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Newtonian gravity

by captain
Tags: gravity, newtonian
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captain
#1
Aug16-07, 02:18 PM
P: 163
how would you describe newtonian gravity as a vector field?
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arildno
#2
Aug16-07, 02:26 PM
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Well, as a simple case, suppose you've got a mass positioned at location [tex]\vec{x}_{0}=(x_{0},y_{0},z_{0})[/tex] with mass [itex]m_{0}[/itex]

Then, for any spatial point [tex](x,y,z)=\vec{x}\neq\vec{x}_{0}[/tex]
that mass generates at that point a force per unit mass:
[tex]\vec{f}(x,y,z)=-\frac{Gm_{0}}{||\vec{x}-\vec{x}_{0}||^{3}}(\vec{x}-\vec{x}_{0})[/tex]

The force [itex]\vec{F}[/itex] acting upon an object of mass M situated at (x,y,z) is then found by multiplying f with M.
jtbell
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Aug16-07, 07:58 PM
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Another form you sometimes see assumes that the mass is at the origin, and uses spherical coordinates:

[tex]\vec F (r, \theta, \phi) = - \frac{G m_0}{r^2} \hat r[/tex]

where [itex]\hat r[/itex] is the unit vector in the outward radial direction at that particular point.


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