In the News
The Voyager 2 spacecraft, launched in 1977, has reached interstellar space, a region beyond the heliosphere – the protective bubble of particles and magnetic fields created by the Sun – where the only other human-made object is its twin, Voyager 1.
The achievement means new opportunities for scientists to study this mysterious region. And for educators, it’s a chance to get students exploring the scale and anatomy of our solar system, plus the engineering and math required for such an epic journey.
How They Did It
Launched just 16 days apart, Voyager 1 and Voyager 2 were designed to take advantage of a rare alignment of the outer planets that only occurs once every 176 years. Their trajectory took them by the outer planets, where they captured never-before-seen images. They were also able to steal a little momentum from Jupiter and Saturn that helped send them on a path toward interstellar space. This “gravity assist” gave the spacecraft a velocity boost without expending any fuel. Though both spacecraft were destined for interstellar space, they followed slightly different trajectories.
Voyager 1 followed a path that enabled it to fly by Jupiter in 1979, discovering the gas giant’s rings. It continued on for a 1980 close encounter with Saturn’s moon Titan before a gravity assist from Saturn hurled it above the plane of the solar system and out toward interstellar space. After Voyager 2 visited Jupiter in 1979 and Saturn in 1981, it continued on to encounter Uranus in 1986, where it obtained another assist. Its last planetary visit before heading out of the solar system was Neptune in 1989, where the gas giant’s gravity sent the probe in a southward direction toward interstellar space. Since the end of its prime mission at Neptune, Voyager 2 has been using its onboard instruments to continue sensing the environment around it, communicating data back to scientists on Earth. It was this data that scientists used to determine Voyager 2 had entered interstellar space.
How We Know
Interstellar space, the region between the stars, is beyond the influence of the solar wind, charged particles emanating from the Sun, and before the influence of the stellar wind of another star. One hint that Voyager 2 was nearing interstellar space came in late August when the Cosmic Ray Subsystem, an instrument that measures cosmic rays coming from the Sun and galactic cosmic rays coming from outside our solar system, measured an increase in galactic cosmic rays hitting the spacecraft. Then on November 5, the instrument detected a sharp decrease in high energy particles from the Sun. That downward trend continued over the following weeks.
The data from the cosmic ray instrument provided strong evidence that Voyager 2 had entered interstellar space because its twin had returned similar data when it crossed the boundary of the heliosheath. But the most compelling evidence came from its Plasma Science Experiment – an instrument that had stopped working on Voyager 1 in 1980. Until recently, the space surrounding Voyager 2 was filled mostly with plasma flowing out from our Sun. This outflow, called the solar wind, creates a bubble, the heliosphere, that envelopes all the planets in our solar system. Voyager 2’s Plasma Science Experiment can detect the speed, density, temperature, pressure and flux of that solar wind. On the same day that the spacecraft’s cosmic ray instrument detected a steep decline in the number of solar energetic particles, the plasma science instrument observed a decline in the speed of the solar wind. Since that date, the plasma instrument has observed no solar wind flow in the environment around Voyager 2, which makes mission scientists confident the probe has entered interstellar space.
Though the spacecraft have left the heliosphere, Voyager 1 and Voyager 2 have not yet left the solar system, and won't be leaving anytime soon. The boundary of the solar system is considered to be beyond the outer edge of the Oort Cloud, a collection of small objects that are still under the influence of the Sun's gravity. The width of the Oort Cloud is not known precisely, but it is estimated to begin at about 1,000 astronomical units from the Sun and extend to about 100,000 AU. (One astronomical unit, or AU, is the distance from the Sun to Earth.) It will take about 300 years for Voyager 2 to reach the inner edge of the Oort Cloud and possibly 30,000 years to fly beyond it. By that time, both Voyager spacecraft will be completely out of the hydrazine fuel used to point them toward Earth (to send and receive data) and their power sources will have decayed beyond their usable lifetime.
Why It’s Important
Since the Voyager spacecraft launched more than 40 years ago, no other NASA missions have encountered as many planets (some of which had never been visited) and continued making science observations from such great distances. Other spacecraft, such as New Horizons and Pioneer 10 and 11, will eventually make it to interstellar space, but we will have no data from them to confirm their arrival or explore the region because their instruments already have or will have shut off by then.
Interstellar space is a region that’s still mysterious because until 2012, when Voyager 1 arrived there, no spacecraft had visited it. Now, data from Voyager 2 will help add to scientists’ growing understanding of the region. Scientists are hoping to continue using Voyager 2’s plasma science instrument to study the properties of the ionized gases, or plasma, that exist in the interstellar medium by making direct measurements of the plasma density and temperature. This new data may shed more light on the evolution of our solar neighborhood and will most certainly provide a window into the exciting unexplored region of interstellar space, improving our understanding of space and our place in it.
