acceleration than ion propulsion can provide – the number and types of missions using these efficient engines is growing. In addition to being used on the Dawn spacecraft and communication satellites orbiting Earth, ion propulsion could be used to boost the International Space Station into higher orbits and will likely be a part of many future missions exploring our own solar system.

### Teach It

Newton’s Laws of Motion are an important part of middle and high school physical science and are addressed specifically by the Next Generation Science Standards as well as Common Core Math standards. The lesson "Ion Propulsion: Using Spreadsheets to Model Additive Velocity" lets students study the relationship between force, mass and acceleration as described by Newton's Second Law as they develop spreadsheet models that apply those principles to real-world situations.

### Explore More

This feature was originally published on May 3, 2016.

TAGS: May the Fourth, Star Wars Day, F=ma, ion propulsion, Dawn, Deep Space 1, lesson, classroom activity, NGSS, Common Core Math

Four pre-service teachers at Cal Poly Pomona are developing their skills in lesson design and delivery as they study Earth science concepts and prepare for graduation.

Clockwise from upper left: Amie Gallardo, Sofia Vallejo, Afiya Kindle, Jacquelin Galvez-Coyt. Image courtesy: Brandon Rodriguez | + Expand image

During the fall semester of 2022, I had the privilege of working with the Education Department at California Polytechnic University in Pomona, specifically with pre-service teachers taking coursework in Earth science. During our collaboration, the curriculum had the students split time in class between learning about geology and Earth’s history and then designing and engaging in classroom activities related to the technical content that they could take to their own classes in the future. This combination had Cal Poly students learning science and education hand-in-hand each week and led to some amazing classroom lessons and lab activities.

One group of young women in the program stood out as exceptionally passionate about their future careers. This team consisted of four seniors: Jacquelin Galvez-Coyt, hoping to someday teach kindergarten; Amie Gallardo, who is planning to teach fourth grade; Afiya Kindle, who is interested in teaching elementary or middle school; and Sofia Vallejo, who is interested in kindergarten through sixth grade.

Despite their interest in working with young students and collaborating to design lessons for those students, each of these pre-service teachers allowed their individuality to shape how they navigated lesson design and implementation. I recently sat down with them to ask about their instructional style and aspirations for classrooms of their own.

Now that we’re back to in-person classes, how is the transition going?

Sofia: Returning from remote instruction felt eerie at first, but it’s so nice to return to communicate with people and build connections in a non-digital way. In-person classes prepare you to communicate with colleagues in real life, build social skills, and read body language. All of these skills are critical for a teacher in order to understand and better help students to succeed.

Amie: Returning from remote instruction has been amazing. While it had its perks, I believe, as students, we learn a lot more while working hands-on with our projects than is possible in distance learning. If we’re trying to develop and assess activities we can do with kids, that really requires being face-to-face.

Amie Gallardo provides an Earth science demonstration to a class of education students at Cal Poly Pomona. Image courtesy: Brandon Rodriguez | + Expand image

What are you most excited about when it comes to having your own classroom, and how will you get your kids excited about STEM?

Afiya: I am most confident about creating a genuine safe space for kids. I’ll be able to communicate how much I care about them and about our shared future, and I think there could never be enough genuinely kind and caring teachers in this world.

Jacquelin: I think my kids will be excited about STEM because of how easy it's become to incorporate activities. There are many resources out there for teachers to use for teaching math and science that don't rely solely on a textbook. Activities that use inexpensive materials or that require a little DIY skills go a long way for students.

Afiya: Exactly! I know I developed my love for science from being hands-on and actually somewhat “in charge” of an experiment on my own. Winning a science fair competition in seventh grade for a greenhouse I built really boosted my confidence and helped reassure me of my scholastic abilities as a kid.

You led a really cool lesson with your classmates where you had them use Oreos to model tectonic boundaries. How do you feel that lesson went?

Jacqueline: I was really proud of our group. After giving a lecture to the students about tectonic plate boundaries, we dispersed Oreos to everyone. We were set up around the classroom demonstrating the activity and giving verbal instructions for everyone to follow. My favorite part was when I saw two students by me go, “Oohhhh,” and smile once they got their Oreos to demonstrate the plate boundaries correctly.

Amie: I thought it went really well! All the students in our classroom enjoyed it. Although we, as adults, may know about plate tectonics, having our hands on the Oreos to understand it made it more enjoyable.

Afiya: Plus, who doesn’t love Oreos? They’re even vegan!

An Oreo cookie is used to demonstrate rock fault movement. Image courtesy: Brandon Rodriguez | + Expand image

Which of the NASA-JPL lessons that you’ve implemented did you enjoy, and why?

Jacqueline: My favorite JPL activity we did was the Moon Phases activity. Having one team member to the side to give the instructions allows another student to view the different Moon phases. Then you switch so both students get to see that perspective. My second favorite activity was creating layers with different colored Play-Doh and demonstrating them as different plate boundaries and folds.

Amie: The NASA lesson that I enjoyed the most was the one we did on lunar eclipses. Much like myself, many students often have an early fascination with the Moon. Learning more about the Moon and lunar eclipses made me excited about the semester.

Sofia Vallejo uses a foam ball and lamp to demonstrate how solar eclipses occur. Image courtesy: Brandon Rodriguez | + Expand image

What’s next for you after you finish at Cal Poly Pomona?

Jacqueline: After I graduate at Cal Poly, I plan to attend UC Riverside to complete my credential program. While I am there, I would love to get my student teaching experience. Once I complete my credential program, I plan to apply to work at schools in the Inland Empire [in Southern California]. I want to be able to give back to the communities that influenced who I am today.

Sofia: My plans after Cal Poly are to take some time off to gain experience in the field as a substitute teacher. I also am looking to gain more volunteer experience, skills, and exposure. In the future, I want to enroll in UC Riverside to earn my teaching credential and master's degree.

Looking for ways to bring NASA STEM into your classroom or already have a great idea? The Education Office at NASA's Jet Propulsion Laboratory serves educators in the greater Los Angeles area. Contact us at education@jpl.nasa.gov.

### Explore More

TAGS: Teachers, School, Remote School, Classroom, Instruction, K-12, STEAM, Science, Math, resources, lessons

Learn how pi is used by NASA and how many of its infinite digits have been calculated, then explore the science and engineering that makes the Pi Day Challenge possible.

Update: March 15, 2023 – The answers are here! Visit the NASA Pi Day Challenge page to view the illustrated answer keys for each problem.

This year marks the 10th installment of the NASA Pi Day Challenge. Celebrated on March 14, Pi Day is the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

Every year, Pi Day gives us a reason to celebrate the mathematical wonder that helps NASA explore the universe and enjoy our favorite sweet and savory pies. Students can join in the fun once again by using pi to explore Earth and space themselves in the NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and find out how students can put their math mettle to the test to solve real problems faced by NASA scientists and engineers as we explore Earth, Mars, asteroids, and beyond!

Visit the Pi in the Sky 10 lesson page to explore classroom resources and downloads for the 2023 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

This illustration shows a concept for multiple robots that would team up to ferry to Earth samples of rocks and soil being collected from the Martian surface by NASA's Mars Perseverance rover. Image credit: NASA/JPL-Caltech | › Full image and caption

Image from animation comparing the relative sizes of James Webb's primary mirror to Hubble's primary mirror. Credit: NASA/Goddard Space Flight Center . | › Full animation

This illustration depicts the metal-rich asteroid Psyche, which is located in the main asteroid belt between Mars and Jupiter. Credits: NASA/JPL-Caltech/ASU | + Full image and caption

This image sequence shows an annular solar eclipse from May 2012. The bottom right frame illustrates the distinctive ring, or "annulus," of such eclipses. A similar eclipse will be visible from the South Pacific on May 10, 2013. Credits: Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons | + Expand image

### How It Works

Dividing any circle’s circumference by its diameter gives you an answer of pi, which is usually rounded to 3.14. Because pi is an irrational number, its decimal representation goes on forever and never repeats. In 2022, mathematician Simon Plouffe discovered the formula to calculate any single digit of pi. In the same year, teams around the world used cloud computing technology to calculate pi to 100 trillion digits. But you might be surprised to learn that for space exploration, NASA uses far fewer digits of pi.

