Why does Earth not remain stationary as the Moon orbits it? This is because, as expected from Newton’s third law, if Earth exerts a force on the Moon, then the Moon should exert an equal and opposite force on Earth (see Figure 6.20). The clear implication is that Earth’s gravitational force causes the Moon to orbit Earth. This agreement is approximate because the Moon’s orbit is slightly elliptical, and Earth is not stationary (rather the Earth-Moon system rotates about its center of mass, which is located some 1700 km below Earth’s surface). The centripetal acceleration of the Moon found in (b) differs by less than 1% from the acceleration due to Earth’s gravity found in (a). The direction of the acceleration is toward the center of the Earth. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Stated in modern language, Newton’s universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. It is always attractive, and it depends only on the masses involved and the distance between them. The gravitational force is relatively simple. Prominent French scientist and philosopher Émilie du Châtelet helped establish Newton's theory in France and mainland Europe. Like many revolutionary discoveries, it was not immediately accepted. Newton’s universal law of gravitation and his laws of motion answered very old questions about nature and gave tremendous support to the notion of underlying simplicity and unity in nature. The inspiration of Newton’s apple is a part of worldwide folklore and may even be based in fact. She also utilized calculus to explain gravity, which helped lead to its acceptance.įigure 6.17 According to early accounts, Newton was inspired to make the connection between falling bodies and astronomical motions when he saw an apple fall from a tree and realized that if the gravitational force could extend above the ground to a tree, it might also reach the Sun. Du Châtelet, who had earlier laid the foundation for the understanding of conservation of energy as well as the principle that light had no mass, translated and augmented Newton's key work. It took the work of another prominent philosopher, writer, and scientist, Émilie du Châtelet, to establish the Newtonian gravitation as the accurate and overarching law. Other prominent scientists and mathematicians of the time, particularly those outside of England, were reluctant to accept Newton's principles. This theoretical prediction was a major triumph-it had been known for some time that moons, planets, and comets follow such paths, but no one had been able to propose a mechanism that caused them to follow these paths and not others. But Newton was the first to propose an exact mathematical form and to use that form to show that the motion of heavenly bodies should be conic sections-circles, ellipses, parabolas, and hyperbolas. Some of Newton’s contemporaries, such as Robert Hooke, Christopher Wren, and Edmund Halley, had also made some progress toward understanding gravitation. His forerunner Galileo Galilei had contended that falling bodies and planetary motions had the same cause. But Newton was not the first to suspect that the same force caused both our weight and the motion of planets. Sir Isaac Newton was the first scientist to precisely define the gravitational force, and to show that it could explain both falling bodies and astronomical motions. It is a force that acts at a distance, without physical contact, and is expressed by a formula that is valid everywhere in the universe, for masses and distances that vary from the tiny to the immense. It is the weakest of the four basic forces found in nature, and in some ways the least understood. Gravity is another example of underlying simplicity in nature. In fact, the same force causes planets to orbit the Sun, stars to orbit the center of the galaxy, and galaxies to cluster together. And the Moon orbits Earth because gravity is able to supply the necessary centripetal force at a distance of hundreds of millions of meters. An apple falls from a tree because of the same force acting a few meters above Earth’s surface. Our feet are strained by supporting our weight-the force of Earth’s gravity on us. What do aching feet, a falling apple, and the orbit of the Moon have in common? Each is caused by the gravitational force. Describe the gravitational effect of the Moon on Earth.By the end of this section, you will be able to:
0 Comments
Leave a Reply. |