Newton's Law of Universal Gravitation - Problems With Newton's Theory

Problems With Newton's Theory

Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities φ/c2 and (v/c)2 are both much less than one, where φ is the gravitational potential, v is the velocity of the objects being studied, and c is the speed of light. For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since

\frac{\Phi}{c^2}=\frac{GM_\mathrm{sun}}{r_\mathrm{orbit}c^2} \sim 10^{-8}, \quad \left(\frac{v_\mathrm{Earth}}{c}\right)^2=\left(\frac{2\pi r_\mathrm{orbit}}{(1\ \mathrm{yr})c}\right)^2 \sim 10^{-8}

where rorbit is the radius of the Earth's orbit around the Sun.

In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.

Read more about this topic:  Newton's Law Of Universal Gravitation

Famous quotes containing the words problems with, problems, newton and/or theory:

    “She has problems with separation; he has trouble with unity—problems that make themselves felt in our relationships with our children just as they do in our relations with each other. She pulls for connection; he pushes for separateness. She tends to feel shut out; he tends to feel overwhelmed and intruded upon. It’s one of the reasons why she turns so eagerly to children—especially when they’re very young.”
    —Lillian Breslow Rubin (20th century)

    “While the onset of puberty can vary by as much as six years, every adolescent wants to be right on the 50-yard line, right in the middle of the field. One is always too tall, too short, too thin, too fat, too hairy, too clear-skinned, too early, too late. Understandably, problems of self-image are rampant.”
    —Joan Lipsitz (20th century)

    “The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
    —Horace Walpole (1717–1797)

    “Thus the theory of description matters most.
    It is the theory of the word for those
    For whom the word is the making of the world,
    The buzzing world and lisping firmament.”
    —Wallace Stevens (1879–1955)