Here at NASA, we use pi to measure the area of telescope mirrors, determine the composition of asteroids, and calculate the volume of rock samples. But pi isn’t just used for exploring the cosmos. Since pi can be used to find the area or circumference of round objects and the volume or surface area of shapes like cylinders, cones, and spheres, it is useful in all sorts of ways. Transportation teams use pi when determining the size of new subway tunnels. Electricians can use pi when calculating the current or voltage passing through circuits. And you might even use pi to figure out how much fencing is needed around a circular school garden bed.

In the United States, March 14 can be written as 3.14, which is why that date was chosen for celebrating all things pi. In 2009, the U.S. House of Representatives passed a resolution officially designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi. And that's precisely what the NASA Pi Day Challenge is all about!

### The Science Behind the 2023 NASA Pi Day Challenge

This 10th installment of the NASA Pi Day Challenge includes four noodle-nudgers that get students using pi to calculate the amount of rock sampled by the Perseverance Mars rover, the light-collecting power of the James Webb Space Telescope, the composition of asteroid (16) Psyche, and the type of solar eclipse we can expect in October.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

#### Tubular Tally

NASA’s Mars rover, Perseverance, was designed to collect rock samples that will eventually be brought to Earth by a future mission. Sending objects from Mars to Earth is very difficult and something we've never done before. To keep the rock cores pristine on the journey to Earth, the rover hermetically seals them inside a specially designed sample tube. Once the samples are brought to Earth, scientists will be able to study them more closely with equipment that is too large to make the trip to Mars. In Tubular Tally, students use pi to determine the volume of a rock sample collected in a single tube.

When NASA launched the Hubble Space Telescope in 1990, scientists hoped that the telescope, with its large mirror and sensitivity to ultraviolet, visible, and near-infrared light, would unlock secrets of the universe from an orbit high above the atmosphere. Indeed, their hope became reality. Hubble’s discoveries, which are made possible in part by its mirror, rewrote astronomy textbooks. In 2022, the next great observatory, the James Webb Space Telescope, began exploring the infrared universe with an even larger mirror from a location beyond the orbit of the Moon. In Rad Reflection, students use pi to gain a new understanding of our ability to peer deep into the cosmos by comparing the area of Hubble’s primary mirror with the one on Webb.

#### Metal Math

Orbiting the Sun between Mars and Jupiter, the asteroid (16) Psyche is of particular interest to scientists because its surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. By sending a spacecraft to study Psyche up close, scientists hope to learn more about terrestrial planet cores and our solar system’s history. That's where NASA's Psyche comes in. The mission will use specialized tools to study Psyche's composition from orbit. Determining how much metal exists on the asteroid is one of the key objectives of the mission. In Metal Math, students will do their own investigation of the asteroid's makeup, using pi to calculate the approximate density of Psyche and compare that to the density of known terrestrial materials.

#### Eclipsing Enigma

On Oct. 14, 2023, a solar eclipse will be visible across North and South America, as the Moon passes between Earth and the Sun, blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. Depending on those distances, the Sun's disk area might be fully or only partially blocked during a solar eclipse. In Eclipsing Enigma, students get a sneak peek at what to expect in October by using pi to determine how much of the Sun’s disk will be eclipsed by the Moon and whether to expect a total or annular eclipse.

### Teach It

Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in the NASA Pi Day Challenge. In addition to solving this year’s challenge, you can also dig into the more than 30 puzzlers from previous challenges available in our Pi Day collection. Completing the problem set and reading about other ways NASA uses pi is a great way for students to see the importance of the M in STEM.

#### Pi Day Resources

Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.

#### Interactives

TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, sun, moon, earth, eclipse, asteroid, psyche, sample return, mars, perseverance, jwst, webb, hubble, telescope, miri

As NASA retires its InSight Mars lander, here's a look at some of the biggest discoveries from the first mission designed to study the Red Planet's interior – plus, how to make connections to what students are learning now.

After more than four years listening to the “heartbeat” of Mars, NASA is saying goodbye to the InSight lander as the mission on the Red Planet comes to an end. On Dec. 21, 2022 scientists wrapped up the first-of-its-kind mission to study the interior of Mars as dust in the Martian atmosphere and on the spacecraft’s solar panels prevented the lander from generating enough power to continue.

Read on to learn how the mission worked, what it discovered, and how to bring the science and engineering of the mission into the classroom.

### How It Worked

The locations of InSight's three main science tools, SEIS, HP3, and RISE are labeled in this illustration of the lander on Mars. | + Expand image | › Full image and caption

The InSight lander was designed to reveal the processes that led to the formation of Mars – as well as Earth, the Moon, and all rocky worlds. This meant meeting two main science goals.

First, scientists wanted to understand how Mars formed and evolved. To do that, they needed to investigate the size and make-up of Mars’ core, the thickness and structure of its crust, the structure of the mantle layer, the warmth of the planet's interior, and the amount of heat flowing through the planet.

Second, to study tectonic activity on Mars, scientists needed to determine the power, frequency, and location of “marsquakes” as well as measure how often meteoroids impacted the Red Planet, creating seismic waves.

Engineers equipped InSight with three main science tools that would allow researchers to answer these questions about Mars.

SEIS, a seismometer like the ones used on Earth to record earthquakes, measured the seismic waves on Mars. These waves, which travel through the Red Planet, can tell scientists a lot about the areas they pass through. They even carry clues about whether it was a marsquake or meteorite impact that created the waves.

InSight captured these images of clouds drifting in the distance, visible just beyond the dome-like top of the SEIS instrument. Credit: NASA/JPL-Caltech | + Expand image | › Full image and caption

InSight's Heat Flow and Physical Properties Package, or HP3, was an instrument designed to burrow 16 feet (five meters) into Mars to measure the temperature at different depths and monitor how heat flowed out toward the surface. However, the self-hammering probe, informally called the "mole," struggled to dig itself in due to the unexpected consistency of the top few inches of Mars regolith at the landing site. Using full-size models of the lander and probe, engineers recreated InSight’s environment here on Earth to see if they could find a solution to the issue. They tested solutions that would allow the probe to penetrate the surface, including pressing the scoop attached to InSight’s robotic arm against the probe. While the effort serves as a great real-world example of how engineers work through problems with distant spacecraft, ultimately, none of the solutions allowed the probe to dig past the surface when attempted on Mars.

In 2019, InSight mission scientist/engineer Troy Hudson shared the game plan for getting the mission's heat probe digging again on Mars. Ultimately, the team wasn't able to to get the "mole" working, but the effort is a great real-world example of how engineers work through problems with distant spacecraft. | Watch on YouTube

InSight’s third experiment, called RISE, used the spacecraft’s radio antennas to precisely measure the lander's position on the surface of Mars. The interior structure of Mars affects the planet’s motion, causing it to wobble. Measuring InSight’s position as the planet wobbled helped scientists gain a better understanding of the core and other layered structures that exist within the interior of Mars.

### What We Discovered

Using its seismometer, InSight gained a deeper understanding of the interior layers of Mars, as detailed in this graphic. Image credit: NASA/JPL-Caltech | + Expand image | › Full image and caption

InSight’s instruments enabled the mission science team to gain an understanding of not only the depth of Mars’ crust, mantle, and core, but also the composition of those features. They also learned just how active Mars really is.

