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:
“Glorious things of thee are spoken, Zion city of our God!
He, whose word cannot be broken, Form’d for thee his own abode:
On the rock of ages founded, What can shake thy sure repose?
With salvation’s walls surrounded Thou may’st smile at all thy foes.”
—John Newton (1725–1807)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)