Orbital Motion Jean Brainard, Ph.D. Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2012 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/NonCommercial/Share Alike 3.0 Unported (CC BY-NC-SA) License (http://creativecommons.org/licenses/by-nc-sa/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated herein by this reference. Complete terms can be found at http://www.ck12.org/terms. Printed: January 14, 2013 AUTHOR Jean Brainard, Ph.D. www.ck12.org C ONCEPT Concept 1. Orbital Motion 1 Orbital Motion • Define orbital motion and explain why it occurs. • Describe the orbits of Earth around the sun and the moon around Earth. As you can see in this NASA photo, Earth is tiny compared with the massive sun. The sun’s gravity is relatively strong because the force of gravity between two objects is directly proportional to their masses. Gravity between the sun and Earth pulls Earth toward the sun, but Earth never falls into the sun. Instead, it constantly revolves around the sun, making one complete revolution every 365 days. Q: Why doesn’t the sun’s gravity pull Earth down to the surface of the sun? A: Earth has enough forward velocity to partly counter the force of the sun’s gravity. What Is Orbital Motion? Earth and many other bodies—including asteroids, comets, and the other planets—move around the sun in curved paths called orbits. Generally, the orbits are elliptical, or oval, in shape. You can see the shape of Earth’s orbit in the Figure 1.1. Because of the sun’s relatively strong gravity, Earth and the other bodies constantly fall toward the sun, but they stay far enough away from the sun because of their forward velocity to fall around the sun instead of into it. As a result, they keep orbiting the sun and never crash to its surface. The motion of Earth and the other bodies around the sun is called orbital motion. Orbital motion occurs whenever an object is moving forward and at the same time is pulled by gravity toward another object. You can explore orbital motion and gravity in depth with the animation at this URL: http://phet.colorado.edu/en/simulation/gravity-and-orbits 1 www.ck12.org FIGURE 1.1 Orbital Motion of the Moon Just as Earth orbits the sun, the moon also orbits Earth. The moon is affected by Earth’s gravity more than it is by the gravity of the sun because the moon is much closer to Earth. The gravity between Earth and the moon pulls the moon toward Earth. At the same time, the moon has forward velocity that partly counters the force of Earth’s gravity. So the moon orbits Earth instead of falling down to the surface of the planet. The Figure 1.2 shows the forces involved in the moon’s orbital motion around Earth. In the diagram, v represents the forward velocity of the moon, and a represents the acceleration due to gravity between Earth and the moon. The line encircling Earth shows the moon’s actual orbit, which results from the combination of v and a. You can see an animated version of this diagram at: http://en.wikipedia.org/wiki/File:Orbital_motion.gif FIGURE 1.2 Summary • Orbital motion occurs whenever an object is moving forward and at the same time is pulled by gravity toward another object. • The forward velocity of the object combines with acceleration due to gravity toward the other object. The result is a circular or oval path called an orbit, in which one object keeps moving around the other. • Because of the relatively great gravity of the sun, Earth orbits the sun. The moon orbits Earth rather than the sun because it is much closer to Earth. 2 www.ck12.org Concept 1. Orbital Motion Vocabulary • orbit: Path of one object around another, such as the path of the moon around Earth or of Earth around the sun. • orbital motion Practice At the following URL, experiment with the gravity-and-orbit simulator. Set different initial velocities for the cannon ball and observe whether the cannon ball crashes, escapes from Earth, or is set into orbit. Then answer the questions below. http://home.snc.edu/takamasatakahashi/login/AstroSp10/Animations/Active_Figures/10/ 1. Which range of initial velocities for the cannon ball puts it into orbit? 2. What happens to the cannon ball if its initial velocity is less than this range? 3. What happens to the cannon ball if its initial velocity is greater than this range? Review 1. Define orbit and orbital motion, and explain why orbital motion occurs. 2. In addition to the moon, artificial satellites also orbit Earth. What factors do you think must be taken into account to ensure that a satellite keeps orbiting Earth rather than falling back to Earth’s surface? 3. Earth is closer to nearby planets including Venus and Mars than it is to the sun. Why don’t these other planets pull Earth toward them and cause it to veer off its orbit around the sun. 3
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