#### The Structure of Mars

Working our way from the surface to the center of the planet, scientists found Mars’ crust was thinner than expected. Seismic waves detected by SEIS indicate that the crust is made up of three sub-layers, similar to Earth’s crust. The top-most layer of the crust is about six miles (10 kilometers) deep, while the denser layers of the crust, which contain more felsic, or iron-rich, material extend downward to about 25 miles (40 kilometers) below the surface. As seismic waves from a marsquake or a meteorite impact spread across the surface and through the interior of the planet, they can reflect off of underground layers, giving scientists views into the unseen materials below. Measuring how the waves change as a result of these reflections is how scientists unveiled the underground structure of Mars.

Like Earth, Mars has a lithosphere, a rigid layer made up of the crust and upper mantle. The Martian lithosphere extends about 310 miles (500 kilometers) below the surface before it transitions into the remaining mantle layer, which is relatively cool compared with Earth’s mantle. Mars’ mantle extends to 969 miles (1,560 kilometers) below the surface where it meets the planet’s core.

In this lesson from the "Pi in the Sky" math challenge, students use measurements from InSight along with pi to calculate the density of Mars' core. Image credit: NASA/JPL-Caltech | + Expand image | › Go to the lesson

Scientists measured the core of Mars and found it to be larger than expected, with a radius of 1,137 miles (1,830 kilometers). With this information, scientists were able to estimate the density of Mars' core, which turned out to be less dense than anticipated, meaning it contains lighter elements mixed in with iron. Scientists also confirmed that the planet contains a liquid core. While we know that Earth has a liquid outer core and solid inner core, scientists will need to further study the data returned from InSight to know if there is also a solid inner core on Mars.

As scientists continue to study the data returned from InSight, we could learn even more about how Mars formed, how its magnetic field developed, and what materials make up the core, which could ultimately help us better understand how Earth and other planets formed.

#### Marsquakes

InSight discovered that Mars is a very active planet. A total of 1,319 marsquakes were detected after the SEIS instrument was placed on the surface. The largest, which was estimated to be a magnitude 5, was detected in May of 2022.

Unlike Earth, where the crust is broken into large pieces called plates that continually shift around causing earthquakes, Mars’ crust is made up of one solid plate, somewhat like a shell. However, as the planet cools, the crust shrinks, creating breaks called faults. This breaking action is what causes marsquakes, and the seismic waves generated by the quakes are what help scientists figure out when and where the quakes occurred and how powerful they were.

In this math problem from the "Pi in the Sky" series, students use pi to identify the timing and location of a hypothetical marsquake recorded by InSight. Image credit: NASA/JPL-Caltech | + Expand image | › Go to the lesson

Nearly all of the strongest marsquakes detected by InSight came from a region known as Cerberus Fossae, a volcanic region that may have had lava flows within the past few million years. Volcanic activity, even without lava flowing on the surface, can be another way marsquakes occur. Images from orbiting spacecraft show boulders that have fallen from cliffs in this region, perhaps shaken loose by large marsquakes.

This seismogram shows the largest quake ever detected on another planet. Estimated at magnitude 5, this quake was discovered by InSight on May 4, 2022. Listen to a sonification of this seismogram. | + Expand image | › Full image and caption

Conversely, InSight didn't detect any quakes in the volcanic region known as Tharsis, the home of three of Mars’ largest volcanos that sit approximately one-third of the way around the planet from InSight. This doesn’t necessarily mean the area is not seismically active. Scientists think there may be quakes occurring, but the size of Mars’ liquid core creates what’s known as a shadow zone – an area into which seismic waves don’t pass – at InSight's location.

#### Meteorite Impacts

On Sept. 5, 2021, InSight detected the impacts of a meteoroid that entered the Martian atmosphere. The meteoroid exploded into at least three pieces that reached the surface and left behind craters. NASA’s Mars Reconnaissance Orbiter passed over the impact sites to capture images of the three new craters and confirm their locations.

This image, captured by the Mars Reconnaissance Orbiter, shows the craters (in blue) formed by a meteroid impact on Mars on Sept. 5, 2021. The impact was the first to be detected by InSight. Image credit: NASA/JPL-Caltech/University of Arizona | + Expand image | › Full image and caption

“After three years of waiting for an impact, those craters looked beautiful,” said Ingrid Daubar of Brown University, a Mars impacts specialist.

Mars’ thin atmosphere, which is less than 1% as dense as Earth’s, means meteoroids have a better chance of not disintegrating in the heat and pressure that builds up as they pass through the atmosphere to the planet’s surface. Despite this fact and Mars' proximity to the asteroid belt, the planet proved to be a challenging location to detect meteorite impacts because of "noise" in the data created by winds blowing on SEIS and seasonal changes in the atmosphere.

With the confirmation of the September 2021 impacts, scientists were able to identify a telltale seismic signature to these meteorite impacts. With this information in hand, they looked back through InSight's data and found three more impacts – one in 2020 and two in 2021. Scientists anticipate finding even more impacts in the existing data that might have been hidden by the noise in the data.

This collage shows three other meteoroid impacts on Mars that were detected by the seismometer on InSight and captured by the Mars Reconnaissance Orbiter. Image credit: Credit: NASA/JPL-Caltech/University of Arizona | + Expand image | › Full image and caption

Meteorite impacts are an invaluable piece of understanding the planet’s surface. On a planet like Earth, wind, rain, snow and ice wear down surface features in a process known as weathering. Plate tectonics and active volcanism refresh Earth’s surface regularly. Mars’ surface is older and doesn't go through those same processes, so a record of past geologic events like meteorite impacts is more apparent on the planet's surface. By counting impact craters visible on Mars today, scientists can update their models and better estimate the number of impacts that occurred in the early solar system. This gives them an improved approximation of the age of the planet’s surface.

Learn how InSight detected the first seismic waves from a meteoroid on Mars and how the lander captured the sound of the space rock striking the surface. | Watch on YouTube

### Why It's Important

Before InSight touched down, all Mars missions – landers, rovers, orbiters and flyby spacecraft – studied the surface and atmosphere of the planet. InSight was the first mission to study the deep interior of Mars.

Even with the InSight mission drawing to a close, the science and engineering of the mission will continue to inform our understanding of the Red Planet and our solar system for years as researchers further examine the data returned to Earth. Keep up to date with the latest findings from InSight scientists and engineers on the mission website.

### Teach It

Explore these lessons in geology, physics, math, coding and engineering to connect student learning to the InSight mission and the real-world STEM that happens at NASA.

### Explore More

TAGS: K-12 Education, Classrooms, Teaching, Teachers, Resources, Teachable Moments, Mars, InSight, Missions, Spacecraft, Marsquakes

Explore how and why the SWOT mission will take stock of Earth's water budget, what it could mean for assessing climate change, and how to bring it all to students.

Update: Dec. 15, 2022 – NASA, the French space agency, and SpaceX are now targeting 3:46 a.m. PST (6:46 a.m. EST) on Friday, Dec.16, for the launch of the Surface Water and Ocean Topography (SWOT) satellite. Visit NASA's SWOT launch blog for the latest updates.

NASA is launching an Earth-orbiting mission that will map the planet’s surface water resources better than ever before. Scheduled to launch on Dec. 16 from Vandenberg Space Force Base in California, the Surface Water and Ocean Topography, or SWOT mission is the latest international collaboration designed to monitor and report on our home planet. By providing us with a highly detailed 3D view of rivers, lakes, and oceans, SWOT promises to improve our understanding of Earth’s water cycle and the role oceans play in climate change, as well as help us better respond to drought and flooding.

Read on to find out why we're hoping to learn more about Earth's surface water, get to know the science behind SWOT's unique design, and follow along with STEM teaching and learning resources.

### Why It's Important

Observing Earth from space provides scientists with a global view that is important for understanding the whole climate system. In the case of SWOT, we will be able to monitor Earth’s surface water with unprecedented detail and accuracy. SWOT will provide scientists with measurements of water volume change and movement that will inform our understanding of fresh water availability, flood hazards, and the mechanisms of climate change.

