﻿ Welcome to Space Math @ NASA !

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