Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.
UPDATE - May 9, 2016: NASA's Solar Dynamics Observatory, or SDO, spacecraft captured stunning images of the May 9, 2016 transit of Mercury. Visit the mission's Transit of Mercury page to see a collection of videos of the transit compiled using SDO images. And have students play "Can You Spot Mercury?" in our educational slideshow.
In the News
It only happens about 13 times per century and hasn’t happened in nearly a decade, but on Monday, May 9, Mercury will transit the sun. A transit happens when a planet crosses in front of a star. From our perspective on Earth, we only ever see two planets transit the sun: Mercury and Venus. (Transits of Venus are even more rare. The next one won't happen until 2117!) On May 9, as Mercury passes in front of the sun, viewers around Earth (using the proper safety equipment) will be able to see a tiny dark spot moving slowly across the disk of the sun.
CAUTION: Looking directly at the sun can cause permanent vision damage – see below for tips on how to safely view the transit.
Why It's Important
Then and Now
In the early 1600s, Johannes Kepler discovered that both Mercury and Venus would transit the sun in 1631. It was fortunate timing: The telescope had been invented just 23 years earlier and the transits wouldn’t happen in the same year again until 13425. Kepler didn’t survive to see the transits, but French astronomer Pierre Gassendi became the first person to see the transit of Mercury (the transit of Venus wasn’t visible from Europe). It was soon understood that transits could be used as an opportunity to measure the apparent diameter – how large a planet appears from Earth – with great accuracy.
In 1677, Edmond Halley observed the transit of Mercury and realized that the parallax shift of the planet – the variation in Mercury’s apparent position against the disk of the sun as seen by observers at distant points on Earth – could be used to accurately measure the distance between the sun and Earth, which wasn’t known at the time.
Today, radar is used to measure the distance between Earth and the sun with greater precision than can be found using transit observations, but the transit of Mercury still provides scientists with opportunities for scientific investigation in two important areas: exospheres and exoplanets.
Some objects, like the moon and Mercury, were originally thought to have no atmosphere. But scientists have discovered that these bodies are actually surrounded in an ultra-thin atmosphere of gases called an exosphere. Scientists want to better understand the composition and density of the gases that make up Mercury’s exosphere and transits make that possible.
“When Mercury is in front of the sun, we can study the exosphere close to the planet,” said NASA scientist Rosemary Killen. “Sodium in the exosphere absorbs and re-emits a yellow-orange color from sunlight, and by measuring that absorption, we can learn about the density of gas there.”
When Mercury transits the sun, it causes a slight dip in the sun’s brightness as it blocks a tiny portion of the sun's light. Scientists discovered they could use that phenomenon to search for planets orbiting distant stars, called exoplanets, that are otherwise obscured from view by the light of the star. When measuring the brightness of far-off stars, a slight recurring dip in the light curve (a graph of light intensity) could indicate an exoplanet orbiting and transiting its star. NASA’s Kepler mission has found more than 1,000 exoplanets by looking for this telltale drop in brightness.
Additionally, scientists have begun exploring the exospheres of exoplanets. By observing the spectra of the light that passes through an exosphere – similar to how we study Mercury’s exosphere – scientists are beginning to understand the evolution of exoplanet atmospheres as well as the influence of stellar wind and magnetic fields.
Mercury will appear as a tiny dot on the sun’s surface and will require a telescope or binoculars with a special solar filter to see. Looking at the sun directly or through a telescope without proper protection can lead to serious and permanent vision damage. Do not look directly at the sun without a solar filter.
The transit of Mercury will begin at 4:12 a.m. PDT, meaning by the time the sun rises on the West Coast, Mercury will have been transiting the sun for nearly two hours. Fortunately, it will take seven and a half hours for Mercury to completely cross the sun’s face, so there will be plenty of time for West Coast viewers to witness this event. See the transit map to learn when and where the transit will be visible.
Don’t have access to a telescope, binoculars or a solar filter? Visit the Night Sky Network website for the location of events near you where amateur astronomers will have viewing opportunities available.
NASA also will stream a live program on NASA TV and the agency’s Facebook page from 7:30 to 8:30 a.m. PDT (10:30 to 11:30 a.m. EDT) -- an informal roundtable during which experts representing planetary, heliophysics and astrophysics will discuss the science behind the Mercury transit. Viewers can ask questions via Facebook and Twitter using #AskNASA.
