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# National Aeronautics and Space Administration

## ILabs: Interactive Excel Spreadsheets that Support Inquiry-based Learning

Each of the .xlsx files below is a ready-to-go Excel spreadsheet with interactive 'sliders' that let students experiment with a variety of mathematical models for planetary structure, heat flow and rotation among other modeled properties. After downloading, open the file and click on the 'enable editing' button in the top menu bar so that the sliders will function properly. Each file comes with an Introduction page followed by one or more interactive labs. Note that older versions of Excel may not have background images or slider functionality enabled.These iLabs have been designed to operate properly for MS Office Excel version 2010 or later.

Interaction with the iLabs is entirely open-ended. Students may explore what happens when the values of specific variables are changed in the various embedded mathematical models. A common feature is to interactively 'fit' real-world data with a linear equation, where sliders control the slope and intercept values.

Modeling the Interior of Pluto
This interactive Excel spreadsheet lets you create a model of the interior of Pluto based on its diameter, mass and the densities of ice and rock. Although we can never visit the interior of a far-off planet, we can use the observed mass and radius of the planet, plus some assumptions about what is inside (rock, water, ice, gas, etc) to create a plausible model of the interior of the planet. Each material has its own unique density and its way of changing under pressure and temperature. The interior of a planet is then just a series of concentric shells of matter, each with its own density and size, which together add up to give the observed mass and radius of the planet that we see. This eLab will let you approximate a planet by a 'core' and a 'mantle'. [Grade: 8-10 ] (.xlsx file)

The Distance Between Two Points on Mars
The location of the InSight lander will be determined when it touches down in terms of its martian latitude and longitude. A marsquake or the impact of a meteor will occur at some other spot on Mars, also given by its latitude and longitude. This program calculates how far apart these two spots are from each other by entering their latitudes and longitudes. [Grade: 8-10 ] (.xlsx file)

Arrival times for martian surface waves
The InSight seismometer will detect the arrival of marsquake or meteor impact seismic waves. These waves, like the ripples of water from a stone dropped in a pond, travel on the surface of Mars. As the figure shows, there are two waves that travel around Mars called Rayleigh 1 and Rayleigh 2. The R1 wave arrives first, and the R2 wave travels a longer distance and arrives next. These waves can also continue to travel around Mars back to the seismometer and are then called R3 and R4. This program calculates how long these Rayleigh waves take to reach the InSight seismometer. [Grade: 8-10 ] (.xlsx file)

Exploring Seismic Travel Times and Speeds in a Layered Medium
Seismic pressure waves or 'P-waves' are expansions and contractions of a medium similar to sound waves. As the density of a rock layer changes, the speed of these P-waves also changes. This calculator lets you simulate a stack of four different rock types and calculate the speed and travel times of P-waves [Grade: 8-10 | Topics: ] (.xlsx file)

Exploring Impact Energy and Seismic Effects on Mars
Mars is pelted by thousands of meteors every year; some of these are large enough to leave craters. With a thin atmosphere and close proximity to the Asteroid Belt, the scars of these large impacts remain on the surface for billions of years. Scientists can predict from the energy of the impact the size of the crater that will result. A simple seismic model of the surface of Mars can also predict how much vertical shaking will occur far from the impact. This program lets you adjust the properties of the impactor and its distance from a seismic station to calculate the vertical shaking. [Grade: 8-10 ] (.xlsx file)

Exploring Insulation and Heat Flow
Heat transfer, or heat flow, happens in solid materials when the faster-moving particles are in contact with slower-moving particles and transfer some of their energy. The slower moving particles start to move more rapidly and thereby the kinetic energy moves into the cooler medium to 'heat it up'. If a material is a good insulator, it gets harder and harder for the kinetic energy to move forward and so the more distant particles in the insulator remain cool. The insulator has absorbed the heat, or even reflected it back to the source of the heat. In this lab, you will examine how a common 'fiber glass' insulator works to keep your home warm in the winter and cool in the summer. You will also explore how water boils in several different kinds of pots made from materials that conduct heat differently. [Grade: 8-10 ] (.xlsx file)