Scientists and engineers provide an overview of the SWOT mission. Credit: NASA/JPL-Caltech | Watch on YouTube

#### Water Flow

Scientists use a variety of methods to track Earth’s water. These include stream and lake gauges and even measurements from space such as sea surface altimetry and gravitational measurements of aquifer volumes. Monitoring of river flow and lake volume is important because it can tell us how much freshwater is readily available and at what locations. River flow monitoring can also help us make inferences about the downstream environmental impact. But monitoring Earth’s surface water in great detail with enough frequency to track water movement has proven challenging. Until now, most monitoring of river flow and lake levels has relied on water-flow and water-level gauges placed across Earth, which requires that they be accessible and maintained. Not all streams and lakes have gauges and previous space-based altimetry and gravitational measurements, though useful for large bodies of water, have not been able to adequately track the constant movement of water through smaller rivers or lakes.

Here's why understanding Earth’s "water budget" is an important part of understanding our planet and planning for future water needs.

SWOT will be able to capture these measurements across the globe in 3D every 21 days. The mission will monitor how much water is flowing through hundreds of thousands of rivers wider than 330 feet (100 meters) and keep a close watch on the levels of more than a million lakes larger than 15 acres (6 hectares). Data from the mission will be used to create detailed maps of rivers, lakes, and reservoirs that will enable accurate monitoring to provide a view of freshwater resources that is not reliant on physical access. Meanwhile, SWOT’s volumetric measurements of rivers, lakes, and reservoirs will help hydrologists better track drought and flooding impacts in near-real-time.

#### Coastal Sea Level Rise

SWOT will measure our oceans with unprecedented accuracy, revealing details of ocean features as small as 9 miles (15 kilometers) across. SWOT will also monitor sea levels and tides. Though we have excellent global sea level data, we do not have detailed sea level measurements near coastlines. Coastal sea levels vary across the globe as a result of ocean currents, weather patterns, land changes, and other factors. Sea levels are rising faster than ever, and higher sea levels also mean that hurricane storm surges will reach farther inland than ever before, causing substantially more damage than the same category of hurricanes in the past. SWOT will be able to monitor coastal sea level variations and fill gaps in the observations we currently have from other sources.

What is sea level rise and what does it mean for our planet? | › View Transcript

#### Ocean Heat Sinks

Further contributing to our understanding of the role Earth’s oceans play in climate change, SWOT will explore how the ocean absorbs atmospheric heat and carbon, moderating global temperatures and climate change. Scientists understand ocean circulation on a large scale and know that ocean currents are driven by temperature and salinity differences. However, scientists do not currently have a good understanding of fine-scale ocean currents, where most of the ocean's motion-related energy is stored and lost. Circulation at these fine scales is thought to be responsible for transporting half of the heat and carbon from the upper ocean to deeper layers. Such downward ocean currents have helped to mitigate the decades-long rise in global air temperatures by absorbing and storing heat and carbon away from the atmosphere. Knowing more about this process is critical for understanding the mechanisms of global climate change.

JPL scientist Josh Willis uses a water balloon to show how Earth's oceans are absorbing most of the heat being trapped on our warming world. | › Related lesson

These fine-scale ocean currents also transport nutrients to marine life and circulate pollutants such as crude oil and debris. Understanding nutrient transport helps oceanographers assess ocean health and the productivity of fisheries. And tracking pollutants aids in natural hazard assessment, prediction, and response.

### How It Works

A joint effort between NASA and the French space agency – with contributions from the Canadian and UK space agencies – SWOT will continue NASA’s decades-long record of monitoring sea surface height across the globe. But this mission will add a level of detail never before achieved.

SWOT will measure more than 90% of Earth’s surface water, scanning the planet between 78°N latitude and 78°S latitude within 1 centimeter of accuracy and retracing the same path every 21 days. Achieving this level of accuracy from a spacecraft height of 554 miles (891 kilometers) requires that the boom using radar to measure water elevation remain stable within 2 microns – or about 3% of the thickness of a human hair.

This visualization shows ocean surface currents around the world during the period from June 2005 through December 2007. With its new, high resolution wide-swath measurements, SWOT will be able to observe eddies and current features at greater resolution than previously possible. Credit: NASA Scientific Visualization Studio | Watch on YouTube

Prior to SWOT, spacecraft have used conventional nadir, or straight-down, altimetry to measure sea surface height. Conventional nadir altimetry sends a series of radar or laser pulses down to the surface and measures the time it takes for each signal to return to the spacecraft, thus revealing distances to surface features. To acquire more detailed information on surface water, SWOT will use an innovative instrument called the Ka-band Radar Interferometer, or KaRIn, to measure water height with exceptional accuracy. Ka-band is a portion of the microwave part of the electromagnetic spectrum. SWOT uses microwaves because they can penetrate clouds to return data about water surfaces.

SWOT will track Earth's surface water in incredible detail using an innovative instrument called the Ka-band Radar Interferometer, or KaRIn. Image credit: NASA/JPL-Caltech | + Expand image

The KaRIn instrument uses the principles of synthetic aperture radar combined with interferometry to measure sea surface height. A radar signal is emitted from the end of the 10-meter-wide boom on the spacecraft. The reflected signal is then received by antennas on both ends of the boom, capturing data from two 30-mile (50-kilometer) wide swaths on either side of the spacecraft. The received signals will be slightly out of sync, or phase, from one another because they will travel different distances to return to the receivers on either end of the boom. Knowing the phase difference, the distance between the antennas, and the radar wavelength allows us to calculate the distance to the surface.

Radar signals bounced off the water’s surface will be received by antennas on both ends of SWOT's 10-meter-wide boom. The received signals will be slightly out of phase because they will travel different distances as they return to the receivers. Scientists use this phase difference and the radar wavelength to calculate the distance to the surface. Image credit: NASA/JPL-Caltech | + Expand image

The observations acquired by the two antennas can be combined into what is known as an interferogram. An interferogram is a pattern of wave interference that can reveal more detail beyond the 1-centimeter resolution captured by the radar. To explain how it works, we'll recall a couple of concepts from high school physics. When out-of-phase waves from the two antennas are combined, constructive and destructive interference patterns result in some wave crests being higher and some wave troughs being lower than those of the original waves. The patterns that result from the combination of the waves reveal more detail with resolution better than the 1-centimeter wavelength of the original Ka-band radar waves because the interference occurs over a portion of a wavelength. An interferogram can be coupled with elevation data to reveal a 3D representation of the water’s surface.

The KaRIn instrument illuminates two parallel tracks of approximately 50 kilometres on either side of a nadir track from a traditional altimeter. The signals are received by two antennas 10 metres apart and are then processed to yield interferometry measurements. Image credit: NASA/JPL-Caltech | + Expand image

This highly accurate 3D view of Earth’s surface water is what makes SWOT so unique and will enable scientists to more closely monitor the dynamics of the water cycle. In addition to observing ocean currents and eddies that will inform our understanding of the ocean’s role in climate change, SWOT's use of interferometry will allow scientists to track volumetric changes in lakes and quantify river flooding, tasks that cannot yet be done on a wide scale in any other way.

This interferogram was captured by the air-based UAVSAR instrument of the magnitude 7.2 Baja California earthquake of April 4, 2010. The interferogram is overlaid atop a Google Earth image of the region. Image credit: NASA/JPL/USGS/Google | › Learn more

SWOT is scheduled to launch no earlier than Dec. 16, 2022, on a SpaceX Falcon 9 rocket from Vandenberg Space Force Base in California. Tune in to watch the launch on NASA TV.