Here are two ways to turn the transit of Mercury into a lesson for students.
- Exploring Exoplanets with Kepler - Students use math concepts related to transits to discover real-world data about Mercury, Venus and planets outside our solar system.
- Pi in the Sky 3 - Try the "Sun Screen" problem on this illustrated math problem set that has students calculate the percentage drop in sunlight reaching Earth when Mercury transits.
- NASA TV (live transit coverage)
- NASA Transit Website (near real-time images of the transit)
- Night Sky Network Events
- Video: What’s Up – May 2016
- Transit Map
- Solar System Transits
- NASA Museum Alliance Resources
- Kepler Mission Website
- Exoplanet Exploration Website
- Eyes on Exoplanets Interactive
- Exoplanet Travel Bureau Posters
- Video: What’s in an Exoplanet Name?
- Video: The Search for Another Earth
- Kepler Education Activities
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.
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 Does It Work?
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.
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.› See the lesson!
This lesson meets the following Next Generation Science and Common Core Math Standards:
- MS-PS2-2: Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.
- HS-PS2-1: Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
- HS-PS2-1: Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.
Common Core Math Standards:
Grade 8: Expressions and Equations A.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
High School: Algebra CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
High School: Functions LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.
High School: Functions BF.A.1: Write a function that describes a relationship between two quantities.
High School: Statistics and Probability ID.C: Interpret linear Models
High School: Number and Quantity Q.A.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays."
- Website: Dawn Mission
- Blog: Dawn Journal
- Video: Crazy Engineering - Ion Propulsion
- Ion propulsion interactives
- Eyes on the Solar System: Dawn Mission Tour (scroll to "Solar System Tours" and click the "Dawn" link)
In the News
A century ago, Albert Einstein theorized that when objects move through space they create waves in spacetime around them. These gravitational waves move outward, like ripples from a stone moving across the surface of a pond. Little did he know that 1.3 billion years earlier, two massive black holes collided. The collision released massive amounts of energy in a fraction of a second (about 50 times as much as all of the energy in the visible universe) and sent gravitational waves in all directions. On September 14, 2015 those waves reached Earth and were detected by researchers at the Laser Interferometer Gravitational-Wave Observatory (LIGO).
Why It's Important
Einstein published the Theory of General Relativity in 1915. In it, he predicted the existence of gravitational waves, which had never been directly detected until now. In 1974, physicists discovered that two neutron stars orbiting each other were getting closer in a way that matched Einstein’s predictions. But it wasn’t until 2015, when LIGO’s instruments were upgraded and became more sensitive, that they were able to detect the presence of actual gravitational waves, confirming the last important piece of Einstein’s theory.
It's also important because gravitational waves carry information about their inception and about the fundamental properties of gravity that can’t be seen through observations of the electromagnetic spectrum. Thanks to LIGO’s discovery, a new field of science has been born: gravitational wave astronomy.
How They Did It
LIGO consists of facilities in Washington and Louisiana. Each observatory uses a laser beam that is split and sent down 2.5-mile (4-kilometer) long tubes. The laser beams precisely indicate the distance between mirrors placed at the ends of each tube. When a gravitational wave passes by, the mirrors move a tiny amount, which changes the distance between them. LIGO is so sensitive that it can detect a change smaller than 1/10,000 the width of a proton (10-19 meter). Having two observatories placed a great distance apart allows researchers to approximate the direction the waves are coming from and confirm that the signal is coming from space rather than something nearby (such as a heavy truck or an earthquake).
Creating a model that demonstrates gravitational waves traveling through spacetime is as simple as making a gelatin universe!
Middle school students can develop a model that shows gravitational waves traveling through spacetime while working toward the following Next Generation Science Standard:
- MS-PS4-2 - Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.
- Gravitational waves news, videos and resources
- Laser Interferometer Gravitational-Wave Observatory (LIGO) Website
This post was originally published on March 9, 2016
In the News
Pi Day, the informal holiday beloved by math enthusiasts – and even by the math averse – is almost here! March 14 marks the yearly celebration of the mathematical constant (pi), which represents the ratio of a circle’s circumference to its diameter. More than just a number for mathematicians, pi has all sorts of applications in the real world, including on missions developed by NASA’s Jet Propulsion Laboratory. And as a holiday that encourages more than a little creativity – whether it’s making pi-themed pies or reciting from memory as many of the never-ending decimals of pi as possible (the record is 70,030 digits) – it’s a great way to have fun and celebrate the M in STEM.
