# They found that the size of the semi major axis of

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Chapter 1 / Exercise 56
Calculus
Stewart
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the 1970’s. They found that the size of the semi-major axis of the orbit decreases with time at a rate that is predicted by the equations of General Relativity. The orbital decay occurs because energy is lost from the system as it emits gravitational waves. Instruments designed to observe gravitational waves directly are now in operation, but thus far the sensitivity has not been sufficient to detect the weak wave signals expected from cosmic objects. Summary The speed of light c is the speed limit of the universe. No information or energy can move faster than light and no matter can even reach c . After Michelson measured the speed of light, he and Morley determined that c does not depend on the relative motion between the source of the light and the observer. Einstein adopted this, along with the requirement that all observers measure the same results of experiments that take place in their own rest frame. He used these assumptions as the basis of Special Relativity, which describes measurements of phenomena that occur in non-accelerating reference frames that are in motion relative to one another. Einstein found that the measurements of such fundamental quantities as length and time are not absolute. Instead, they depend on the velocity of the object or system relative to the observer. For example, certain particles that are very short-lived if they are stationary have much longer lives if they move at a velocity very close to the speed of light relative to the observer. This is not an illusion: a measurement represents reality. It only seems strange to us because we are not accustomed to observing objects that move at speeds near that of light. In fact, the predictions of Special Relativity have been verified many times to extremely high precision. An important parameter of Special Relativity is the Lorentz factor Γ , which corresponds to how many times shorter an object is measured to be than its rest length and how many times more slowly time passes in a moving reference frame as viewed by an outside observer. Einstein also formulated his famous equation E=mc 2 that defines the rest-mass energy. This means that mass and energy are really just two manifestations of a single property of matter, mass-energy. Scientists later used this formula to explain the energy sources of stars and also to build nuclear weapons and reactors. After deriving Special Relativity, Einstein developed General Relativity, which considers accelerating reference frames and gravity. His interpretation of gravity as bending of space-time is qualitatively different from Newton’s “action at a distance” description, yet the two produce nearly identical results except near very massive objects. The curvature of space-time causes light to follow a bent path around a massive object such as the sun. Galaxies can even act as gravitational lenses, causing the appearance of multiple images of objects that lie at large distances beyond them. A remote observer measures time
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Chapter 1 / Exercise 56
Calculus
Stewart
Expert Verified