This is called the principle of equivalence. In Einstein’s general theory, there is no difference between free fall and being weightless. Indeed, it is common to speak of astronauts orbiting Earth as being weightless, despite the fact that Earth’s gravity is still quite strong there. The Principle of EquivalenceĮinstein came to his general theory in part by wondering why someone who was free falling did not feel their weight. The mathematics of the general theory is beyond the scope of this text, but we can look at some underlying principles and their consequences. It was not a theory of gravitational forces. His theory was a theory of space-time geometry and how mass (and acceleration) distort and interact with that space-time. In Einstein’s subsequent theory of general relativity (1916), both of these issues were addressed. Again, there is no underlying principle that this must be, but experimental results are consistent with this assumption. We made that assumption in many of our derivations in this chapter. The masses are assumed to be exactly the same as those used in Newton’s second law, F → = m a → F → = m a →. It is fair to say that most scientists were not completely comfortable with the action-at-a-distance concept.)Ī second assumption also appears in Newton’s law of gravitation Equation 13.1. (The same was believed of electromagnetic forces, as well. This assumption does not come from any first principle, as Newton’s theory simply does not address the question. That is, without physical contact, any change in the position of one mass is instantly communicated to all other masses. This speed limit on the Universe was also a challenge to the inherent assumption in Newton’s law of gravitation that gravity is an action-at-a-distance force. Almost all of the mechanics you learned in previous chapters, while remarkably accurate even for speeds of many thousands of miles per second, begin to fail when approaching the speed of light. Two people moving relative to one another do not agree on the length of objects or the passage of time. However, it has incredible consequences-space and time are no longer absolute. This simple fact has been verified in countless experiments. In this theory, no motion can exceed the speed of light-it is the speed limit of the Universe. This theory is discussed in great detail in Relativity, so we say only a few words here. In 1905, Albert Einstein published his theory of special relativity. In this section, we examine a different way of envisioning gravitation. Nevertheless, many phenomena have shown a discrepancy from what Newton’s laws predict, including the orbit of Mercury and the effect that gravity has on light. The paths of Earth-crossing asteroids, and most other celestial objects, can be accurately determined solely with Newton’s laws. Indeed, only Newton’s laws have been needed to accurately send every space vehicle on its journey. Newton’s law of universal gravitation accurately predicts much of what we see within our solar system. Calculate the Schwarzschild radius of an object.Describe how the theory of general relativity approaches gravitation.By the end of this section, you will be able to:
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