Why March 14?
Pi is what’s known as an irrational number, meaning its decimal representation never ends and it never repeats. It has been calculated to more than one trillion digits, but 3.14 is often a precise enough approximation, hence the celebration occurring on March 14, or 3/14 (when written in US month/day format). The first known celebration occurred in 1988, and in 2009, the US House of Representatives passed a resolution designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi.
Why It’s Important
Pi Day is lots of fun, but its importance lies in the role that pi plays in the everyday work of scientists and engineers at JPL.
Fred Calef, a geospatial information scientist at JPL, uses pi to make measurements – like perimeter, area and volume – of features on Mars. “I use pi to measure the circularity of features, or how round or compact they are," said Calef. "Craters become more elliptical if the projectile hits the surface at a lower angle, so I use pi to measure how round a crater is to see if it impacted at a low angle.”
"We use pi every day commanding rovers on Mars," said Hallie Gengl, a rover planner for the Mars Exploration Rover Opportunity, "Everything from taking images, turning the wheels, driving around, operating the robotic arm, and even talking to Earth.”
Bryana Henderson, who specializes in planetary ices, uses lasers to explode ice samples and study their composition. "I use pi to calculate the width of my laser beam, which in turn can be used to calculate the amount of energy, or fluence, that hits my ice sample," said Henderson. "A larger fluence equals a bigger explosion in the ice, so this is a very important parameter for us."
The Pi Day Challenge
JPL has released the third installment of its popular Pi Day challenge, which gives students and the public a chance to put their pi skills to the test to solve some of the same problems NASA scientists and engineers do. The set of four illustrated math problems are compiled into a graphic (as well as classroom handouts) designed for students in grade 4 through high school – but fun for all!
› Check out this year's Pi Day challenge!
This year’s problem set shows how pi can be used to map the surface of Saturn’s hazy moon Titan, track the Mars Reconnaissance Orbiter as it explores the Red Planet, keep Earth’s satellites powered as Mercury transits the sun, and put the Juno spacecraft into orbit around Jupiter.
“For Pi Day, we like to give students and the public a glimpse into how math is used at JPL through questions that feature current events involving our space missions,” said Ota Lutz, an education specialist at JPL who helped create the problem set. “For instance, to put the Juno spacecraft into orbit around Jupiter on July 4, engineers will have to slow the spacecraft just the right amount. In the Pi Day challenge, students use pi to calculate that change in velocity.”
In the challenge, students will also use pi to calculate how much sunlight is blocked by our solar system’s innermost planet as it passes between Earth and the sun. This year, Pi Day comes just a few months before the May 9 transit of Mercury, making this a timely problem.
On March 16, the answers to all four problems and the steps needed to find those answers will be released in a companion infographic on the Pi Day challenge activity page.
In addition to the Pi Day challenge, JPL is inviting the public to share their Pi Day pictures and stories online. On March 14, JPL will join in on the fun with Pi Day photos and stories from the lab.› Share Your Pi Day photos and stories
To see a compilation of all 12 Pi Day challenge questions optimized for mobile devices and screen readers, visit: http://www.jpl.nasa.gov/edu/nasapidaychallenge
Pi Day Challenges
Facts and Figures
In the News
NASA’s Juno mission, the first solar-powered mission to Jupiter, has become the farthest solar-powered spacecraft ever! Juno, and its eight science instruments designed to study the interior of Jupiter, has passed the mark previously held by the European Space Agency’s Rosetta mission and reached a distance of 5.3 astronomical units from the sun (an astronomical unit is equal to the average distance between Earth and the sun – about 149.6 million kilometers). Using only power from the sun, Juno will complete the five-year trip to Jupiter in July 2016 and begin studying the solar system’s most massive world in an attempt to better understand the origins of the planet, and in turn, our solar system.
What Made It Possible
Just as a bright source of light dims as you move away from it, sunlight becomes less intense the farther a spacecraft travels from the sun, limiting the amount of power that can be generated using solar cells. Previous missions that visited Jupiter, like Galileo, Voyager 1 and Voyager 2, couldn’t use solar power and instead used radioisotope thermoelectric generators (RTGs) to supply power.
Advances in solar panel efficiency along with improvements in the way spacecraft and their instruments use power have recently made solar power a viable option for spacecraft heading as far as Jupiter – though going beyond will require further technological advances.