As power wanes on Voyager 2, scientists will have to make tough choices about which instruments to keep turned on. Further complicating the situation is the freezing cold temperature at which the spacecraft is currently operating – perilously close to the freezing point of its hydrazine fuel. But for as long as both Voyager spacecraft are able to maintain power and communication, we will continue to learn about the uncharted territory of interstellar space.
Use these standards-aligned lessons and related activities to get students doing math and science with a real-world (and space!) connection.
Solar System Bead Activity
Students create a scale model of the solar system using beads and string.
Time 30 mins - 1 hr
Catching a Whisper from Space
Students kinesthetically model the mathematics of how NASA communicates with spacecraft.
Time 1-2 hrs
Solar System Scroll
Students predict the scale of our solar system and the distance between planets, then check their answers using fractions.
Time < 30 mins
*NEW* Modeling the Structure of the Solar System
Students will learn about the structure of the solar system and be able to identify analogous regions in a dynamic, 2-D kitchen-sink model.
Time 1-2 hrs
Hear Here: A 'Pi in the Sky' Math Challenge
Students use the mathematical constant pi to determine what fraction of a signal from Voyager 1 – the most distant spacecraft – reaches Earth.
Time < 30 mins
- News Release: “NASA’s Voyager 2 Probe Enters Interstellar Space” – Dec. 10, 2018
- News Release: “NASA Spacecraft Embarks on Historic Journey Into Interstellar Space” – September 12, 2013
- Voyager Mission
- Voyager Images
- Voyager 2: Interstellar, by the Numbers
- Commemorative Voyager Posters
In 1975, 10-year-old Nagin Cox’s home life was unraveling. It was a time when Cox grew up hearing that girls were “worthless” and thought only about making it to age 18 so she could be free.
“I remember looking up at the stars and thinking, ‘I’m going to live and get through this,” Cox, now a spacecraft systems engineer for Mars 2020 recalls. “I need to set a goal. I need something so meaningful it will help me get through the next eight years.'”
That goal revealed itself when she was 14, a curly-haired Indian girl fascinated by “Star Trek” and Carl Sagan’s “Cosmos.” She wanted to explore the universe. And no, she didn't want to be an astronaut.
“If you really want to go where someone has never been, you want to be with the robots. They truly explore first,” she says. “There was one place that did that consistently and that was NASA’s Jet Propulsion Laboratory.”
She just needed to figure out how.
Using a test bed that looks like something out of a sci-fi movie, Becca Foust is exploring ways to bring spacecraft components together in space. Here’s how the NASA Space Technology Research Fellow, who’s earning her Ph.D. at the University of Illinois at Urbana-Champaign, is helping create spacecraft of the future.
What are you working on at JPL?
I like to call it space K’nex, like the toys. We're using a bunch of component satellites and trying to figure out how to bring all of the pieces together and make them fit together in orbit. Then, once they're together, can you pop them apart and make something new? Using many satellites allows for much more versatility than with a conventional single satellite, plus some structures you need are simply too big to fit into the rockets we have today. So this summer, I'm testing my algorithm for assembling satellites on some actual robots in our new test bed.
Meet JPL Interns
Read stories from interns pushing the boundaries of space exploration and science at the leading center for robotic exploration of the solar system.
Tell me about the test bed.
We have five spacecraft simulators that “fly” in a specially designed flat-floor facility. The spacecraft simulators use air bearings to lift the robots off the floor, kind of like a reverse air hockey table. The top part of the spacecraft simulators can move up and down and rotate all around in a similar way to real satellites. All these things combine to let the robots move around using the same components used on real satellites in space. The floor has to be very precisely flat and we have to clean frequently because, if a single hair is on the ground, it will affect the motion of the simulators. We also have two rails with highly articulated robot arms on the side and the back of the room to interact with the simulators as other satellites or as a comet to be mapped.
What happens during the simulations?
Most of what our group does is guidance and control, so telling spacecraft where to go and how to get there. When we're testing those algorithms, it's really important that we know where our spacecraft is because we can't tell it where to go if we don't know where it is. So, in the test bed, our robots are all tracked using a motion capture system. It's sort of like CGI. The system tracks these little reflective dots and tells us very precisely the position and orientation of the object.
So if we're testing a guidance and control algorithm, we will turn on the motion capture system, make sure everything is working, and then we just turn on the robots and press go. Our simulators are autonomous and everything runs on board, so we do a lot of legwork before running experiments to make sure things will run as expected.
What is it that you're looking for during these simulations in the test bed?
Before we had this test bed, we did a ton of simulations on the computer, but it's very different having it work on an actual robot. So we're trying to see that when we run things on the robots, it works the way it did in the simulations. Is it tracking the expected trajectory nicely? Is it computing properly? Is everything working?
