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NASA.gov brings you the latest images, videos and news from America's space agency. Get the latest updates on NASA missions, watch NASA TV live, and learn about our quest to reveal the unknown and benefit all humankind.

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maaaaaaathhhh!!!!!

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Search the entire 700-problem archive

Follow this link to the page where you can perform a full keyword search on all 700 problems to find the one that exactly suits your needs for a specific science and math topic!

SEARCH THE ARCHIVE

Math problems sorted by space science topic

Here you will find hundreds of math problems related to all of the major astronomical objects from asteroids and planets to galaxies and black holes! Click on the topic below to see which problems are available.

Math problems sorted by grade level

If you are a teacher or just someone who enjoys mathematics challenges, these problems cover space science topics but are sorted more-or-less by the kinds of mathematics you will encounter from simple counting and fractions problems through calculus. Click on the grade bands below to see the collections of problems.

Math problems sorted by NASA Mission

If you are looking for math problems specific to a particular mission's investigations, here you will find problems organized by NASA mission name. Click on the mission or program name in the grid below to go to the associated problem listing.

SOHO | SDO | Solar Probe Plus | Spitzer | STEREO | Terra | THEMIS | TRACE | Van Allen Belts Probe | Webb Space Telescope | WISE | WMAP | XMM |

Math problems sorted by Engineering Topics

Math problems related to NASA press releases

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This website offers teachers and students authentic mathematics problems based upon NASA press releases, mission science results, and other sources. All problems are based on STEM, common core standards and real-world applications for grades 3 to 12 and beyond.

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'Marsquake': first tremor detected on Red Planet

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Scientists said Tuesday they might have detected the first known seismic tremor on Mars in a discovery that could shed light on the ancient origins of Earth's neighbour.

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My NASA Data web site with phenomena for K-12 ESS 

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My NASA Data web site with phenomena for K-12 ESS 

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The My NASA Data website offers a variety of opportunities to explore Earth Science phenomena of the Atmosphere, Biosphere, Cryosphere, Geosphere, and Hydrosphere using uniquely NASA related content.

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In this instructional sequence, students examine seismic evidence to determine that the Earth must have a layered internal structure and to estimate the size of Earth's core. Using an inquiry approach, students are divided into two teams (theoreticians and seismologists) to test the simplest hypothesis for what is inside of Earth; the Earth is homogeneous throughout. Theoreticians use a paper and pencil, scale model of a homogeneous Earth combined with an average seismic wave velocity to make predictions about when seismic waves should arrive at various points around Earth (predicted). Meanwhile, seismologists interpret seismic data from a recent earthquake to determine when seismic waves actually arrive at various points around Earth (observations). After comparing and discussing the fit of the predicted data with the observed data, students use a second scale model to further interpret these results. Ultimately, students measure the diameter of Earth's outer core based on their data and can compare it to widely accepted measurements. Before undertaking this activity, students should know what earthquakes are, understand the basics of seismic waves and their prorogation, and be able to explain how seismograms are created.

View Instructor's Guide in the files list.

Objectives:

Students will be able to: - Demonstrate that Earth can't be homogenous by comparing a seismic record section to predicted arrivals from a homogeneous Earth model.

Explain how the internal structure of Earth (concentric layers of different density and composition) is inferred through the analysis of seismic data.

Explain the role models play in the scientific process, especially when used in combination with observational data.

Explain how models are refined through the collection of additional data

Discuss how working in a team to make data-gathering and procedural decisions provides an efficient means for completing tasks, provides peer support to check work and to develop conceptual understanding.

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Determining and Measuring Earth's Layered Interior- Incorporated Research Institutions for Seismology

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Learning occurs as students work first in small groups and then as a whole class to compare predicted seismic wave travel times, generated by students from a scaled Earth model, to observed seismic data from a recent earthquakes. This activity uses models, real data and emphasizes the process of science.

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and a bunch of other neat-o stuff, too!

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STEM Resources for Students | NASA/JPL Edu

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NASA STEM resources for kids and students, including websites, videos, images and planet facts.

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Wobbles in the rotation of Mars swung the planet into about 40 extreme ice ages in the past 5 million years and allowed thick ice layers to remain far away from the poles, an astronomer says.

