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Field equations of Newton.

  1. Sep 23, 2014 #1
    Am I right when I say during Newton's time there was no idea of fields?

    Now I have been looking for books and courses which are meant for amateurs. So I came across this video of one of my favourite professors Prof Leonard Susskind. http://theoreticalminimum.com/courses/general-relativity/2012/fall/lecture-9.

    In this lecture he has mentioned about Newtons field equations. How can there be newtons field equations? Can somebody explain me what it means and what the variables stand for?

    F= ma= -m∇Φ(x)

    a= -∇Φ(x)
  2. jcsd
  3. Sep 23, 2014 #2


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    Newton didn't know about fields when he proposed his gravity law. But that doesn't mean his law can't be formulated in terms of fields.
    In this formulation, there is a scalar field called [itex] \Phi [/itex] called the gravitational potential and a vector field [itex] \vec g=-\vec \nabla \Phi [/itex] called gravitational acceleration such that a particle at position [itex] \vec r [/itex] has acceleration [itex] \vec g (\vec r) [/itex].
  4. Sep 23, 2014 #3
    The term "field" did not exist in Newton's time. However, the concept is implicit in Newton's gravitational law, because it assigns a particular value and direction of the force of gravity to every spatial location.
  5. Sep 26, 2014 #4
    Do you mean that the spacial location is the r (Distance from centre of object of mass M)? Also how does the vector "a" (Mentioned as "g" by Shyan) have a direction?
  6. Sep 27, 2014 #5


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    The magnitude of the force depends on the distance r between the objects and therefore on where in space the objects are located. Having a direction is what sets vectors apart from normal numbers. In the case of gravity, the force (and hence acceleration) has the direction "towards the gravitating body".
  7. Sep 27, 2014 #6
    Poisson's equation, ## \nabla^2 \Phi = 4 \pi G \rho ##, is the appropriate field equation for Newtonian gravity. The potential Φ is a scalar, and g is a vector because it has for each space dimension the gradient of Φ along that dimension.
  8. Sep 27, 2014 #7
    You cannot say "a spatial location is the distance from something", because there are infinitely many spatial locations at a distance from something, all in different directions. In addition to the distance, you must specify a direction.
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