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Hi, we're from Bridge Street Middle School in Wheeling, West Virginia.

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NASA Connect asked us to show you the student activity for this program.

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When you think of the Earth or Mars orbiting the planet,

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you might think that the orbit is in the shape of a circle.

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It's really in the shape of a squashed circle or an ellipse.

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The German mathematician and astronomer Johannes Kepler

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discovered this fact a long time ago.

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In this activity, you'll use measurement and observation

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to understand the meaning of the eccentricity of an ellipse.

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You'll calculate the distance between Earth and Mars,

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determine the length of their orbits,

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and learn about their orbital rates as compared to their distances from the sun.

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But before we get started, here are the materials you'll need.

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A computer with a Spreadsheet program or calculators,

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centimeter graph paper,

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two push pins for each group,

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a string 25 centimeters long for each group,

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cardboard, and one metric ruler for each group.

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Kepler stated that the orbit of Mars or of any planet

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is an ellipse with the sun at one focus.

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The other focus is an imaginary point.

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There is nothing there.

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During part of its orbit around the sun,

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Mars is closer to the sun than it is at other times.

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This relationship can be seen in solar system data charts

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that show the maximum and minimum distances from the sun to each planet.

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Astronomers often use the average or mean distance from the sun

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instead of the minimum or maximum.

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Enter the data from the chart into a Spreadsheet program

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or use a calculator,

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and for each planet, find the mean distance from the sun.

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Now make a sketch of the orbits of the Earth and Mars around the sun.

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Another column of data on the planet chart

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lists the eccentricity of each planet's orbit.

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Eccentricity gives an indication of roundness or squashness of each ellipse.

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To understand what this number means,

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here is an experiment to do with your team.

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On a piece of centimeter graph paper, draw two lines,

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one near the middle vertically and one near the middle horizontally.

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The lines intersect at the center point.

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Measure and cut a piece of string about 25 centimeters long.

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Tie a knot near the ends of the string to form a loop.

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Place the graph paper on a piece of cardboard,

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then place two push pins along the horizontal line,

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each one centimeter from the center point.

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These pins represent the foci.

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At this point, the foci are two centimeters apart.

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Loop the string around the push pins,

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then use a pencil to keep the string tight and draw an ellipse.

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Measure, in centimeters, the length of the ellipse along its major axis.

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Record the distance between the two foci and the length of the major axis on a chart.

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Then divide the distance between the foci by the length of the major axis

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and record the quotient on the chart.

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Now repeat these steps using the following distances between foci.

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Three centimeters, four centimeters, five centimeters.

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Choose your own distance.

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After you have recorded the distances between the foci

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and the length of the major axis on the data chart,

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use a calculator to divide the distance by the major axis length.

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The quotient will give you the eccentricity for the ellipses.

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Remember, the value of the eccentricity should be a decimal with a value of less than one.

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On the chart, make sketches of the ellipses you've created.

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Analyze your data, guys.

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This would be a great time to stop the video and consider the following questions.

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How does the distance between the foci affect the shape of the ellipse?

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What is the relationship between the value of the eccentricity

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and the roundness or squashedness of the ellipse?

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Although the orbits of both Earth and Mars are ellipses,

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their orbits are close enough to being circles

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that we can estimate the distance from the Earth to Mars.

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Let's assume both planets are on the same side of the Sun.

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Consider the mean distance from the Sun to each planet as the radius of a circle.

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Use the mean distance you calculated from the Sun to Earth and the Sun to Mars

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to determine the estimated direct distance between the Earth and Mars.

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What if Earth and Mars were on opposite sides of the Sun, like this?

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These activities and more are located in the Educator's Lesson Guide,

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which can be downloaded from our NASA Connect website.