F is often the weight of an object on the surface of a large object with mass M, which is usually known. Several of the values in this equation are either constants or easily obtainable. The first is Newton’s equation, F = G m M r 2 F = G m M r 2. Two equations involving the gravitational constant, G, are often useful. This may be a rather long-winded explanation of the mass-weight distinction, but it should drive home the point. It is also another connection that any particle with mass or energy (e.g., massless photons) is affected by gravity. This is another radical change in our concept of space and time. The bending of light by matter is equivalent to a bending of space itself, with light following the curve. Einstein was now a folk hero as well as a very great scientist. This discovery created a scientific and public sensation. Not only was this shift observed, but it agreed with Einstein’s predictions well within experimental uncertainties. Those on a line of sight nearest the sun should have a shift in their apparent positions. (See Figure 7.11.) During an eclipse, the sky is darkened and we can briefly see stars. (b) Gravity must have the same effect on light, since it is not possible to tell whether the elevator is accelerating upward or is stationary and acted upon by gravity.Įinstein’s theory of general relativity got its first verification in 1919 when starlight passing near the sun was observed during a solar eclipse. Since the elevator moves up during the time the light takes to reach the wall, the beam strikes lower than it would if the elevator were not accelerated. Thus, gravity affects the path of light, even though we think of gravity as acting between masses, while photons are massless.įigure 7.10 (a) A beam of light emerges from a flashlight in an upward-accelerating elevator. The person in the elevator cannot tell whether the elevator is accelerating in zero gravity or is stationary and subject to gravity. The effect on light is the same: it “falls” downward in both situations. In Figure 7.10 (b), the room is not accelerating but is subject to gravity. In Figure 7.10 (a), the elevator accelerates upward in zero gravity. Figure 7.10 shows this effect (greatly exaggerated) in an accelerating elevator. He concluded that light must fall in both a gravitational field and in an accelerating reference frame. Einstein based his theory on the postulate that acceleration and gravity have the same effect and cannot be distinguished from each other. Einstein’s Theory of General RelativityĮinstein’s theory of general relativity explained some interesting properties of gravity not covered by Newton’s theory. Modern experiments of this type continue to explore gravity. The distance between the masses can be varied to check the dependence of the force on distance. It had been known for some time that moons, planets, and comets follow such paths, but no one had been able to propose an explanation of the mechanism that caused them to follow these paths and not others.įigure 7.9 Cavendish used an apparatus like this to measure the gravitational attraction between two suspended spheres ( m) and two spheres on a stand ( M) by observing the amount of torsion (twisting) created in the fiber. This theoretical prediction was a major triumph. 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. Concepts Related to Newton’s Law of Universal Gravitation General relativity is broader and includes special relativity, which was published first. General relativity is a theory of gravity and applies to observers that are accelerating. Special relativity is a theory of spacetime and applies to observers moving at constant velocity. Ask if anyone knows the difference between special relativity and general relativity. Compare the contributions of Kepler, Newton, and Einstein. In this section, students will apply Newton’s law of universal gravitation to objects close at hand and far off in the depths of the solar system.
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