Abdus Khan - Unit 2 -- Week 8 -- Physics in the Universe

Physics in the Universe Unit 2 -- Week 8 Assignments - Kepler’s Laws Capital City - Mrs. Oetinger 1.Textbook Reading Assignment In your Student STEMscopedia Physics in the Universe textbook, review/reread (as needed) from “Kepler’s Laws,” pages 29-37. 2. Concept Review Game Play the game entitled “Concept Review Game”. To access this game: 1) Log into your SCUSD Clever Page. 2.) Click on your digital textbook app for Stemscopes 3) When you open up Stemscopes, you will be able to see the link to the Concept Review Game that you will be taking. 3. Math Connections German mathematician and astronomer Johannes Kepler formulated three laws that describe the orbital paths of the planets in space. Kepler’s Laws The first law, known as the law of ellipses , suggests that planets move in an elliptical path with the Sun at one focus. An ellipse with both foci on the same location (the center) is called a circle . The eccentricity of an ellipse is a measure of how much it deviates from being a circle (eccentricity of 0). Since the Sun is not in the center of the orbit, as a planet orbits the Sun, sometimes it is closer to and other times it is farther away from the Sun. The closest point a planet gets to the Sun is called the perihelion . The farthest point is called the aphelion . 1

Use the following to fill out the table below. 1. The mean distance from the Sun is also known as the length of the semimajor axis of a planet’s orbit. Also, 1 astronomical unit (AU) = 1.496 x 10^8 km . Calculate the mean distance in kilometers and record your answers in the chart below, using scientific notation. 2. The perihelion distance can be calculated using the formula a(1-e) , in which a is the length of the semimajor axis and e is the eccentricity. Calculate the perihelion distance for each planet and record it in the chart below, using scientific notation. 3. The aphelion distance can be calculated using the formula a(1+e) , in which a is the length of the semimajor axis and e is the eccentricity. Calculate the perihelion distance for each planet and record it in the chart below, using scientific notation. 4. Use the eccentricities to rank the planet’s orbital shapes from 1 - 8, with 1 being closest to a circle. Planet Mean Distance to Sun (AU) Semimajor Axis (km) Orbital Eccentricity Orbital Rank Perihelion (km) Aphelion (km) Mercury 0.387 5.790x10^7 km 0.2056 Venus 0.723 0.0068 1.074x10^8 km Earth 1.000 0.0167 Mars 1.524 0.0934 2.493x10^8 km Jupiter 5.203 0.0484 2

6. Calculate the average velocity of Mercury. a. The actual average velocity is 48.927 km/s. How does your calculation compare? b. What could make your calculation more accurate? 4. Kepler’s Laws Review Key Terms- Ellipse, Foci, Major axis, Minor axis, Semimajor axis, Eccentricity, Kepler’s first law, Kepler’s second law, Kepler’s third law, Orbital period, Perihelion, Aphelion Reviewing Key Terms: Use each of the following terms in a separate sentence. 1. Aphelion 2. Eccentricity 3. Astronomical Unit 4. Focus 5. Orbital Period Use the correct key term to complete each of the following sentences. 1. ________ is the point closest to the Sun in the orbit of a celestial body. 4

2. Kepler’s first law that states that all planets move in a(n) ________ orbit around the Sun. 3. Orbital ________ is the time a given astronomical object takes to complete one orbit around another object. Reviewing Main Ideas: Highlight the correct answer please. 1. What is the main idea behind Kepler’s second law? a. All planets have elliptical orbits. b. Ratio between the area and time. c. Equal area in equal time. d. Ratio between time and distance. 2. Which description of eccentricity is correct? a. An eccentricity of zero is a line. b. An eccentricity of zero is a circle. c. An eccentricity of one is a circle. d. An eccentricity of one is circular. 3. The widest part of an ellipse is called-- a. The semimajor axis. b. The minor axis. c. The foci. d. The major axis. Making Connections: 1. Describe the relationship between the time it takes a planet to orbit the Sun and the planet’s distance from the Sun.. 5

C. The mass of Earth in kilograms, the mass of the satellite in kilograms, and the acceleration due to gravity (g) D. The mass of the satellite, the time it takes to orbit Earth, and the Universal Gravitational Constant (G) 3. A scientist is examining the orbital path of two comets. Comet A has an orbital eccentricity 0.70, while Comet B has an orbital eccentricity of 0.90. What can the scientist conclude about the orbits of the two comets? A. Both Comet A and B have similar orbital paths. B. Comet B’s orbit is less circular than Comet A’s orbit. C. Comet B takes longer to complete an orbit than Comet A. D. Comet A is closer to the Sun than Comet B. 4. Kepler’s second law states that the area swept out by a planet’s motion will be the same regardless of where it is in its orbit. A comet moves much faster when it is closer to the Sun than when it is further out from the Sun. What is the primary cause if the change of the comet’s orbital velocity? A. Jupiter’s gravitational field B. The Sun’s solar wind C. The Sun’s gravitational field D. Saturn’s magnetic field 5. The Moon orbits the Earth as the Earth orbits the Sun.The Moon’s orbit is elliptical, and changes its distance from the Earth by around 10% over the course of an orbit. Any ellipse has two centers, which are called foci. For the Moon’s orbit, what must exist at one of the two foci? A. Earth B. The Sun C. Jupiter D. Mars 7