Exploring Temperature Changes in Earth's Crust
The center of Earth is hotter than the surface of our sun at nearly 6000 Celsius. Meanwhile the surface remains a balmy and habitable 20 Celsius. Between the core and the surface, the temperature decreases with each kilometer traveled away from the center. Near the surface, we travel down to the core and the temperature steadily increases with depth. Miners are well-aware of this effect. Geologists call it the geothermal gradient, and it can be measured in deep mines, providing valuable information about the flow of heat through Earth's crust and interior. In this lab module, you will use actual data from five different mines to calculate the geothermal gradient. The actual data is represented by points on a graph. Your assignment in each case is to use the sliders to create a linear model of how the temperature changes with depth. This linear model is of the form T = b+Mx, where b is the starting surface temperature and m is the slope representing the geothermal gradient in degrees per kilometer. [Grade: 8-10 ] (.xlsx file)

Exploring Temperature Changes Beneath the Lunar Crust
The interior of planets and most large moons is hotter than the surface, because the energy of formation of these bodies, plus any radioactive decays among trapped minerals, causes the interiors to heat up. Rock, meanwhile, is a very good insulator, so the internal heat of a planet or moon takes a long time to reach the surface. On Earth, geologists measure the 'geothermal gradient' at the surface, which is a measure of how hot Earth is as you travel closer to the core from the surface. They also can measure how much of the internal heat is leaking out from the interior at the surface, which is usually measured in milliwatts per square meter. In this lab, you will use actual data from the Apollo 12 mission to the moon, to calculate the thermal gradient for the moon. When combined with the measure of the heat leaking out from the lunar interior, the thermal gradient can be used to determine what kind of rock makes up the outer layer of the lunar surface. [Grade: 8-10 ] (.xlsx file)

Exploring Heat Flow and Temperature Differences in the Martian Crust
In the winter, you heat the inside of your home to a comfortable temperature. To make sure that this heat stays inside your home you add insulation to your walls and attic. The inside of Mars is very warm, just like the core of our planet Earth. This heat travels through the planet and escapes through its surface. The rock and surface material of Mars acts like the insulation in the attic of a house. Heat energy escaping the planet's surface, called the heat flux. The change in temperature with depth can be used to figure out what kind of material is in the surface of Mars. This lab lets you adjust the heat flow and type of surface material to predict how the surface temperature changes with depth. [Grade: 8-10 ] (.xlsx file)

Exploring Earth's Chandler Wobble
We all know that Earth rotates once every 24 hours about an axis that passes exactly through the North and South geographic poles of Earth. The tilt of this axis is exactly 23.4 degrees, and this results in Earth having four distinct seasons every year. But when scientists look at this rotation they see that it is a bit more complicated than this simple picture. As far back as the ancient Greeks, it was known that the polar axis takes a 25,000 year circle through the constellations. Our Pole Star Polaris is only the most recent North Star, and it is replaced by other stars along the 25,000 year precession of the axis. This precession does not affect the tilt of Earth's axis which remains 23.4 degrees. It is like a spinning top whose spinning axis rotates along a circle, but the top still tilts the same amount as it goes. On top of this 25,000 year precession of the poles, there is a second motion called a nutation. The orbiting moon and distant sun apply a gravitational force to our Earth. Because Earth is spinning like a gyroscope, this force causes Earth to bob slightly as it turns around on its 25,000-year precession cycle. The time to complete one of these bobs is 18.6 years and is called the nutation period. If you were standing at the North Pole of Earth, the nutation cycle causes the North Pole to trace a circle about 600 meters in radius. The speed of the North Pole along this circle is about 3 meters per month so you can easily out-run the motion of Earth's North Pole. In addition to precession and nutation, there is a third motion of Earth's North Pole called the Chandler Wobble. On top of the precession and nutation circular motions, the Chandler wobble is another circular motion that has a period of about 430 days, and a radius of about 9 meters. Even though this is a faster motion, its speed is only about 2 centimeters or 1 inch per day, so you can still out-run even this motion. The Chandler Wobble is caused by the way that the spin of Earth reacts to the movement of ocean water, and air in the atmosphere. During severe storms, and even earthquakes, you can see how the spin of Earth reacts to these changes near Earth's surface. Studying the Chandler Wobble tells scientists a lot about the surface and interior of Earth. [Grade: 8-10 ] (.xlsx file)

