Informal Version of The Newton n-body Problem
The physical problem can be informally stated as:
- Given only the present positions and velocities of a group of celestial bodies, predict their motions for all future time and deduce them for all past time.
More precisely,
- Consider point masses, ..., in three-dimensional (physical) space. Suppose that the force of attraction experienced between each pair of particles is Newtonian. Then, if the initial positions in space and initial velocities are specified for every particle at some present instant, determine the position of each particle at every future (or past) moment of time.
In mathematical terms, this means to find a global solution of the initial value problem for the differential equations describing the -body problem.
Read more about this topic: n-body Problem
Famous quotes containing the words informal, version, newton and/or problem:
“We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.”
—James P. Comer (20th century)
“Exercise is the yuppie version of bulimia.”
—Barbara Ehrenreich (b. 1941)
“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)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)