Various spacecraft have revealed evidence for ice ages on Mars. Around 4 million to 5 million years ago, precipitation events sent piles of snow and ice that accumulated around the ice caps. Nowadays, the only visible ice on Mars is the pair of polar caps. But in recent years, orbiting probes have found solid evidence for vast sheets of underground ice near the red planet's equator, at what scientists call mid-latitudes.

How ice ended up so far from the poles has remained a mystery.

The answer could be in the wobble of Mars, concludes Norbert Sch?rghofer of the University of Hawaii's Astrobiology Institute.
Moon mechanics
Earth's rotation axis is tilted by about 23.5 degrees, a slant that is pretty much fixed due to the gravitational influence of our moon. Mostly due to Mars' lack of a stabilizing moon, its tilt can wobble as much as 10 degrees from the current 25-degree angle.

Using computer simulations, Sch?rghofer found that while not topsy-turvy, the wobbles change the amount of sunlight reaching Mars' surface and can cause vast amounts of ice to shift between the poles and the rest of the planet every 120,000 years.

Here's how it works: When the planet's axis swayed one way, sun rays vanished from some areas and beamed down on others. Regions beneath sunlight became dry with warmer temperatures, causing the ice to recede or disappear entirely except at the highest latitudes.

The receding ice, lost to evaporation, provided plentiful water vapor for new ice to form once the sun retracted and humidity soared. In the humid climate, Sch?rghofer said, the water vapor diffused into the Martian soil and froze to form "pore-ice," which is mainly soil with bits of ice that plug pore spaces.
Dual processes
The wobble would leave two types of ice on or near the surface of Mars: the very old massive ice sheet and the recent pore-ice, less than half a million years old. Dry soil covers both types of ice.

"Today, this gives rise to pore-ice at mid-latitudes and a three-layered depth distribution in the high latitudes," Sch?rghofer writes in the Sept. 13 issue of the journal Nature. At high latitudes, the original ice sheet is covered by a layer of pore-ice, which is veiled by a layer of dry sediment.

When the Phoenix Lander spacecraft arrives at Mars, which is expected in 2008 and will land in the Martian north polar region, Sch?rghofer expects it will "see" the abundant and layered ice forms.

VOTE NOW! The Best of the Mars Rovers

Image Gallery: Ice on Mars

Mars Madness: A Multimedia Adventure

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Wobbles in the rotation of Mars swung the planet into about 40 extreme ice ages in the past 5 million years and allowed thick ice layers to remain far away from the poles, an astronomer says. Various spacecraft have revealed evidence for ice ages on Mars.

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Seriously. Everything Waves and Slinky.

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Lessons, activities and demonstrations using the SeisVolE earthquake and volcanic eruption mapping software

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Additional information on the properties of waves can be found in Bolt (1993, p. 29-30) or Rutherford and Bachmeyer (1995). Sometimes the actual wave looks very much like the representation in the graph (Figure 1). Examples are water waves and a type of seismic surface waves called Rayleigh waves.

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Everyone loves Pi! And Pi Day is March 14. Treat your students to Pi!

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In this illustrated problem set, students use pi to reveal the size of a planet outside our solar system, find out how much helium is raining out from Jupiter's cloud tops, locate a seismic event on Mars and study an interstellar object detected in our so

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Design a mission to explore the planet!

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Educator Guide: Mission to Mars Unit | NASA/JPL Edu

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In this standards-aligned unit, students learn about Mars, design a mission to explore the planet, build and test model spacecraft and components, and engage in scientific exploration.

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Play with the InSight lander

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An interactive 3D introduction to the InSight Mars mission, its technology and its scientific objectives.

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Mars planet facts and information. Compare Earth & Mars. Fun science images for kids, school, family & space fans. Mars in space, night sky & history.

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Middle and High School Focus

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Explore standards-aligned (NGSS and Common Core) STEM lessons and classroom activities for teachers and educators from NASA's Jet Propulsion Laboratory.

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Taking the pulse of Mars!

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The InSight lander will study the interior of Mars and listen for Marsquakes.

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Participate in outer space exploration!