Engineers designed Juno with three massive solar panels, each nearly 30 feet long. Combined, they provide Juno with 49.7 m2 of active solar cells. Once it reaches Jupiter, Juno will generate more than 400 watts of power, which may not sound like a lot, but it’s an impressive feat at so great a distance. For comparison, Juno’s solar panels can generate about 14 kilowatts near Earth.
Juno's record-setting achievement translates into a powerful lesson in exponents.
Middle school students and other students working with exponents will find challenging, real-world applications related to the work being done here at NASA while addressing four Common Core Math standards:
- Grade 6: Expressions and Equations A.1 - "Write and evaluate numerical expressions involving whole-number exponents."
- Grade 6: Expressions and Equations A.2 - "Write, read, and evaluate expressions in which letters stand for numbers."
- Grade 6: Expressions and Equations A.2.C - "Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)."
- Grade 8: Expressions and Equations A.1 - "Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27."
- Juno mission website - News, resources and updates on NASA's mission to Jupiter.
- Eyes on the Solar System - Take a virtual journey to Jupiter with Juno (scroll to "Solar System Tours" and click on Juno).
- To Jupiter with JunoCam! - Find out how classrooms can participate in the Juno mission to Jupiter using the spacecraft's on-board educational camera.
- Infographic: Solar Power Explorers - This graphic shows how NASA’s Juno mission to Jupiter became the most distant solar-powered explorer and influenced the future of space exploration powered by the sun.
Yesterday, NASA announced that it will open the application process to select its next class of astronauts on December 14. That news has gotten a lot of people very excited, including some of the best engineers and scientists at NASA's Jet Propulsion Laboratory. Most people don't think of JPL when they think of astronauts, but everywhere astronauts have been, JPL has sent spacecraft ahead of time. That was true for astronauts in Earth orbit and walking on the moon, and will continue to be true when humans visit a near-Earth asteroid and eventually Mars. But it's not just the idea of sending robots to explore new places in preparation for human visits that is exciting. Some of these scientists and engineers want to be astronauts too!
Maybe you've been following the exploration of Mars by the Curiosity and Opportunity rovers, or maybe you've been watching as we've discovered more and more near-Earth asteroids. Whatever your inspiration has been, you know you want to become an astronaut.
So how do you get there, and what can you do to make it possible?
Let's start with the basic requirements:
- Bachelor's degree in a STEM field
- Three years of related professional experience
- Pass the NASA astronaut physical
Not every STEM (science, technology, engineering and math) degree will qualify you to be an astronaut. NASA is looking for people with a degree in engineering, biological science, physical science (like physics, chemistry or geology) or mathematics. If you're in high school, middle school or even elementary school, now is a great time to explore all of these fields of study to help you better understand the ones you like most, the ones for which you might have a natural talent, and even the ones you don't find as interesting.
How do you explore these fields?
If you have the ability to choose your elective classes, take the challenging math, science and computer programming courses. This will help you to learn the fundamentals of science and math. If your school doesn't offer those classes, look online. There are many free online courses covering a wide range of math, science and programming topics.
What else can you do?
- Join a school or community math, science, engineering or robotics club. If there are none in your school or community, start one!
- Participate in science and engineering fairs. (There is a great "how to" video series to help you develop your project here.)
- Attend maker fairs and develop the skills to design solutions to a variety of problems.
- Apply for an internship at JPL or NASA. You can apply for opportunities as early as the spring of your senior year in high school when you have been accepted to a college or university as a STEM major.
These are some of the steps you can take to better prepare yourself as you enter college. They just happen to be some of the same types of things many JPL scientists and engineers did before starting their college careers that led them to a job with NASA.
- Five Myths About Becoming an Astronaut
- NASA Astronauts Website
- How to Apply to be an Astronaut
- USA Jobs website - Job posting and application will be available Dec. 14, 2015
In the News
Saturn’s icy moon Enceladus has been making news lately, and it could make even bigger news soon! In September, scientists confirmed that there was a global ocean underneath Enceladus’ thick icy shell. That was just the latest in a long history of exciting finds dating back to the beginning of NASA’s Cassini-Huygens Mission to Saturn in 2004 that have helped scientists to better understand this fascinating world!