After launch, the spacecraft will spend 6-months in a calibration and validation phase, during which it will make a full orbit of Earth every day at an altitude of 553 miles (857 kilometers). Upon completion of this phase, SWOT will increase its altitude to 554 miles (891 kilometers) and assume a 21-day repeat orbit for the remainder of its mission.

Visit the mission website to follow along as data are returned and explore the latest news, images, and updates as SWOT provides a new view on one of our planet's most important resources.

### Teach It

The SWOT mission is the perfect opportunity to engage students in studying Earth’s water budget and water cycle. Explore these lessons and resources to get students excited about the STEM involved in studying Earth’s water and climate change from space.

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#### Podcast

TAGS: K-12 Education, Teachers, Educators, Earth Science, Earth, Climate Change, Climate, Satellites, Teachable Moments

While world record holders may have memorized more than 70,000 digits of pi, a JPL engineer explains why you really only need a tiny fraction of that for most calculations – even at NASA.

Update: October 24, 2022 – This article, originally written in 2016, has been updated to reflect the latest values for NASA’s Voyager 1 spacecraft, which continues to venture farther into interstellar space. The author, Marc Rayman, has ventured on too, from the chief engineer for NASA’s Dawn mission, which concluded successfully in 2018, to the chief engineer for mission operations and science at NASA’s Jet Propulsion Laboratory.

This graphic shows more than 500 of the infinite number of decimals in pi. Image credit: NASA/JPL-Caltech | + Expand image

We received this question from a fan on Facebook who wondered how many decimals of the never-ending mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations:

“Does JPL only use 3.14 for its pi calculations? Or do you use more decimals, like say [360 or even more]?”

Here’s JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman, with the answer:

Thank you for your question! This isn't the first time I've heard a question like this. In fact, it was posed many years ago by a sixth-grade science and space enthusiast who was later fortunate enough to earn a doctorate in physics and become involved in space exploration. His name was Marc Rayman.

To start, let me answer your question directly. For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let's look at this a little more closely to understand why we don't use more decimal places. I think we can even see that there are no physically realistic calculations scientists ever perform for which it is necessary to include nearly as many decimal points as you asked about. Consider these examples:

1. The most distant spacecraft from Earth is Voyager 1. As of this writing, it’s about 14.7 billion miles (23.6 billion kilometers) away. Let’s be generous and call that 15 billion miles (24 billion kilometers). Now say we have a circle with a radius of exactly that size, 30 billion miles (48 billion kilometers) in diameter, and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 94 billion miles (more than 150 billion kilometers). We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 30-billion-mile (48-billion-kilometer) diameter circle would be wrong by less than half an inch (about one centimeter). Think about that. We have a circle more than 94 billion miles (more than 150 billion kilometers) around, and our calculation of that distance would be off by no more than the width of your little finger.
2. Put your pi math skills to the test with this problem from NASA's Pi Day Challenge. Can you use pi to determine what fraction of a signal from Voyager 1 reaches Earth? Image credit: NASA/JPL-Caltech | + Expand image | › View lesson page

3. We can bring this closer to home by looking at our planet, Earth. It is more than 7,900 miles (12,700 kilometers) in diameter at the equator. The circumference is roughly 24,900 miles (40,100 kilometers). That's how far you would travel if you circumnavigated the globe – and didn't worry about hills, valleys, and obstacles like buildings, ocean waves, etc. How far off would your odometer be if you used the limited version of pi above? The discrepancy would be the size of a molecule. There are many different kinds of molecules, of course, so they span a wide range of sizes, but I hope this gives you an idea. Another way to view this is that your error by not using more digits of pi would be more than 30,000 times thinner than a hair!
4. Image credit: NASA | + Expand image

5. Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient. Think about how fantastically vast the universe is. It’s certainly far beyond what you can see with your eyes even on the darkest, most beautiful night of sparkling stars. It’s yet farther beyond the extraordinary vision of the James Webb Space Telescope. And the vastness of the universe is truly far, far, far beyond what we can even conceive. Now think about how incredibly tiny a single atom is. Isn’t it amazing that we wouldn’t need to use many digits of pi at all to cover that entire unbelievable range?

If you were to hold a single grain of sand at arm's length, you could cover the entire area of space taken up by this image, which was captured by the James Webb Space Telescope and contains thousands of galaxies. The oldest-known galaxy identified in the image is 13.1 billion years old. Image credit: NASA, ESA, CSA, STScI | + Expand image | › More about the image | Text description (PDF)

Pi is an intriguing number with interesting mathematical properties. It’s fun to think about its truly endless sequence of digits, and it may be surprising how often it appears in the equations scientists and engineers use. But there are no questions – prosaic or esoteric – in humankind’s noble efforts to explore or comprehend the marvels of the cosmos, from the unimaginably smallest scales to the inconceivably largest, that could require very many of those digits.

Hear more from Marc in his inspiring TEDx talk, “If It Isn’t Impossible, It Isn’t Worth Trying” and in his Dawn Journal, where he wrote frequent updates about the Dawn mission’s extraordinary extraterrestrial expedition to the protoplanet Vesta and dwarf planet Ceres.

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#### Recursos en español

TAGS: Pi, Pi Day, Dawn, Voyager, Engineering, Science, Mathematics

A NASA space telescope mission is giving astronomers a whole new way to peer into the universe, allowing us to uncover long-standing mysteries surrounding objects such as black holes. Find out how it works and how to engage students in the science behind the mission.

Some of the wildest, most exciting features of our universe – from black holes to neutron stars – remain mysteries to us. What we do know is that because of their extreme environments, some of these emit highly energetic X-ray light, which we can detect despite the vast distances between us and the source.

Now, a NASA space telescope mission is using new techniques to not only scout out these distant phenomena, but also provide new information about their origins. Read on to learn how scientists are getting exciting new perspectives on our universe and what the future of X-ray astronomy holds.

### How They Did It

In 2021, NASA launched the Imaging X-Ray Polarimeter Explorer, or IXPE, through a collaboration with Ball Aerospace and the Italian Space Agency. The space telescope is designed to operate for two years, detecting X-rays emitted from highly energetic objects in space, such as black holes, different types of neutron stars (e.g., pulsars and magnetars) and active galactic nuclei. In its first year, the telescope is focusing on roughly a dozen previously studied X-ray sources, spending hours or even days observing each target to reveal new data made possible by spacecraft's scientific instruments.

IXPE isn't the first telescope to observe the universe in X-ray light. NASA's Chandra X-ray Observatory, launched in 1999, has famously spent more than 20 years photographing our universe at a wavelength of light exclusively found in high-energy environments, such as where cosmic materials are heated to millions of degrees as a result of intense magnetic fields or extreme gravity.

Using Chandra, scientists can assign colors to the different energy levels, or wavelengths, produced by these environments. This allows us to get a picture of the highly energetic light ejected by black holes and tiny neutron stars – small, but extremely dense stars with masses 10-25 times that of our Sun. These beautiful images, such as from Chandra’s first target, Cassiopeia A (Cas A for short), show the violent beauty of stars exploding.

This image of the supernova Cassiopeia A from NASA’s Chandra X-ray Observatory shows the location of different elements in the remains of the explosion: silicon (red), sulfur (yellow), calcium (green) and iron (purple). Each of these elements produces X-rays within narrow energy ranges, allowing maps of their location to be created. Image credit: NASA/CXC/SAO | › Full image and caption

While Chandra has earned its name as one of “The Great Observatories,” astronomers have long desired to peer further into highly energetic environments in space by capturing them in even more detail.

IXPE expands upon Chandra’s work with the introduction of a tool called a polarimeter, an instrument used to understand the shape and direction of the light that reaches the space telescope's detectors. The polarimeter on IXPE allows scientists to gain insight into the finer details of black holes, supernovas, and magnetars, like which direction they are spinning and their three-dimensional shape.