The Motion of Planetary Rotation Poles
The rotational pole of a planet does not remain fixed, but can move in complex cycles over time. The axis of a spinning top or gyroscope does not remain verticle, but is usually tilted at an angle. As the gyroscope spins under the force of gravity, its axis turns through a circle, called precession. It can also bob slightly as it rotates, which is a faster motion called nutation. The effect of Earth's moon on the rotation of Earth causes the axis of Earth to nutate. The motion of water in the oceans, and the interior layering and composition of Earth also cause a faster motion called the Chandler Wobble. For Mars, there is much we don�t know about its interior, but detailed measurements from Earth have shown that Mars also nutates as it rotates, and has a Chandler Wobble. In this lab, you will examine the nutation and Chandler Wobble of Earth and Mars, and determine the periods of this motion. [Grade: 8-10 ] (.xlsx file)

Basic Properties of Mars as a Planetary Body
Mars is actually a very simple body. It is round, it spins, and it has mass. Although we can't visit the interior of Mars, or any other planet for that matter, there are ways that we can explore a planet's interior just by knowing a few basic things about it as a planet. In this lab, you will create a model of the interior of Mars by knowing three basic things about its bulk properties. Mass: A satellite or moon orbiting a planet can be used to determine the mass of the planet because of the gravitational force it produces to keep the satellite in orbit at a specific distance. In this module, you will use data from the orbit of the moon Phobos to fit the data for the implied mass of Mars. Interior: In this lab, given the radius of Mars and its total mass, you will work with a 3-component model for the interior of the planet consisting of an outer crust, a mantle and a core region. By adjusting the density of the material in each of these zones, you will create a model that is consistent with the measured mass of the planet. Moment of Inertia: The way that a planet rotates when it is acted upon by a force, provides a big clue to how the material inside the planet is distributed. This feature is called the moment of inertia. In this lab, you will adjust the model for the density of rock in the crust, mantle and core, so that it gives the measured moment of inertia for Mars. [Grade: 8-10 ] (.xlsx file)

A Round-trip Message to the InSight Lander on Mars
Astronomers will be in constant contact with the InSight lander on the surface of Mars. Even at the speed of light, communicating with this lander will not be 'instantaneous'. The speed of light is 300,000 kilometers per second, so from the distance of Mars, it will take a long time for the radio message to be sent and then returned to Earth. Astronomers plan to use sensitive 'radio telescopes' on Earth to accurately measure this time delay so that they can figure out exactly how Mars rotates. By measuring the very slight millimeter changes in this rotation over time, they will be able to study how much the core of Mars sloshes about in its liquid state. This is like watching very carefully how a fresh egg spins compared to a hard-boiled egg. [Grade: 8-10 ] (.xlsx file)

Exploring Heat Flow in the Martian Interior
In the winter, you heat the inside of your home to a comfortable temperature, but to make sure that this heat stays inside you add insulation to your walls and attic so that little of this heat escapes. The inside of Mars is very warm, just like the core of our planet Earth. This heat travels through the planet and escapes through its surface. The rock and surface material of Mars acts like the insulation in the attic of a house. For a given amount of heat energy escaping the planet's surface, called the heat flux, the change in temperature with depth can be used to figure out what kind of material is in the surface of Mars, and other features of the planet's interior. This lab lets you adjust the heat flow and type of interior material to match the mass, density and surface temperature of Mars. [Grade: 8-10 ] (.xlsx file)