Even while Cassini was still on its way to Saturn, its Cosmic Dust Analyzer detected microscopic grains of silica (tiny grains of sand). On Earth, grains of silica similar in size to those detected near Saturn form when hydrothermal activity -- the processes involving heated water beneath Earth’s surface or ocean -- causes salty water to chemically interact with rocky material to form silica. But where were these grains coming from in the space around Saturn?
In 2005, scientists were surprised to find out that Enceladus’ south pole is both warmer than expected and warmer than the surrounding areas, suggesting there is a heat source inside Enceladus. Not only that, but they also discovered long parallel cracks in the ice on Enceladus’ south pole. The young age of these cracks, nicknamed Tiger Stripes, meant that Saturn’s icy moon is a geologically active place.
Another piece of this puzzle was put in place with the discovery of jets of material spraying out of the Tiger Stripes. Studies have shown these jets are composed of mostly of water vapor, tiny ice particles and small amounts of other material (for example, microscopic silica grains). Together, over 100 jets make up a feature called a plume. Investigating further, scientists have hypothesized that these silica grains are the result of hydrothermal activity on the ocean floor below Enceladus’ icy crust.
On October 28, Cassini will fly right through the plume jetting out of Enceladus’ south pole at an altitude of only 49 kilometers (30 miles) – closer than any previous passes directly through the plume! This is an exciting moment in the mission -- one that allows science teams to use a combination of tools on board the spacecraft to strengthen previous findings and potentially make new discoveries.
Why It's Important
Cassini will use its Cosmic Dust Analyzer to study the solid plume particles and an instrument called the Ion and Neutral Mass Spectrometer to “sniff” the gas vapor in order to determine the composition of the jets. Specifically, the latter instrument is looking for H2, or molecular hydrogen. Finding H2 in the plume will strengthen the evidence that hydrothermal activity is occurring on Enceladus’ ocean floor. And the amount of H2 in the plume, will tell scientists just how much activity is happening.
In addition to indicating that hydrothermal activity is taking place, figuring out the amount of hydrothermal activity will give scientists a good indication of how much internal energy there is deep inside Enceladus.
That Cassini is making a pass through the plume at such a low, 49-kilometer-high altitude is also important. Organic compounds -- substances formed when carbon bonds with hydrogen, nitrogen, oxygen, phosphorus or sulfur -- tend to be heavy and would fall out of the plume before reaching the heights of Cassini’s previous, higher altitude flybys and be undetected. Organic compounds are the building blocks of life on Earth. Without them, life as we know it wouldn’t exist. If they are present in Enceladus’ oceans, they could be detected when Cassini passes through the plume on this encounter.
Perhaps more important, though, are the implications of finding hydrothermal activity somewhere other than Earth. It was once believed that all forms of life needed sunlight as a source of energy, but in 1977, the first hydrothermal vent -- essentially an underwater geyser of hot, mineral-rich water -- was discovered and it was teeming with life. The organisms were using the heat and minerals as a source of energy! Some scientists have hypothesized that hydrothermal vents could be where life on our planet first took hold and could represent environments in the solar system with the necessary ingredients to support life.
Here are a handful of lessons and resources you can use to teach key concepts related to the October 28 Enceladus flyby and help your students feel connected to this exciting moment in science at Saturn.
- NGSS 5-ESS2-1 - Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact.
Because scientists can’t dig beneath the ice and see what’s below, they rely on creating models that show what is happening beneath the surface. A model helps us imagine what can’t be seen and explains the things that we can see and measure. A model could be a drawing, a diagram or a computer simulation. For this model, students will draw a cut away model of Enceladus and iterate, or improve, their model as you provide more description, just as scientists improved their models as they learned more about Enceladus.
- Tell students there is a moon around Saturn. They should draw a moon (likely a circle, half-circle, or arc, depending on how big you want the drawing to be).
- Explain to students that the moon is covered in a shell of ice (students will need to modify their model by drawing a layer of ice). Thus far, everything students are modeling is observable by looking at the moon.
- Share with students that temperature measurements of the south pole revealed spots that are warmer than the rest of the moon’s surface. Ask students to brainstorm possible sources of heat at the south pole and explain what might happen to ice near a heat source. Based on this new information, and what they think might be causing the heat, allow them to modify their drawing. (Depending on what students brainstorm, their drawing might now include volcanoes, hot spots, magma, hydrothermal vents and a pool of liquid water beneath the ice).