This image of Cassiopeia A was created using some of the first X-ray data collected by IXPE, shown in magenta, combined with high-energy X-ray data from Chandra, in blue. Image credit: NASA/CXC/SAO/IXPE | › Full image and caption

While scientists have just begun putting IXPE's capabilities to use, they're already starting to reveal new details about the inner workings of these objects – such as the magnetic field environment around Cas A, shown in a newly released image.

The lines in this newly released image come from IXPE measurements that show the direction of the magnetic field across regions of Cassiopeia A. Green lines indicate regions where the measurements are most highly significant. These results indicate that the magnetic field lines near the outskirts of the supernova remnant are largely oriented radially, i.e., in a direction from the center of the remnant outwards. The IXPE observations also reveal that the magnetic field over small regions is highly tangled, without a dominant preferred direction. Observations such as this one can help scientists learn how particles shooting out from supernovae interact with the magnetic field created by the explosion. Image credits: X-ray: Chandra: NASA/CXC/SAO; IXPE: NASA/MSFC/J. Vink et al. | + Expand image | › Full image and caption

“For the first time, we will use every collected photon of light to tell us about the nature and shapes of objects in the sky that would be dots of light otherwise,” says Roger Romani, a Stanford professor and the co-investigator on IXPE.

### How It Works

Generally, when light is produced, it is what we call unpolarized, meaning that it oscillates in every direction. For example, our Sun produces unpolarized light. But sometimes, light is produced in a highly organized fashion, oscillating only in one direction. In astronomy, this arises when magnetic fields force particles to incredibly high speeds, creating highly organized, or polarized, light.

This is what makes objects like the supernova Cas A such enticing targets for IXPE. Exploded stars like Cas A generate massive energetic waves when they go supernova, giving scientists a view of how particles shooting out at immense speeds interact with the magnetic fields from such an event. In the case of Cas A, IXPE was able to determine that the x-rays are not very polarized, meaning the explosion created very turbulent regions with multiple field directions.

While the idea of polarized or organized light may sound abstract, you may have noticed it the last time you were outside on a sunny day. If you’ve tried on a pair of polarized sunglasses, you may have noticed that the glare was greatly reduced. That’s because as light scatters, it bounces off of reflective surfaces in all directions. However, polarized lenses have tiny filters that only allow light coming from a narrow band of directions to pass through.

The polarimeter on IXPE works in a similar way. Astronomers can determine the strength of an object's magnetic field by using the polarimeter to measure how much of the light detected by the telescope is polarized. Typically, the more polarized the light the stronger the magnetic field at the source.

Astronomers can even go a step further to measure the direction this light is oscillating by measuring the angle of the light that reaches the telescope. Because the polarized light leaves the source in a predictable fashion – namely perpendicular from its magnetic field – knowing the angle of the oscillating light provides information about the axis of rotation and potentially even the surface structure of objects such as neutron stars and nebulae.

In this demonstration, the rope represents light waves and the open window represents a polarimeter. Depending on the angle of the light waves (rope), more or less information makes it through the polarimeter (window) the narrower it is. By measuring the amount of light received through the polarimeter, IXPE can determine the angle and the polarization of the light. Image credit: NASA/JPL-Caltech | + Expand image

Imagine, for example, that you were holding one end of a piece of rope secured to an object at the other end. If you swung the rope side to side to make horizontal waves, those waves would be able to make it through a narrow target like a window. If you started to shut the window from the top, narrowing the opening, the waves could conceivably still make it through the opening. However, if you made veritcal waves by waving the rope up and down, as the window closed, fewer and fewer waves would make it through the opening. Likewise, by measuring the light that makes it through the polarimeter to the detector on the other side, IXPE can determine the angle of the light received.

To collect this light, IXPE uses three identical mirrors at the end of a four meter (13 foot) boom. The light received by IXPE is carefully focused on the spacecraft’s polarimeter at the other end of the boom, allowing scientists to collect those crucial measurements.

During the IXPE launch broadcast, commentators discuss the components of the spacecraft and how it measures polarization. | Watch on YouTube

### Why It's Important

Building on Chandra's observations from the past two decades, IXPE's novel approach to X-ray science is pulling the curtain back even farther on some of the most fascinating objects in the universe, providing first looks at how and where radiation is being produced in some of the most extreme environments in the universe. IXPE's measurements of Cas A are just the beginning, with even more mysterious targets ready to be explored.

Take it from Martin Weisskopf, the principal scientist on IXPE and project scientist for Chandra, who has spent his 50-year career working in X-ray astronomy, who says, “IXPE will open up the field in ways we’ve been stuck only theorizing about."

### Teach It

Explore more on how NASA uses light to map our universe, and dig deeper into some of the celestial features it allows to study, such as blackholes and neutron stars.

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NASA's Universe of Learning materials are based upon work supported by NASA under award number NNX16AC65A to the Space Telescope Science Institute, working in partnership with Caltech/IPAC, Center for Astrophysics | Harvard & Smithsonian, and the Jet Propulsion Laboratory.

TAGS: Universe, Stars and Galaxies, Space Telescope, IXPE, Astronomy, Science, Electromagnetic Spectrum

Find out more about the historic first test, which could be used to defend our planet if a hazardous asteroid were discovered. Plus, explore lessons to bring the science and engineering of the mission into the classroom.

Update: Oct. 20, 2022 – The DART spacecraft successfully impacted the asteroid Dimorphos on September 26, reducing the period of the asteroid's orbit by 32 minutes. Scientists considered a change of 73 seconds to be the minimum amount for success. This article has been updated to reflect the latest data and images from the impact.

In a successful attempt to alter the orbit of an asteroid for the first time in history, NASA crashed a spacecraft into the asteroid Dimorphos on Sept. 26, 2022. The mission, known as the Double Asteroid Redirection Test, or DART, took place at an asteroid that posed no threat to our planet. Rather, it was an ideal target for NASA to test an important element of its planetary defense plan.

Read further to learn about DART, how it worked, and how the science and engineering behind the mission can be used to teach a variety of STEM topics.

### Why It's Important

The vast majority of asteroids and comets are not dangerous, and never will be. Asteroids and comets are considered potentially hazardous objects, or PHOs, if they are 100-165 feet (30-50 meters) in diameter or larger and their orbit around the Sun comes within five million miles (eight million kilometers) of Earth’s orbit. NASA's planetary defense strategy involves detecting and tracking these objects using telescopes on the ground and in space. In fact, NASA’s Center for Near Earth Object Studies, or CNEOS, monitors all known near-Earth objects to assess any impact risk they may pose. Any relatively close approach is reported on the Asteroid Watch dashboard.

NASA's Planetary Defense Coordination Office runs a variety of programs and initiatives aimed at detecting and responding to threats from potentially hazardous objects, should one be discovered. The DART mission is one component and the first mission being flown by the team. Image credit: NASA | + Expand image

While there are no known objects currently posing a threat to Earth, scientists continue scanning the skies for unknown asteroids. NASA is actively researching and planning for ways to prevent or reduce the effects of a potential impact, should one be discovered. The DART mission was the first test of such a plan – in this case, whether it was possible to divert an asteroid from its predicted course by slamming into it with a spacecraft.

Eyes on Asteroids is a real-time visualization of every known asteroid or comet that is classified as a near-Earth object, or NEO. Asteroids are represented as blue dots and comets as shown as white dots. Use your mouse to explore the interactive further and learn more about the objects and how we track them. Credit: NASA/JPL-Caltech | Explore the full interactive

With the knowledge gained from the demonstration, similar techniques could be used in the future to deflect an asteroid or comet away from Earth if it were deemed hazardous to the planet.

### How It Worked

With a diameter of about 525 feet (160 meters) – the length of 1.5 football fields – Dimorphos is the smaller of two asteroids in a double-asteroid system. Before DART's impact, Dimorphos orbited the larger asteroid called Didymos (Greek for "twin"), every 11 hours and 55 minutes.

