Planetary Motion and Gravitation Guide

SECTION 1 Planetary Motion and Gravitation PHYSICS 4 YOU Our solar system includes the Sun, Earth and seven other major planets, dwarf planets, and interplanetary dust and gas. Various moons orbit the planets. What holds all this together? Early Observations MAIN IDEA The gravitational force between two objects is proportional to the product of their masses divided by the square of the distance between them. Essential Questions • What is the relationship between a planet’s orbital radius and period? • What is Newton’s law of universal gravitation, and how does it relate to Kepler’s laws? • Why was Cavendish’s investigation important? Review Vocabulary Newton's third law states all forces come in pairs and that the two forces in a pair act on different objects, are equal in strength, and are opposite in direction New Vocabulary Kepler’s first law Kepler’s second law Kepler’s third law gravitational force law of universal gravitation 0178_0185_C07_S01_659252.indd 178 In ancient times, the Sun, the Moon, the planets, and the stars were assumed to revolve around Earth. Nicholas Copernicus, a Polish astronomer, noticed that the best available observations of the movements of planets did not fully agree with the Earth-centered model. The results of his many years of work were published in 1543, when Copernicus was on his deathbed. His book showed that the motion of planets is much more easily understood by assuming that Earth and other planets revolve around the Sun. His model helped explain phenomena such as the inner planets Mercury and Venus always appearing near the Sun. Copernicus's view advanced our understanding of planetary motion. He incorrectly assumed, however, that planetary orbits are circular. This assumption did not fit well with observations, and modification of Copernicus's model was necessary to make it accurate. Tycho Brahe was born a few years after Copernicus died. As a boy of 14 in Denmark, Tycho observed an eclipse of the Sun on August 21, 1560. The fact that it had been predicted inspired him toward a career in astronomy. As Tycho studied astronomy, he realized that the charts of the time did not accurately predict astronomical events. Tycho recognized that measurements were required from one location over a long period of time. He was granted an estate on the Danish island of Hven and the funding to build an early research institute. Telescopes had not been invented, so to make measurements, Tycho used huge instruments that he designed and built in his own shop, such as those shown in Figure 1. Tycho is credited with the most accurate measurements of the time. Figure 1 Instruments such as these were used by Tycho to measure the positions of planets. 3/11/11 12:45 PM Figure 2 The orbit of each planet is an ellipse, with the Sun at one focus. Foci Planet Sun (Not to scale) Ellipse Kepler’s Laws View an animation of Kepler's first law. In 1600 Tycho moved to Prague where Johannes Kepler, a 29-year-old German, became one of his assistants. Kepler analyzed Tycho’s observations. After Tycho’s death in 1601, Kepler continued to study Tycho’s data and used geometry and mathematics to explain the motion of the planets. After seven years of careful analysis of Tycho’s data on Mars, Kepler discovered the laws that describe the motion of every planet and satellite, natural or artificial. Here, the laws are presented in terms of planets. Kepler’s first law states that the paths of the planets are ellipses, with the Sun at one focus. An ellipse has two foci, as shown in Figure 2. Although exaggerated ellipses are used in the diagrams, Earth’s actual orbit is very nearly circular. You would not be able to distinguish it from a circle visually. Kepler found that the planets move faster when they are closer to the Sun and slower when they are farther away from the Sun. Kepler’s second law states that an imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals, as illustrated in Figure 3. Concepts In Motion READING CHECK Compare the distances traveled from point 1 to point 2 and from point 6 to point 7 in Figure 3. Through which distance would Earth be traveling fastest? A period is the time it takes for one revolution of an orbiting body. Kepler also discovered a mathematical relationship between periods of planets and their mean distances away from the Sun. 11 12 10 9 Planet 8 1 Figure 3 Kepler found that elliptical orbits Sun 7 sweep out equal areas in equal time periods. Explain why the equal time areas are shaped differently. 6 5 2 3 0178_0185_C07_S01_659252.indd 179 4 (Not to scale) View an animation and a simulation of Kepler’s second law. Concepts In Motion 3/11/11 12:46 PM