- The next piece of information the students will need to incorporate into their drawing is that there are large cracks in the ice over the warmer south-pole region.
- Explain that students have now received images that show jets expelling material from the cracks. They will need to incorporate this new data and add it to their drawing.
- Tell students that by studying the gravity of the moon, scientists now believe there is an ocean covering the whole surface of the moon beneath the ice. Ask students to share how they would represent that in the model. Allow them to modify their drawing.
- Show students the following image depicting a model of Enceladus:
This model shows what scientists believe the interior of Enceladus may look like. Have students compare it to what they drew and note similarities and differences.
Particle Travel Rate
- CCSS.MATH 6.RP.A.3.B - - Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Based on the size of the silica grains (6 to 9 nanometers), scientists think they spend anywhere from several months to a few years (a longer time than that means the grains would be larger) traveling from hydrothermal vents to space, a distance of 40 to 50 km.
- What rate (in km/day) are the particles traveling if it takes them 6 months to travel 50 km (assume 182 days)?
50 km ÷ 182 days = 0.27 km/day
- What rate are they traveling if it takes two years to travel 40 km?
40 km ÷ 730 days = 0.05 km/day
- Do you think the particles in each example traveled at the same speed the entire time they moved?
- Why might the particle rate vary?
- At what point in their journey might particles have been traveling at the highest rate?
- CCSS.MATH 6.RP.A.3.B - Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
- CCSS.MATH 8.G.B.7 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Cassini will be flying past Enceladus at a staggering 8.5 km per second (19,014 mph). At an altitude of 49 km, the plume is estimated to be approximately 130 km across.
- How long will Cassini have to capture particles and record data while within the plume?
130 km ÷ 8.5 km/sec ≈ 15 seconds
- If Cassini is 49 km above the surface of Enceladus at the center of the plume, what is its altitude as it enters and exits the plume (the radius of Enceladus is 252.1 km)?
252.1 km + 49 km = 301.1 km
(301.1 km)2 + (65 km)2 ≈ 95,000 km2
√(95,000 km2) ≈ 308 km
≈ 308 km – 252.1 km ≈ 56 km
- This information can help scientists determine where in the plume heavy particles may fall out if they are not detected on the edge of the plume but are detected closer to the middle of the plume. It is also important because the Cosmic Dust Analyzer uses a high-rate detector that can count impacting particles at over 10,000 parts per second to tell us how much material is being sprayed out.
Volume of Enceladus’ Ocean
- CCSS.MATH 8.G.C.9 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- CCSS.MATH HSG.GMD.A.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Gravity field measurements of Enceladus and the wobble in its orbital motion show a 10 km deep ocean beneath a layer of ice estimated to be between 30 km and 40 km thick. If the mean radius of Enceladus is 252.1 km, what is the minimum and maximum volume of water contained within its ocean?
Volume of a sphere = 4⁄3πr3
Minimum volume with a 40 km thick crust
4⁄3 π212.1 km3 - 4⁄3π202.1 km3 ≈ 40,000,000 km3 – 35,000,000 km3 ≈ 5,000,000 km3
Maximum volume with a 30 km thick crust
4⁄3 π222.1 km3 - 4⁄3 π212.1 km3 ≈ 46,000,000 km3 – 40,000,000 km3 ≈ 6,000,000 km3
This is important because if scientists know how much water is in the ocean and how much vapor is escaping through the plume, they can make estimates about how long the plume has existed -- or could continue to exist.
Download the Full Problem Set
- Enceladus flyby information page
- Slideshow and poster: 8 Real World Science Facts About Saturn's Moon Enceladus
- Enceladus facts and figures
- Enceladus images
- Eyes on the Solar System: Enceladus flyby simulation
- Cassini mission overview
In the News
Twenty years after the first discovery of a planet orbiting another sun-like star, scientists have discovered the most Earth-like exoplanet ever: Kepler-452b. Located in the habitable zone of a star very much like our sun, Kepler-452b is only about 60 percent wider than Earth.
What makes it the most Earth-like exoplanet ever discovered?
First a couple definitions: An exoplanet is simply a planet that orbits another star. And the habitable zone? That’s the area around a star in which water has the potential to be liquid -- not so close to the star that all water would evaporate, and not so far that all water would freeze. Think about Goldilocks eating porridge. The habitable zone is not too hot, and not too cold. It’s just right.