We'll probably end up adding some safeguards in case a command goes astray. We'll probably need to make our algorithms be able to handle issues and faults that come up. That's actually one of the problems we're working on with JPL, increasing satellite autonomy by looking at failures that happen within satellites, trying to figure out what they are and recover from them.
What's the goal of your research?
I hope my research leads to smarter, more efficient satellites for in-space construction and assembly. The algorithm that I'm using is very fuel-efficient and it finds trajectories that aren't really being considered and haven’t been tried yet in space. By watching it in our version of space, we can show that these paths can actually be executed in real space. So maybe we can actually start using these more efficient trajectories and then all of our satellites can live longer, go farther and do more.
What's an average day like for you?
I try to work on some mathematical proofs in the morning when I'm still sharp-ish. So I work on that until I get frustrated. After that, I'll wander over to our lab and do some hands-on robotics-type things, like working on the spacecraft simulators and making them work more efficiently. Then, I'll spend a while teaching our undergraduate interns how to use the Robot Operating System, which runs on all of our robots.
What's the most JPL- or NASA-unique experience you've had so far?
I would say meeting people at JPL. There are so many experts in so many different fields. The first summer I was at JPL, there was a presentation on almost exactly my topic. So I got to meet with that speaker, and we set up a meeting time and talked more about it. He had a bunch of really good ideas for my topic and some other people to talk to. One connection sort of leads to another.
If you could go anywhere in space, where would you go and what would you do there?
We're talking imaginary, right? Because I would like to go to space eventually, if I can. I think I would go to – this is probably a really popular answer but – Jupiter’s moon Europa. I’d just want to figure out what on Earth is going on there.
Explore JPL’s summer and year-round internship programs and apply at: https://www.jpl.nasa.gov/edu/intern
The laboratory’s STEM internship and fellowship programs are managed by the JPL Education Office. Extending the NASA Office of Education’s reach, JPL Education seeks to create the next generation of scientists, engineers, technologists and space explorers by supporting educators and bringing the excitement of NASA missions and science to learners of all ages.
Update – Feb. 24, 2017: The deadline for the Cassini Scientist for a Day Essay Contest has passed. The winners will be announced in May 2017.
In the News
Next week, NASA’s Cassini spacecraft will go where no spacecraft has gone before when it flies just past the edge of Saturn’s main rings. The maneuver is a first for the spacecraft, which has spent more than 12 years orbiting the ringed giant planet. And it’s part of a lead-up to a series of increasingly awesome feats that make up the mission’s “Grand Finale” ending with Cassini’s plunge into Saturn on Sept. 15, 2017.
How They’ll Do It
Cassini's ring-grazing orbits, which will take place from late Novemeber 2016 through April 2017, are shown here in tan. The blue lines represent the path that Cassini took in the time leading up to the new orbits during its extended solstice mission. Image credit: NASA/JPL-Caltech/Space Science Institute | › Larger image
To prepare for the so-called “ring-grazing orbits,” which will bring the spacecraft within 56,000 miles (90,000 km) of Saturn, Cassini engineers have been slowly adjusting the spacecraft’s orbit since January. They do this by flying Cassini near Saturn’s large moon Titan. The moon’s gravity pulls on the spacecraft, changing its direction and speed.
On November 29, Cassini will use a big gravitational pull from Titan to get into an orbit that is closer to perpendicular with respect to the rings of Saturn and its equator. This orbit will send the spacecraft slightly higher above and below Saturn’s north and south poles, and allow it to get as close as the outer edge of the main rings – a region as of yet unexplored by Cassini.
This graphic illustrates the Cassini spacecraft's trajectory, or flight path, during the final two phases of its mission. The view is toward Saturn as seen from Earth. The 20 ring-grazing orbits are shown in gray; the 22 grand finale orbits are shown in blue. The final partial orbit is colored orange. Image credit: NASA/JPL-Caltech/Space Science Institute | › Larger image
Why It’s Important
Cassini’s ring-grazing orbits will allow scientists to see features in Saturn's rings, up close, that they’ve only been able to observe from afar. The spacecraft will get so close to the rings, in fact, that it will pass through the dusty edges of the F ring, Saturn’s narrow, outermost ring. At that distance, Cassini will be able to study the rings like never before.
Among the firsts will be a “taste test” of Saturn’s rings from the inside out, during which Cassini will sample the faint gases surrounding the rings as well as the particles that make up the F ring. Cassini will also capture some of the best high-resolution images of the rings, and our best views of the small moons Atlas, Pan, Daphnis and Pandora, which orbit near the rings' outer edges. Finally, the spacecraft will do reconnaissance work needed to safely carry out its next planned maneuver in April 2017, when Cassini is scheduled to fly through the 1,500-mile (2,350-kilometer) gap between Saturn and its rings.