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Exploration of the Planet Mars - missions, videos, images and information

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Search IRIS - Incorporated Research Institutions for Seismology

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IRIS is a consortium of universities dedicated to the operation of science facilities for the acquisition, management, and distribution of seismological data.

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IRIS

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Seismic Waves Viewer Open

Novice

Seismic Waves is a browser-based tool to visualize the propagation of seismic waves from historic earthquakes through Earth's interior and around its surface. Easy-to-use controls speed-up, slow-down, or reverse the wave propagation. By carefully examining these seismic wave fronts and their propagation, the Seismic Waves tool illustrates how earthquakes can provide evidence that allows us to infer Earth's interior structure.

Shear waves (S waves), for example, travel through the Earth at approximately one-half the speed of compression waves (P waves). Stations close to the earthquake record strong P, S, and Surface waves in quick succession just after the earthquake occurred. Stations farther away record the arrival of these waves after a few minutes, and the times between the arrivals are greater.

The tool also illustrates how seismic waves inform our current understanding of Earth's interior structure. Users will see that between approximately 104 and 140 degrees away from the epicenter, direct P waves do not arrive as they are refracted away from this zone. This suggests the presence of a lower velocity material, Earth's outer core. Users will also observe that no direct S waves arrive beyond 104 degrees.

The Seismic Waves tool was produced through a collaboration between Alan Jones & Jeff Baker ( Binghamton University) and IRIS EPO.

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Seismic Waves Viewer- Incorporated Research Institutions for Seismology

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Seismic Waves is a browser-based tool to visualize the propagation of seismic waves from historic earthquakes through Earth's interior and around its surface. Easy-to-use controls speed-up, slow-down, or reverse the wave propagation. By carefully examining these seismic wave fronts and their propagation, the Seismic Waves tool illustrates how earthquakes can provide evidence that allows us to infer Earth's interior structure.

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Meenakshi Wadhwa is the first to say she is lucky to be alive.

On August 2, 2017, Wadhwa and colleagues were prospecting for volcanic rocks in the cooled lava fields of Iceland. After collecting some samples of basaltic rock, which they hoped to use as a proxy for Martian rocks, the team hopped in their vehicles to drive back to their lodgings. Wadhwa sat in the back seat of one of the SUVs, snapping pictures out the window.

Their caravan encountered another group of cars, and her driver decided to pass them. As her vehicle overtook the others, one of the other cars swerved, colliding with her SUV and flipping it. Wadhwa was thrown 30 feet from the vehicle. She suffered a broken pelvis, a punctured lung, broken ribs, a broken shoulder, and several other injuries. "I was a mess," she said.

She was airlifted from Iceland to Massachusetts General Hospital and later moved to Memorial Hermann Hospital in Houston, where she underwent several months of rehab and physical therapy. Last December during her rehab, Wadhwa used a treadmill equipped with assistive devices that simulate lower gravity, easing the burden on her bones. She was enthusiastic about it, imagining herself running on Mars.

Wadhwa, 50, is a meteoritics researcher at Arizona State University who focuses on how meteorites can tell stories about the early solar system. She grew up in Chandigarh, in northern India, in the foothills of the Himalayas. She hoped to attend architecture school, but when she didn't get in, she began wondering about the mountains - how they formed, and what stories they could tell. She studied geology in college and wound up doing her graduate work at Washington University in St. Louis. There, someone handed her a piece of Mars, and she's been in its thrall ever since.

The fourth planet may be dry and barren now, but in its past it was much like Earth: a warm, watery world full of mountains like the ones where Wadhwa grew up, and with deserts like the one she lives in now. Wadhwa studies the rocky planets' shared past, including how Earth and Mars formed and how they got their water. To do this, she uses Earth rocks and meteorites, including some from the asteroid belt and some from Mars and the moon.

Like Earth, Mars is continually pelted by asteroids - leftovers from the early solar system that did not grow up into planets. In the past, big collisions have sheared off chunks of Mars, which then soared into space and, rarely, landed here on Earth. Wadhwa's research on trace elements inside these meteorites has helped geochemists understand the history of Mars, including its watery past. By comparing these meteorites with Earth rocks, scientists can begin to learn how terrestrial planets begin to form and grow.

