Teacher Notes



Teacher Notes
Publication No. 12813
Planetary OrbitsStudent Laboratory KitMaterials Included In Kit
Bolts, 20
Felt bumpers, 50 Hexagonal nuts, 60 Planetary Orbits plastic platforms with holes, 10 String Washers, ½" diam., 10 Additional Materials Required
(for each lab group)
Calculator (optional) Pencil, wood (not mechanical) Ruler, metric Scissors Tape, transparent Prelab Preparation
Lab HintsEnough materials are provided in this kit for 30 students working in groups of 3 or for 10 groups of students. Both parts of this laboratory activity can reasonably be completed in one 45 to 50minute class period. The prelaboratory assignment may be completed before coming to lab, and the calculations and analysis may be completed the day after the lab.If a bolt has too much play after being securely fastened onto the platform, unscrew the nut and turn it over or try using a different nut. A few hexagonal nuts may not be completely flat on one side, preventing a tight fit.Allow students as a class to brainstorm and collectively agree upon a definition of an ellipse for Question 9. Teacher Tips
Correlation to Next Generation Science Standards (NGSS)^{†}Science & Engineering PracticesDeveloping and using modelsPlanning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Constructing explanations and designing solutions Disciplinary Core IdeasMSESS1.B: Earth and the Solar SystemHSESS1.B: Earth and the Solar System Crosscutting ConceptsPatternsSystems and system models Performance ExpectationsHSESS15. Evaluate evidence of the past and current movements of continental and oceanic crust and the theory of plate tectonics to explain the ages of crustal rocks. Answers to Prelab Questions
Sample DataData Table 1 {12813_Data_Table_2}
Data Table 2
{12813_Data_Table_3}
Answers to Questions
Teacher HandoutsReferencesPlanetary Fact Sheets. http://nssdc.gsfc.nasa.gov/planetaryplanetfact.html (accessed May, 2009). Recommended Products


Student Pages


Student PagesPlanetary OrbitsIntroductionJohannes Kepler (1571–1630) determined that orbits of the planets around the Sun are not circles as originally thought, but “stretched out circles” called ellipses. Explore the shape of a planet’s orbit and investigate Kepler’s laws of planetary motion. Concepts
BackgroundBefore Isaac Newton (1642–1727) developed his laws of gravity and motion, Johannes Kepler observed the planets and formulated his own laws of planetary motion. In 1543, just before he died, Nicolaus Copernicus (1473–1543) published a book in which he proposed that the Sun, not the Earth, was the center of the solar system and the planets orbited the Sun in circular paths. Although placing the Sun at the center of the solar system explained many observations of planetary motion, certain observations did not fit with the proposed circular orbits. In 1609, Kepler published a book entitled New Astronomy. In his manuscript, Kepler presented detailed observations made by the wellrespected astronomer Tycho Brahe (1546–1601), as well as his own observations and calculations, to show that the planets do not travel in perfect circular orbits. Instead, they travel in oblong paths known as ellipses. An ellipse is an elongated circle that has two separate points of rotation, or foci (singular focus), instead of one central point (see Figure 1). The longest distance from end to end through the center of the ellipse is the major axis and the shortest distance through the center is the _{minor axis}. {12813_Background_Figure_1}
The “oblongness” of the ellipse is known as its eccentricity. The eccentricity (e) is calculated as the ratio of the distance between the foci (f) to the length of the major axis (a) of the ellipse (Equation 1).
{12813_Background_Equation_1}
An ellipse with an eccentricity of zero (both foci at the same point) is a circle. The larger the eccentricity, the more flattened the ellipse (see Figure 2). Elliptical orbits have an eccentricity between zero and one.
{12813_Background_Figure_2}
The eccentricities of most of the planets are very close to zero; therefore, on a small classroomscale model, the difference between a circular orbit and an elliptical orbit of a planet is difficult to discern. Mercury, Pluto, and Halley’s Comet are exceptions (see Table 1). These orbiting bodies have larger eccentricities and therefore follow more elongated paths.
{12813_Background_Table_1}
*AU is an abbreviation for the Astronomical Unit which is equal to the Earth’s average distance to the Sun (1.50 x 10^{11} m). Kepler’s first law of planetary motion states that the orbits of the planets are ellipses and the center of the Sun is one focus of the ellipse. As a result, a planet’s distance to the Sun is constantly changing. When a planet crosses the major axis of its orbit, the planet will be either at its farthest distance from the Sun or at its closest distance. The farthest distance is known as the aphelion and the closest distance a planet is to the Sun is the perihelion (see Figure 3). As a consequence of the conservation of angular momentum, the orbital speed of a planet is inversely proportional to its distance from the Sun. In other words, as a planet’s distance from the Sun increases, its orbital speed decreases. The closer a planet is to the Sun, the faster it orbits. Kepler noticed this change in the orbiting speed of the planets and discovered that the area of space swept by a planet in a given amount of time is always the same, no matter where the planet is in its orbit. Kepler called this second law the Law of Equal Areas (see Figure 3). If the time a planet takes to travel along arc A in Figure 3 is the same as the time traveled along arc B, then the area of space produced by arc A is equal to the area of space produced by arc B. {12813_Background_Figure_3}
Kepler’s observations also allowed him to formulate an equation to show the relationship between the period of revolution and the major axis of the planets; this relationship is known as the Law of Planetary Periods. Years later, Newton validated this third law of planetary motion when he derived Kepler’s equation from his own equations of universal gravitation.
Experiment OverviewThe purpose of this activity is to investigate the shape of planetary orbits by constructing three different ellipses. Data will be collected and the eccentricity of each ellipse will be calculated. The factors that affect the eccentricity of an ellipse will also be determined. Materials
Bolts, 2
Hexagonal nuts, 6 Pencil, wood (not mechanical) Planetary Orbits paper templates, 3 Planetary Orbits platform with holes Ruler, metric Scissors String, 53 cm Tape, transparent Washer Prelab Questions
Safety PrecautionsPlease follow all laboratory safety guidelines. ProcedurePart 1. Drawing the Ellipses
Part 2. Investigating the Ellipses
Student Worksheet PDF 