These orbits are a great example of scientific research in action. Much of what scientists will be seeing in detail during these ring-grazing orbits are features that, despite Cassini’s 12 years at Saturn, have remained a mystery. These new perspectives could help answer questions scientists have long puzzled over, but they will also certainly lead to new questions to add to our ongoing exploration of the ringed giant.
As part of the Cassini Scientist for a Day Essay Contest, students in grades 5-12 will write an essay describing which of these three targets would provide the most interesting scientific results. › Learn more and enter
What better way to share in the excitement of Cassini’s exploration than to get students thinking like NASA scientists and writing about their own questions and curiosities?
NASA’s Cassini Scientist for a Day Essay Contest, open to students in grades 5-12, encourages students to do just that. Participants research three science and imaging targets and then write an essay on which target would provide the most interesting scientific results, explaining what they hope to learn from the selected target. Winners of the contest will be featured on NASA’s Solar System Exploration website and get an opportunity to speak with Cassini scientists and engineers via video conference in the spring.
More information, contest rules and videos can be found here.
The deadline to enter is Feb. 24, 2017.
- Find educational lessons and activities about Saturn
- Discover free educational materials and resources about Saturn
- Students can discover more about Saturn with these slideshows, games and videos
- Download this timeline featuring milestones from Cassini's mission at Saturn or explore the interactive version!
- Explore the Cassini mission to Saturn website
- Browse our Cassini news archive
NASA is giving people around the world a reason to ooh and aah this July Fourth. At 8:18 p.m. PDT, as fireworks are streaming through the skies across the U.S., the Juno spacecraft will be taking the on-ramp to an orbit around Jupiter.
See the full problem set (optimized for screen readers and mobile devices) and answers, here
While maybe not as dramatic as a jet-powered landing on Mars, the Juno Orbit Insertion (the name for the process, also called JOI) requires that the spacecraft slow down just enough to not go zooming past Jupiter. As of Thursday, the spacecraft’s fate rested on a series of 1s and Os as a command sequence made the 48-minute journey from a gargantuan antenna in Goldstone, California, to the spacecraft 534 million miles away.
While a successful orbit insertion is now largely out of mission controllers’ hands, there will be no shortage of nail biting on July Fourth. With a five-year journey behind it and lofty goals ahead – which include peering through Jupiter’s thick cloud cover to uncover clues about how our solar system was formed – Juno has a lot resting on what will amount to a 35-minute engine burn. And perhaps even bigger risks are still to come as Juno begins its 33.5 oblong orbits around Jupiter, which will bring the spacecraft closer than ever before to the planet’s cloud tops – and to its lethal radiation.
To follow along on July 4 as Juno begins its journey into Jupiter’s orbit, watch NASA TV live coverage beginning at 7:30 p.m. PDT.
For a mission countdown, images, facts about Jupiter and Juno and other resources, visit NASA’s Solar System Exploration website.
And check out these educational activities for students and teachers from NASA/JPL Edu:
- Pi in the Sky: Gravity Grab - In this illustrated math problem, students calculate how much the Juno spacecraft needs to slow down to go into orbit about Jupiter. (See the full Pi in the Sky problem set with answers)
- Pi in the Sky: Jupiter Jockey - Students use the mathematical constant pi to calculate the distance Juno will travels in one orbit around Jupiter. (See the full Pi in the Sky problem set with answers)
- Exploring Jupiter Slideshow - Find out how many spacecraft have been to Jupiter so far and what they've discovered. Plus download a free poster!
- Powering Through the Solar System with Exponents - This educational activity has students use exponents and division to understand how the Juno spacecraft got to Jupiter using solar power.
- Why with Nye: Mission to Jupiter - In this video series, Bill Nye explains why NASA is sending a spacecraft to the most giant (and possibly most dangerous) planet in our solar system.
UPDATE - Aug. 31, 2016: Our Mars Bulletin Board materials are out of stock. To download and print out the resources, click on the links next to each product.
Get the school year back in gear with a Mars-themed bulletin board for your school, classroom, library or educational program. The Educator Resource Center at NASA's Jet Propulsion Laboratory is offering a set of free posters and lithographs with fun facts about the Red Planet and NASA's Mars missions.
The Mars Bulletin Board includes:
This poster highlights the likenesses and differences between the Red Planet and Earth.
This lithograph set features images of NASA's Mars rover Curiosity as well as images the rover has taken on the Red Planet. Facts about Curiosity and its discoveries are included on the back of each image.
Learn about the twin Mars Exploration Rovers, Spirit and Opportunity, and their key discoveries. (Opportunity is still roving on Mars, more than 10 years after landing on the Red Planet!)
As part of its "Journey to Mars" initiative, NASA is developing spacecraft and technologies that will pave the way for a future manned mission to the Red Planet. This graphic shows some of the key milestones of that initiative.
Learn about the history, composition and exploration of Mars on this lithograph featuring images of the Red Planet on one side and fun facts on the other.
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