Quanta talked to Wadhwa about the hazards of fieldwork, the eerie feeling of holding a chunk of another world, and her efforts to construct a holistic picture of the solar system's history using the crumbs left over from its formation. The interview has been condensed and edited for clarity.

You grew up at the base of one of this planet's most impressive geological features. How did you get interested in geology on other worlds?

I grew up in India, and I always loved science. I went to an all-girls school, and I never grew up with the type of peer pressure that you sometimes encounter here in the U.S. among young girls, where you're afraid to speak in front of your colleagues or friends because you don't want to look nerdy. We were all trying to do our best.

My freshman year in college was the first time I felt like I didn't belong. It was an all-male faculty. Someone told me, "Geology is hard for a girl, because you have to do fieldwork, and usually women have a tough time with that." I was sort of made to feel like I didn't fit in.

After that, I applied to grad school. I was always kind of fascinated with other planets, and I thought, wouldn't it be cool to be able to apply my geological insight to learning something about the solar system? I didn't know how I would go about doing this, but I knew there weren't many places in India where I could do it, so I started applying to schools in the United States.

Applying from India, at a time when there was no internet, I had the Barron's guide to graduate schools in the U.S., which was outdated by like 10 years at that point. I didn't care about geography or any of that. I didn't care if it was East Coast or West Coast or the Midwest. It was all half a world away.

So I was accepted into Washington University. I wasn't sure what I wanted to do, and I took a class with my adviser. I hadn't seen many women faculty in this area at all, besides her. And then she asked me, "Hey, do you want to work on these Martian rocks?" And I was like, "What? Really? We have Martian rocks?" She said, "We are pretty confident they are from Mars." I was totally intrigued. I thought, "Wow, this is really cool, I can actually do geology on Mars!"

What is it like to hold a piece of Mars or the moon? Why are these samples so special?

It's kind of like a book chapter in the history of a planet. If you know how to read it, it can tell you a lot about what went on in a particular time and place. There's a lot of information encoded in these rocks. We've got the tools to be able to read that code. To me, it's a really cool way to be able to see a planet sometime in the past and learn something about how it came to be the way it is now. We use Earth rocks all the time for that purpose. These rocks are no different.

Speaking of bits of Mars, a meteorite from Mars fell to Earth in 2011 and landed in Morocco. You sliced one piece of this meteorite into three chunks and left them exposed to the elements in Arizona's Sonoran Desert for three years. Did you feel weird about it? Like, "We're going to throw this fresh meteorite outside and see what happens"?

That was a serendipitous experiment. I'm not going to take credit for the idea. Our collections manager at the Center for Meteorite Studies, Laurence Garvie, is super interested in what happens to things when they are sitting out in the desert. In a half-kidding way, he was like, "Here's this fresh sample, let's put it out there." And I was like, "Huh. You know, that's actually a great idea." Because we don't have anything from Mars that is that fresh. The previous [meteorite] fall happened like 50 years ago. So this was a great way to do a reality check - what's going on with these samples?

We left it in a part of the desert that is not traversed so much. But every so often during monsoon season, there are these gully washers that go through there. We put it under a steel wire mesh, but that wouldn't have kept it from being washed away in a really big rain. We did the best we could in terms of placing it in a place where it was a little out of the way. But we were lucky we were able to locate it again after two or three years.

What is fieldwork like for you? Can you tell me about your car accident? Did it change anything about how you approach your work?

This was one of these projects I had been waiting to do for a while, and I was super excited about it. I had done some fieldwork in Antarctica to collect meteorites, but this was going to be the first fieldwork where we would be collecting Icelandic volcanic rocks as analogues of Martian volcanic materials, with the goal of understanding the role of water and hydrogen.

It was a total fluke accident. We were in a very remote part of Iceland, and I would be hard-pressed to imagine there would be more than two cars on the road at any given time. We had lunch and we were heading back, and there was a caravan of cars right in front of us. My colleague who was driving decided to pass them. We were doing it at high speed when one of the cars from the caravan pulled out into us. The whole thing just kind of rolled over three times. I had been taking photographs out the back window and hadn't put my seat belt on. I ended up being ejected. I was super lucky to have survived it.