Okay, back to Kepler-452b. Out of more than a thousand exoplanets that NASA’s Kepler spacecraft has detected, only 12 have been found in the habitable zone of their stars and are smaller than twice the size of Earth, making Earth-like planets a rarity. Until this discovery, all of them have orbited stars that are smaller and cooler than our sun.
Kepler-452b is the first to be discovered orbiting a star that is about the same size and temperature as our sun. Not only that, but it orbits at nearly the same distance from its star as Earth does from our sun! Conditions on Kepler-452b could be similar to conditions here on Earth and the light you would feel there would be much like the sunlight you feel here on Earth. Scientists believe that Kepler-452b has been in the habitable zone for around six billion years -- longer than Earth has even existed!
How They Did It
The Kepler spacecraft, named for mathematician and astronomer Johannes Kepler, has been working since 2009 to find distant worlds like Kepler-452b. It does so by looking at more than 100,000 stars near the constellation Cygnus. If one of those stars dims temporarily, it could be that an object passed between the spacecraft and the star. If it dims with a repeatable pattern, there’s a good chance an exoplanet is passing by again and again as it orbits the star. The repeated dimming around one of those stars is what led to the discovery of Kepler-452b.
This exciting discovery provides opportunities for students to practice math skills in upper elementary and middle school, and gives high school students a practical application of Kepler’s third law of planetary motion. Take a look below to see where these might fit into your curriculum.
Upper Elementary and Middle School
After learning about Earth’s cousin, students might wonder about a trip to this world. Scientists have calculated the distance between Earth and Kepler-452b at 1,400 light years. A light year is a measure of distance that shows how far light travels in one year. It’s equal to about 10 trillion kilometers (six trillion miles) or, to be more precise, 9,461,000,000,000 kilometers (5,878,000,000,000 miles). Ask students to calculate the distance between Earth and Kepler-452b at various levels of precision, depending on what they are prepared for or learning. For an added challenge, have them determine how long it would take a fast moving spacecraft like Voyager 1 traveling at 61,000 kph (38,000 mph) to reach this new world.
Note: Due to the approximations of spacecraft speed and light year distance used for these problems in both standard and metric units, there is a variation among the answers.
Distance: 10 trillion km x 1,400 = 14,000 trillion km (that’s 14,000,000,000,000,000 kilometers!)
Travel time: 14,000 trillion km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 26,000,000 years
Distance: 6 trillion miles x 1,400 = 8,400 trillion miles (that’s 8,400,000,000,000,000 miles!)
Travel time: 8,400 trillion miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years
or more precisely…
Distance: 9,461,000,000,000 km x 1,400 = 13,245,400,000,000,000 km
Travel time: 13,245,400,000,000,000 km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 25,000,000 years
Distance: 5,878,000,000,000 miles x 1,400 = 8,229,200,000,000,000 miles
Travel time: 8,229,200,000,000,000 miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years
or using exponents and powers of 10…
Distance: 9.461 x 1012 x km x 1.4 x 103 = 1.32454 x 1016 km
Travel time: 1.32454 x 1016 km ÷ 6.1 x 104 kph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years
Distance: 5.878 x 1012 miles x 1.4 x 103 = 8.2292 x 1015 miles
Travel time: 8.2292 x 1015 miles ÷ 3.8 x 104 mph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years
Middle and High School
The time between detected periods of dimming, the duration of the dimming, and the amount of dimming, combined with a little math, can be used to calculate a great deal of information about an exoplanet, such as the length of its orbital period (year), the distance from its star, and its size.
Kepler-452b has an orbital period of 384.84 days -- very similar to Earth’s 365.25 days. Students can use the orbital period to find the distance from its star in astronomical units. An astronomical unit is the average distance between Earth and our Sun, about 150 million kilometers (93 million miles).
Kepler’s 3rd law states that the square of the orbital period is proportional to the cube of the semi-major axis of an ellipse about the sun. For planets orbiting other stars, we can use R = ∛(T2 ∙ Ms) where R = semi-major axis, T = orbital period in Earth years, and Ms = the mass of the star relative to our sun (the star that Kepler-452b orbits has been measured to be 1.037 times the mass of our sun).
T = 384.84 ÷ 365.25 = 1.05
R = ∛(1.052 ∙ 1.037)
R = ∛1.143 = 1.05 AU
- Exoplanet Travel Bureau Posters
- Video: What’s a “habitable zone?”