The sizes of the two asteroids in the Didymos system relative to objects on Earth. Image credit: NASA/Johns Hopkins APL | + Expand image

Neither asteroid poses a threat to our planet, which is one reason why this asteroid system was the ideal place to test asteroid redirection techniques. At the time of DART's impact, the asteroid pair was 6.8 million miles (11 million kilometers) away from Earth as they traveled on their orbit around the Sun.

The DART spacecraft was designed to collide head-on with Dimorphos to alter its orbit, shortening the time it takes the small asteroid to travel around Didymos. Compared with Dimorphos, which has a mass of about 11 billion pounds (five billion kilograms), the DART spacecraft was light. It weighed just 1,210 pounds (550 kilograms) at the time of impact. So how did such a light spacecraft affect the orbit of a relatively massive asteroid?

You can use your mouse to explore this interactive view of DART's impact with Dimorphos from NASA's Eyes on the Solar System. Credit: NASA/JPL-Caltech | Explore the full interactive

DART was designed as a kinetic impactor, meaning it transferred its momentum and kinetic energy to Dimorphos upon impact, altering the asteroid's orbit in return. Scientists were able to make predictions about some of these effects thanks to principles described in Newton's laws of motion.

Newton’s first law told us that the asteroid’s orbit would remain unchanged until something acted upon it. Using the formula for linear momentum (p = m * v), we could calculate that the spacecraft, which at the time of impact would be traveling at 3.8 miles (6.1 kilometers) per second, would have about 0.5% of the asteroid’s momentum. The momentum of the spacecraft may seem small in comparison, but calculations suggested it would be enough to make a detectable change in the speed of Dimorphos' orbit. However, mission planners felt that changing Dimorphos’ orbit by at least 73 seconds would be enough to consider the test a success.

But there was more to consider in testing whether the technique could be used in the future for planetary defense. For example, the formula for kinetic energy (KE = 0.5 * m * v2) tells us that a fast moving spacecraft possesses a lot of energy.

When DART hit the surface of the asteroid, its kinetic energy was 10 billion joules! A crater was formed and material known as ejecta was blasted out as a result of the impact. Scientists are still studying the data returned from the mission to determine the amount of material ejected out of the crater, but estimates prior to impact put the number at 10-100 times the mass of the spacecraft itself. The force needed to push this material out was then matched by an equal reaction force pushing on the asteroid in the opposite direction, as described by Newton’s third law.

This animation shows conceptually how DART's impact is predicted to change Dimorphos' orbit from a larger orbit to a slightly smaller one that's several minutes shorter than the original. Credit: NASA/Johns Hopkins APL/Jon Emmerich | Watch on YouTube

How much material was ejected and its recoil momentum is still unknown. A lot depends on the surface composition of the asteroid, which scientists are still investigating. Laboratory tests on Earth suggested that if the surface material was poorly conglomerated, or loosely formed, more material would be blasted out. A surface that was well conglomerated, or densely compacted, would eject less material.

After the DART impact, scientists used a technique called the transit method to see how much the impact changed Dimorphos' orbit. As observed from Earth, the Didymos pair is what’s known as an eclipsing binary, meaning Dimorphos passes in front of and behind Didymos from our view, creating what appears from Earth to be a subtle dip in the combined brightness of the pair. Scientists used ground-based telescopes to measure this change in brightness and calculate how quickly Dimorphos orbits Didymos. By comparing measurements from before and after impact, scientists determined that the orbit of Dimorphos had slowed by 32 minutes to 11 hours and 23 minutes.

The green circle shows the location of the Dimorphos asteroid, which orbits the larger asteroid, Didymos, seen here as the bright line across the middle of the images. The blue circle shows where Dimorphos would have been had its orbit not changed due to NASA’s DART mission purposefully impacting the smaller asteroid on Sept. 26, 2022. The images were obtained from the NASA Jet Propulsion Laboratory’s Goldstone planetary radar in California and the National Science Foundation’s Green Bank Observatory in West Virginia. Image credit: NASA/Johns Hopkins APL/JPL/NASA JPL Goldstone Planetary Radar/National Science Foundation’s Green Bank Observatory | + Expand image | › DART image gallery

One of the biggest challenges of the DART mission was navigating a small spacecraft to a head-on collision with a small asteroid millions of miles away. To solve that problem, the spacecraft was equipped with a single instrument, the DRACO camera, which worked together with an autonomous navigation system called SMART Nav to guide the spacecraft without direct control from engineers on Earth. About four hours before impact, images captured by the camera were sent to the spacecraft's navigation system, allowing it to identify which of the two asteroids was Dimorphos and independently navigate to the target.

A composite of 243 images of Didymos and Dimorphos taken by the DART spacecraft's DRACO camera on July 27, 2022, as the spacecraft was navigating to its target. Image credit: JPL DART Navigation Team | + Expand image | › DART image gallery

DART was not just an experimental asteroid impactor. The mission also used cutting-edge technology never before flown on a planetary spacecraft and tested new technologies designed to improve how we power and communicate with spacecraft.

Learn more about the engineering behind the DART mission, including the innovative Roll Out Solar Array and NEXT-C ion propulsion system, in this video featuring experts from the mission. Credit: APL | Watch on YouTube

One such technology that was first tested on the International Space Station and was later used on the solar-powered DART spacecraft, is the Roll Out Solar Array, or ROSA, power system. As its name suggests, the power system consisted of flexible solar panel material that was rolled up for launch and unrolled in space.

The Roll Out Solar Array, shown in this animated image captured during a test on the International Space Station, is making its first planetary journey on DART. Image credit: NASA | + Expand image

Some of the power generated by the solar array was used for another innovative technology, the spacecraft's NEXT-C ion propulsion system. Rather than using traditional chemical propulsion, DART was propelled by charged particles of xenon pushed from its engine. Ion propulsion has been used on other missions to asteroids and comets including Dawn and Deep Space 1, but DART's ion thrusters had higher performance and efficiency.

In the days following the event, NASA received images of the impact from a cubesat, LICIACube, that was deployed by DART before impact. The cubesat, which was provided by the Italian Space Agency, captured images of the impact and the ejecta cloud.

This image from LICIACube shows plumes of ejecta streaming from Dimorphos after DART's impact. Each rectangle represents a different level of contrast to better see fine structure in the plumes. By studying these streams of material, scientists will be able to learn more about the asteroid and the impact process. | + Expand image | › DART image gallery

Meanwhile, the James Webb Space Telescope, the Hubble Space Telescope, and the Lucy spacecraft observed Didymos to monitor how soon reflected sunlight from the ejecta plume could be seen. Going forward, DART team members will continue observing the asteroid system to measure the change in Dimorphos’ orbit and determine what happened on its surface. And in 2024, the European Space Agency plans to launch the Hera spacecraft to conduct an in-depth post-impact study of the Didymos system.

This animation, a timelapse of images from NASA’s James Webb Space Telescope, covers the time spanning just before DART's impact at 4:14 p.m. PDT (7:14 p.m. EDT) on Septtember 26 through 5 hours post-impact. Plumes of material from a compact core appear as wisps streaming away from where the impact took place. An area of rapid, extreme brightening is also visible in the animation. Image credit: Science: NASA, ESA, CSA, Cristina Thomas (Northern Arizona University), Ian Wong (NASA-GSFC); Joseph DePasquale (STScI) | + Expand image | › DART image gallery

Continue following along with all the science from DART, including the latest images and updates on the mission website. Plus, explore even more resources on this handy page.

### Teach It

The mission is a great opportunity to engage students in the real world applications of STEM topics. Start exploring these lessons and resources to get students engaging in STEM along with the mission.

