OrbitalMotionSE+(1)

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Miami Dade College, Miami *

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2011

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Physics

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Feb 20, 2024

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docx

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2019 Name: Ashlee Garcia Date: 1/22/2023 Student Exploration: Orbital Motion – Kepler’s Laws Vocabulary: astronomical unit, eccentricity, ellipse, force, gravity, Kepler’s first law, Kepler’s second law, Kepler’s third law, orbit, orbital radius, period, vector, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. The orbit of Halley’s Comet, shown at right, has an oval shape. In which part of its orbit do you think Halley’s Comet travels fastest? Slowest? Mark these points on the diagram at right. 2. How might a collision between Neptune and Halley’s Comet affect Neptune’s orbit? It would not affect Neptune’s orbit Gizmo Warm-up The path of each planet around the Sun is determined by two factors: its current velocity (speed and direction) and the force of gravity on the planet. You can manipulate both of these factors as you investigate planetary orbits in the Orbital Motion – Kepler’s Laws Gizmo. On the CONTROLS pane of the Gizmo, turn on Show trails and check that Show vectors is on. Click Play ( ). 1. What is the shape of the planet’s orbit? An eplise 2. Watch the orbit over time. Does the orbit ever change, or is it stable? Stable 3. Click Reset ( ). Drag the tip of the purple arrow to shorten it and reduce the planet’s initial velocity. Click Play . How does this affect the shape of the orbit? The eclipse becomes more elongated /flatter Activity A: Shape of orbits Get the Gizmo ready : Click Reset . Turn on Show grid . Introduction: The velocity of a planet is represented by an arrow called a vector . The vector is described by two components: the i component represents east-west speed and the j component represents north-south speed. The unit of speed is kilometers per second (km/s).
2019 Question: How do we describe the shape of an orbit? 1. Sketch : The distance unit used here is the astronomical unit (AU), equal to the average Earth-Sun distance. Place the planet on the i axis at r = –3.00 i AU. Move the velocity vector so that v = -8.0 j km/s (| v | = 8.00 km/s). The resulting vectors should look like the vectors in the image at right. (Vectors do not have to be exact.) Click Play , and then click Pause ( ) after one revolution. Sketch the resulting orbit on the grid. 2. Identify : The shape of the orbit is an ellipse , a type of flattened circle. An ellipse has a center (C) and two points called foci (F 1 and F 2 ). If you picked any point on the ellipse, the sum of the distances to the foci is constant. For example, in the ellipse at left: a 1 + a 2 = b 1 + b 2 Turn on Show foci and center . The center is represented by a red dot, and the foci are shown by two blue dots. What do you notice about the position of the Sun? The sun is located at one of the foci. 3. Experiment : Try several other combinations of initial position and velocity. A. What do you notice about the orbits? The orbits are either circular or elliptical shape. B. What do you notice about the position of the Sun? The sun remains at the center as one of the foci. You have just demonstrated Kepler’s first law , one of three laws discovered by the German astronomer Johannes Kepler (1571–1630). Kepler’s first law states that planets travel around the Sun in elliptical orbits with the Sun at one focus of the ellipse. (Activity A continued on next page)
2019 Activity A (continued from previous page) 4. Observe : Use the Gizmo to create an orbit that is nearly circular. Then create an orbit that is flattened. Observe the foci in each ellipse. A. What do you notice about the spacing of the foci when the ellipse is very round? The closer the foci are, the more round the ellipse is. B. What do you notice about the spacing of the foci when the ellipse is very flat? The foci are further apart. 5. Calculate : The eccentricity of an ellipse is a number that describes the flatness of the ellipse. Eccentricity is equal to the distance between foci divided by the total width of the ellipse. There are no units for eccentricity. Click Reset . Move the planet to r = –5.00 i AU (does not have to be exact) and drag the velocity vector to set the velocity close to –8.0 j km/s. Click Play , and then click Pause after one full revolution. A. What is the distance between the foci? 2 B. What is the approximate width of the ellipse? 8 C. What is the eccentricity of the ellipse? 0.25 D. Click Reset , and change the initial velocity to –4.0 j km/s. Click Play . What is the eccentricity of this ellipse? Distance between foci: 4.5 Width: 5.5 Eccentricity: 0.81 6. Draw conclusions : Think about the eccentricity and shape of each ellipse. A. What is the relationship between the eccentricity of an ellipse and its shape? The lower the eccentricity the smaller the ellipse. The larger the eccentricity the larger the ellipse. B. What is the eccentricity of a circle? Explain. The eccentricity of a circle is zero because the distance between foci and the center are zero. C. What is the eccentricity of a completely flat ellipse? Explain. A completely flat ellipse would have an eccentricity closer to one because the foci and the center are further apart. D. The eccentricity of Earth’s orbit is 0.017. What can you infer about the shape of Earth’s orbit? Earth’s orbit is more circular in shape.
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