Teachable Moments | May 1, 2017
May the Force = mass x acceleration
This feature was originally published on May 3, 2016.
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.
Use It in the Classroom
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 in this standards-aligned lesson from NASA/JPL Education.
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.
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.
› See the lesson!This lesson meets the following Next Generation Science and Common Core Math Standards:
NGSS 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."
Explore More
- 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)
TAGS: May the Fourth, Star Wars Day, F=ma, ion propulsion, Dawn, Deep Space 1, lesson, classroom activity, NGSS, Common Core Math
Teachable Moments | March 10, 2017
Celebrate Pi Day Like a NASA Rocket Scientist
UPDATE: March 16, 2017 – An illustrated answer key for the 2017 NASA Pi Day Challenge is now available here.
Were you able to solve these stellar mysteries using pi? Check your answers on our illustrated answer key and download the free "Pi in the Sky^{4}" poster set.
NASA is giving space fans a reason to celebrate Pi Day, the March 14 holiday created in honor of the mathematical constant pi. For the fourth year in a row, the agency’s Jet Propulsion Laboratory has created an illustrated Pi Day Challenge featuring four math problems NASA scientists and engineers must solve to explore space. The challenge is designed to get students excited about pi and its applications beyond the classroom. This year’s problem set, designed for students in grade six through high school – but fun for all – features Mars craters, a total solar eclipse, a close encounter with Saturn, and the search for habitable worlds.
› Take the NASA Pi Day Challenge!
› Educators, get the standards-aligned Pi Day Challenge lesson and download the free poster and handouts. The answers to all four problems will be released in a companion infographic on March 16.
Read on for more about Pi Day, the science behind the 2017 problem set and to learn how NASA scientists and engineers use pi.
Take the NASA Pi Day Challenge
Solve a Martian crater mystery, measure the size of the moon’s shadow during a total solar eclipse, get into a daring orbit around Saturn, and discover potentially habitable worlds beyond our solar system. You don’t have to be a NASA rocket scientist to do stellar math with pi.
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 NASA scientists and engineers actually use far fewer digits in their calculations (see “How Many Decimals of Pi Do We Really Need?”). The approximation 3.14 is often precise enough, 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
While many of us celebrate by eating pi-themed pie and trying to memorize as many digits of pi as possible (the record is 70,030 digits), scientists and engineers at NASA take pi even further, using it in their day-to-day work exploring space!
“Finding the volume of a sphere, area of a circle (and thus volume of a cylinder) are well known applications of pi,” said Charles Dandino, a JPL engineer who designs robots for extreme environments. “But those relationships also form the basis for how stiff a structure is, how it will vibrate, and understanding how a design might fail.”
Rachel Weinberg works on the Orbiting Carbon Observatory 3, or OCO-3, instrument, which will track the distribution of carbon dioxide across Earth. She says pi came in handy during her studies at MIT and still does today for her work at JPL. “Just the other day during a meeting, the team went to the whiteboard and used pi to discuss the angles and dimensions of optical components on OCO-3,” she said.
Pi allows us to calculate the size and area of two- and three-dimensional shapes, says Anita Sengupta, a JPL engineer, who has worked on a variety of planetary missions. “In my career, pi has allowed me to calculate the size of a shield needed to enter the atmosphere of Venus and the size of a parachute that could safely land the Curiosity rover on the surface of Mars. Most recently we used pi in our calculations of the expanding atom cloud we will create for an experiment called the Cold Atom Laboratory, which will fly aboard the International Space Station.”
The Science Behind the Challenge
The Pi Day Challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers.
“Students always want to know how math is used in the real world,” said Ota Lutz, a senior education specialist at JPL who helped create the Pi Day Challenge. “This problem set demonstrates the interconnectedness of science, math and engineering, providing teachers with excellent examples of cross-cutting concepts in action and students with the opportunity to solve real-world problems.”
NASA's Pi Day Challenge in the Classroom!
The NASA Pi Day Challenge is available as a standards-aligned lesson for grades 6-12. In the illustrated math problem set, students use pi to solve real-world science and engineering problems related to craters on Mars, a total solar eclipse, a daring orbit about Saturn, and the search for habitable worlds.
Here’s some of the science behind this year’s problem set.
The craters that cover Mars can tell us a lot about the Red Planet. Studying ejecta – the material blasted out during an impact – can tell us even more. Information about ejecta patterns even came up during a recent workshop to discuss and select the final candidates for the Mars 2020 rover landing site. For the first problem in our Pi Day Challenge, students use pi and the area and perimeter of two craters to identify which was made by an impactor that struck Mars at a low angle. Researchers found that low-angle impactors create an unusual ejecta pattern around craters on Mars. As part of the research, scientists are currently working to identify and catalog these craters.
The year 2017 brings a unique astronomical event to the United States for the first time in nearly 40 years! On August 21, 2017, a total solar eclipse will cross the continental United States. Starting in Oregon, the shadow of the moon will cross the country at more than 1,000 miles per hour, making its way to the Atlantic Ocean off the coast of South Carolina. Everyone inside the moon’s shadow will witness one of the most impressive sights nature has to offer. So how big is the shadow? In the second part of NASA’s Pi Day Challenge, students will use pi to calculate the area of the moon’s shadow on Earth during the total solar eclipse.
This year also marks the final chapter in the exciting story of NASA’s Cassini mission at Saturn. Since 2004, Cassini has been orbiting the ringed giant, vastly improving our understanding of the second largest planet in the solar system. After more than 12 years around Saturn, Cassini’s fuel is running low, so mission operators have devised a grand finale that will take the spacecraft closer to Saturn than ever before – inside the gap between the planet and its rings – and finally into Saturn’s cloud tops, where it will burn up. The finale is designed to prevent the spacecraft from crashing into and possibly contaminating any of Saturn’s scientifically intriguing moons. In the Pi Day Challenge, students will use pi to safely navigate the spacecraft on its final orbits and dive into Saturn.
Finally, students will investigate a relatively new and very exciting realm in astronomy, the search for habitable worlds. The discovery of exoplanets – worlds orbiting stars outside of our solar system – has changed our understanding of the universe. Until 1995, exoplanets hadn’t even been detected. Now, using the transit method – where planets are detected by measuring the light they block as they pass in front of a star – more than 2,300 exoplanets have been discovered. Recently, astronomers discovered a record seven Earth-size planets orbiting a single star called Trappist-1. Students will use pi to identify which of Trappist-1’s planets orbit in the star’s habitable zone – the area where liquid water could exist.
Explore More
Join the Conversation
- Join the conversation and share your Pi Day Challenge answers with @NASA/JPL_Edu on social media using the hashtag #NASAPiDayChallenge
- Pi Day: What’s Going ‘Round – Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
Standards-Aligned Lessons
Multimedia
Facts and Figures
Missions
Websites
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K-12, Lesson, Activity, Slideshow
Teachable Moments | January 13, 2016
Cruising to Jupiter: A Powerful Math Lesson
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 m^{2} 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.
Teach It
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, 3^{2} × 3^{-5} = 3^{-3} = 1/3^{3} = 1/27."
Explore More!
- 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.
TAGS: Juno, Jupiter, Exponents, Math, Lesson, Activity, Teachable Moment