#### Resources for Kids

Check out these related resources for kids from NASA Space Place:

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TAGS: Asteroids and Comets, DART, near-Earth objects, planetary defense, Science, K-12 Education, Teachers, Educators, Parents, Teachable Moments

There’s no better time to learn about the Moon than during a lunar eclipse. Here’s how eclipses work, what to expect, and how to get students engaged.

This article has been updated to include information about the visibility and timing of the total lunar eclipse on Nov. 8, 2022. See What to Expect for details.

A full moon is always a good reason to go outside and look up, but a total or partial lunar eclipse is an awe-inspiring site that gives students a great opportunity to engage in practical sky watching. Whether it’s the Moon's reddish hue during a total lunar eclipse or the "bite" taken out of the Moon during a partial lunar eclipse, there's always something exciting to observe during these celestial events.

Read on to see what to expect during the next lunar eclipse. Plus, explore resources you can use at home or in the classroom to teach students about moon phases, craters, and more!

### How It Works

These side-by-side graphics show how the Moon, Sun, and Earth align during a lunar eclipse (left) versus a non-eclipse full moon (right). Credit: NASA Goddard Visualization Studio | + Enlarge image

Eclipses can occur when the Sun, the Moon and Earth align. Lunar eclipses can only happen during the full moon phase, when the Moon and the Sun are on opposite sides of Earth. At that point, the Moon could move into the shadow cast by Earth, resulting in a lunar eclipse. However, most of the time, the Moon’s slightly tilted orbit brings it above or below the shadow of Earth.

The time period when the Moon, Earth and the Sun are lined up and on the same plane – allowing for the Moon to pass through Earth’s shadow – is called an eclipse season. Eclipse seasons last about 34 days and occur just shy of every six months. When a full moon occurs during an eclipse season, the Moon travels through Earth’s shadow, creating a lunar eclipse.

When a full moon occurs during an eclipse season, the Moon travels through Earth's shadow, creating a lunar eclipse. Credit: NASA/JPL-Caltech | + Enlarge image

Unlike solar eclipses, which require special glasses to view and can only be seen for a few short minutes in a very limited area, a total lunar eclipse can last over an hour and be seen by anyone on the nighttime side of Earth – as long as skies are clear!

### Why It’s Important

Lunar eclipses have long played an important role in understanding Earth and its motions in space.

In ancient Greece, Aristotle noted that the shadows on the Moon during lunar eclipses were round, regardless of where an observer saw them. He realized that only if Earth were a spheroid would its shadows be round – a revelation that he and others had many centuries before the first ships sailed around the world.

Earth wobbles on its axis like a spinning top that’s about to fall over, a phenomenon called precession. Earth completes one wobble, or precession cycle, over the course of 26,000 years. Greek astronomer Hipparchus made this discovery by comparing the position of stars relative to the Sun during a lunar eclipse to those recorded hundreds of years earlier. A lunar eclipse allowed him to see the stars and know exactly where the Sun was for comparison – directly opposite the Moon. If Earth didn’t wobble, the stars would appear to be in the same place they were hundreds of years earlier. When Hipparchus saw that the stars’ positions had indeed moved, he knew that Earth must wobble on its axis!

Additionally, modern-day astronomers have used ancient eclipse records and compared them with computer simulations. These comparisons helped scientists determine the rate at which Earth’s rotation is slowing.

### What to Expect

The Moon passes through two distinct parts of Earth’s shadow during a lunar eclipse. The outer part of the cone-shaped shadow is called the penumbra. The penumbra is less dark than the inner part of the shadow because it’s penetrated by some sunlight. (You have probably noticed that some shadows on the ground are darker than others, depending on how much outside light enters the shadow; the same is true for the outer part of Earth’s shadow). The inner part of the shadow, known as the umbra, is much darker because Earth blocks additional sunlight from entering the umbra.

Here's what to expect during the total lunar eclipse on Nov. 8, 2022, which will be visible in North and South America, as well as Asia and Australia. Viewers in the most eastern parts of the continental U.S. will see the Moon set below the horizon as it exits Earth’s shadow in the second half of the eclipse.

At 12:02 a.m. PST (3:02 a.m. EST), the edge of the Moon will begin entering the penumbra. The Moon will dim very slightly for the next 67 minutes as it moves deeper into the penumbra. Because this part of Earth’s shadow is not fully dark, you may only notice some dim shading (if anything at all) on the Moon near the end of this part of the eclipse. Should you decide to skip this part of the eclipse, you won’t miss much.

During a total lunar eclipse, the Moon first enters into the penumbra, or the outer part of Earth's shadow, where the shadow is still penetrated by some sunlight. Credit: NASA | + Enlarge image

At 1:09 a.m. PST (4:09 a.m. EST), the edge of the Moon will begin entering the umbra. As the Moon moves into the darker shadow, significant darkening will be noticeable. Some say that during this part of the eclipse, the Moon looks as if it has had a bite taken out of it. That “bite” gets bigger and bigger as the Moon moves deeper into the shadow.

As the Moon starts to enter into the umbra, the inner and darker part of Earth's shadow, it appears as if a bite has been taken out of the Moon. This "bite" will grow until the Moon has entered fully into the umbra. Credit: NASA | + Enlarge image

At 2:16 a.m. PST (5:16 a.m. EST), the Moon will be completely inside the umbra, marking the beginning of the total lunar eclipse, also known as totality.

The total lunar eclipse starts once the moon is completely inside the umbra. And the moment of greatest eclipse happens with the Moon is halfway through the umbra as shown in this graphic. Credit: NASA | + Enlarge image

The moment of greatest eclipse, when the Moon is halfway through its path across the umbra, occurs at 2:59 a.m. PST (5:59 a.m. EST). As the Moon moves completely into the umbra – the part of the eclipse known as totality – something interesting happens: The Moon begins to turn reddish-orange. The reason for this phenomenon? Earth’s atmosphere. As sunlight passes through it, the small molecules that make up our atmosphere scatter blue light, which is why the sky appears blue. This leaves behind mostly red light that bends, or refracts, into Earth’s shadow. We can see the red light during an eclipse as it falls onto the Moon in Earth’s shadow. This same effect is what gives sunrises and sunsets a reddish-orange color.

As the Moon moves completely into the umbra, it turns a reddish-orange color. Credit: NASA | + Enlarge image

A variety of factors affect the appearance of the Moon during a total lunar eclipse. Clouds, dust, ash, photochemical droplets and organic material in the atmosphere can change how much light is refracted into the umbra. The potential for variation provides a great opportunity for students to observe and classify the lunar eclipse based on its brightness. Details can be found below in the Teach It section.

At 3:41 a.m. PST (6:41 a.m. EST), the edge of the Moon will begin exiting the umbra and moving into the opposite side of the penumbra, reversing the “bite” pattern seen earlier. At this point, the Moon will have just set in the most northeastern portions of the continental United States. More and more eastern states will see the Moon set over the next hour as the eclipse progresses.

At 4:49 a.m. PST, the Moon will be completely outside of the umbra and no longer visible in the eastern United States. Those in the central United States will see the Moon begin setting around this time (6:49 a.m. CST). The Moon will continue exiting the penumbra until the eclipse officially ends at 5:56 a.m. PST, remaining visible only to viewers in the western United States, including many in the Mountain Time Zone one hour ahead.

### Teach It

Ask students to observe the lunar eclipse and evaluate the Moon’s brightness using the Danjon Scale of Lunar Eclipse Brightness. The Danjon scale illustrates the range of colors and brightness the Moon can take on during a total lunar eclipse and is a tool observers can use to characterize the appearance of an eclipse. View the lesson guide here. After the eclipse, have students compare and justify their evaluations of the eclipse.

Use these standards-aligned lessons and related activities to get your students excited about the eclipse, moon phases, and Moon observations.

### Explore More

TAGS: Lunar Eclipse, Moon, Super Blue Blood Moon, Observe the Moon, Eclipse, K-12, Classroom Activities, Teaching