Newton's Theory
In the field theoretic elaboration of Newtonian gravity, the central quantity is the gravitational potential, which obeys the Poisson equation
where is the mass density of any matter present. Note that this equation implies that in a vacuum solution, the potential is simply a harmonic function.
The tidal tensor is given by the traceless part
of the Hessian
where we are using the standard Cartesian chart for E3, with the Euclidean metric tensor
Using standard results in vector calculus, this is readily converted to expressions valid in other coordinate charts, such as the polar spherical chart
Read more about this topic: Tidal Tensor
Famous quotes containing the words newton and/or theory:
“I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
—Isaac Newton (1642–1727)
“It makes no sense to say what the objects of a theory are,
beyond saying how to interpret or reinterpret that theory in another.”
—Willard Van Orman Quine (b. 1908)