I had to be airlifted out of Iceland. There was not a single orthopedist in the country who could deal with the level of trauma I had experienced. I was pumped full of morphine lying there for three days before they were able to airlift me out. I don't really remember a whole lot of it. I spent much of the last fall in a wheelchair recovering and doing lots of physical therapy.

But I hope to be able to go back. My colleague from Iceland was able to send us most of the rocks we had collected. So we have the samples, and we are working on them now and hope to be able to go back and collect a few more to finish out the project.

I think I would feel some form of PTSD working on those rocks. I wouldn't want anything to do with them.

Well, the accident itself is completely erased from my memory. My doctor tells me that is not uncommon in traumatic accidents like that. I just remember waking up in the ER, and obviously all the pain and discomfort afterward. But for a geologist, Iceland is a magical place. It looks like another world to me. Where we were doing fieldwork, it was mostly dark basaltic rock, and it was like a volcanic wonderland.

You've done a lot of work on geochronology - determining the age of rocks. How has this changed our view of how planets are made?

The two thrusts that are important are trying to understand the origin of water, and understanding the timescales of the solar system - the chronology of when and how planets were starting to form. When did planets start to accrete, differentiate, melt, form a crust? In terms of the formation history of the solar system, there are three ways you can get a handle on that. There is the theoretical aspect, and astrophysical observations that constrain that, but the only way we can really get a handle on planetary formation at the level of precision we really want is through samples. The materials we have in our meteorite collection are one way to do it.

What do these rocks tell us about the solar system, and how we all got here? What do we learn about ourselves from them?

There's a lot of commonality. The way we understand processes on Earth, you really can apply that to processes on other planets. And there are some fundamental differences, in terms of how much water there might have been, how the history may have diverged early on, in terms of loss of an early atmosphere, or impacts. As a case in point: Venus, Earth and Mars, if you think about them in the context of other solar systems, all three of these planets would fall in what we call the habitable zone. But they are so different! For Venus, certainly we don't imagine there is any kind of life currently on that planet. For Mars, maybe there was in the past, and maybe still in the subsurface, but clearly it's a different place than it used to be. History is different in these places. And in some ways that [history of life] has fundamentally changed the way these planets evolved over time.

The common thread is, if you have a sample of rock, you can pull it apart, atom by atom, and get into some really detailed information, which you can't do by remote sensing. It's telling how much more we know about the moon, for example, just by having so many rocks from there.

How often do you get to study newly fallen meteorites? How many of them are falling on us?

We get something like 100 tons of stuff falling on the Earth every single day. Spread over the entire planet, it's not all that much if you think about it. Most of that is sand-size particles - tiny, tiny particles. Things that are about the size of a car, or van-size bolides, they hit a few times a year. Something the size of the Chelyabinsk meteor [which exploded over Russia in 2013], that's a few times a year.

We just found a new meteorite that fell in Phoenix a couple months ago. It was really funny because it happened during one of these monsoon rainstorms, and I think people missed the fireball because they thought it was lightning. A person called us and said, "Hey, I found this rock in my backyard." Most times when we get people contacting us, it's not a meteorite. But this one was.

I imagine you get a lot of people calling about "meteowrongs."

Yes! We had to suspend our meteorite ID program, because we just get so many requests. We don't have enough people to really address it. We have a couple open-door events, and we encourage people to bring them by.

What is it like when they're right? Or when you're right? Have you ever walked onto the ice in Antarctica and found one?

It is the weirdest feeling in the world. As someone studies this and comes to understand a little bit about meteorites and why they are where they are, it is still amazing and just astounding. You are sitting on top of the ice, and it's like, a space rock, wow. It's surreal. Sometimes we find hundreds of them in an area the size of a football field. You realize there has to be some concentration of these because of how the ice flows and ablates in certain regions. But it's still really kind of astounding when you actually find them. It's magical, really.

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It's Raining Mars: Interview With Meteor Scientist Meenakshi Wadhwa | Quanta Magazine

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Meenakshi Wadhwa is the first to say she is lucky to be alive. On August 2, 2017, Wadhwa and colleagues were prospecting for volcanic rocks in the cooled lava fields of Iceland. After collecting some samples of basaltic rock, which they hoped to use as a proxy for Martian rocks, the team hopped in their vehicles to drive back to their lodgings.