Teachable Moments | March 23, 2016
Modeling Gravitational Waves
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).
Teach It
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.
Explore More
- Gravitational waves news, videos and resources
- Laser Interferometer Gravitational-Wave Observatory (LIGO) Website
TAGS: Gravitational Waves, Teachable Moment, LIGO, Black Holes, Einstein
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
Teachable Moments | July 16, 2015
NASA's New Horizons Mission Flies by Pluto
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/m^{3} to 1,879 kg/m^{3} with this new finding. Most rock has a density between 2000-3000 kg/m^{3} and ice at very cold temperatures has a density of 927 kg/m^{3}, 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!
Teach It
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 r^{2} = 17,646,012 km^{2} - Find the volume of Pluto.
4/3 π r^{3} = 6,970,174,651 km^{3} - Find the density of Pluto in kg/m^{3}.
mass/volume
Pluto mass = 1.31 × 10^{22}kg
Convert volume in km^{3} to m^{3}: 6,970,174,651 × 1,000,000,000 = 6.970174651 × 10^{18}m^{3}
1.31 × 10^{22}kg / 6.970174651 × 10^{18}m^{3} = 1,879 kg/m^{3} - How does this new density calculation compare to the previous calculation (2051 kg/m^{3}) when Pluto’s diameter was thought to be 2,302 km?
Explore More
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.
TAGS: Pluto, New Horizons, Math, Teachable Moment