- Video: What’s in an Exoplanet Name?
Facts and Figures
In the News
We visited Pluto!
On July 14, 2015 at 4:49 a.m. PDT, NASA's New Horizons spacecraft sped past Pluto -- a destination that took nearly nine and a half years to reach -- and collected scientific data along with images of the dwarf planet.
Pluto, famous for once being the ninth planet, was reclassified as a dwarf planet in 2006 after new information emerged about the outer reaches of our solar system. Worlds similar to Pluto were discovered in the region of our solar system known as the Kuiper Belt. The Kuiper Belt --named for astronomer Gerard Kuiper --is a doughnut-shaped area beyond the orbit of Neptune that is home to Pluto, other dwarf planets such as Eris, Makemake, and Haumaea, as well as hundreds of thousands of other large icy bodies, and perhaps trillions of comets orbiting our sun. Over the next several years, the New Horizons spacecraft is expected to visit one to two more Kuiper Belt objects.
Even though it will take 16 months for New Horizons to return all the Pluto science data to Earth, we have already made some interesting and important discoveries about Pluto.
Why It's Important
Through careful measurements of new images, scientists have determined that Pluto is actually larger than previously thought: 2,370 kilometers in diameter. This is important information for scientists because it helps them understand the composition of Pluto. Because of the orbital interactions between Pluto and its moon Charon, Pluto’s mass is well known and understood. Having a more precise diameter gives scientists the ability to more accurately calculate the average density. A greater diameter means Pluto’s density is less than we thought. If you do the math, you’ll see that Pluto’s calculated density dropped from 2,051 kg/m3 to 1,879 kg/m3 with this new finding. Most rock has a density between 2000-3000 kg/m3 and ice at very cold temperatures has a density of 927 kg/m3, so we can conclude that Pluto is a bit more icy than previously believed. In addition to helping scientists calculate the density of Pluto, this measurement confirms Pluto as the largest known object in the Kuiper Belt!
We’ve provided some math problems (and answers) for you to use in the classroom. They’re a great way to provide students with real-world examples of how the math they’re learning in class is used by scientists. There are also some additional resources below that you can use to integrate the Pluto flyby into your lessons, or use the flyby as a lesson opener!
Pluto Math Problems
- Find the radius(r) of Pluto.
2,370 kilometers ÷ 2 = 1,185 km
- Find the circumference of Pluto.
C = 2 π r = 7,446 km
- Find the surface area of Pluto.
SA = 4 π r2 = 17,646,012 km2
- Find the volume of Pluto.
4/3 π r3 = 6,970,174,651 km3
- Find the density of Pluto in kg/m3.
Pluto mass = 1.31 × 1022kg
Convert volume in km3 to m3 × 6,970,174,651 × 1,000,000,000 = 6.970174651 × 1018m3
1.31 × 1022kg / 6.970174651 × 1018m3 = 1,879 kg/m3
- How does this new density calculation compare to the previous calculation (2051 kg/m3) when Pluto’s diameter was thought to be 2,302 km?
Take a look at some of the lessons, videos, activities and interactives related to Pluto. They’re a great way to engage students in STEM and learning more about their solar system!
- Video: What is a Dwarf Planet? (K-12)
Dwarf planets are a lot like regular planets. What’s the big difference? Find out in 60 seconds.
- Activity: Solar System Bead Activity (4-8)
The solar system is big, and Pluto is way out there! Students calculate scale distances to create a model of objects in our solar system.
Next Generation Science Standards: MS-ESS1-3
Common Core Math: 4.MD.A.2, 5.NBT.B.7
- Activity: How Far? How Faint? (9-12)
Calculate how much light Pluto receives from the sun, compared to Earth.
Common Core Math: HSF.IF.C.7.E
- Resource: Pluto Facts and Figures
Get lots of facts and figures about this dwarf planet in the Kuiper belt!
- Interactive: Eyes on Pluto
Ride along with New Horizons in this simulation of its closest approach to Pluto!
- Participate: Pluto Time
Though Pluto is a distant world with very different characteristics from Earth, for just a moment near dawn and dusk each day, you can experience “Pluto Time.” This is when the amount of light reaching Earth matches that of noon on Pluto. Find out exactly when Pluto Time happens in your area and share your photos online!
- News and Images: NASA New Horizons Website
Get the latest news and images from NASA's New Horizons mission.