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Newtonian gravity 
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#1
Aug1607, 02:18 PM

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how would you describe newtonian gravity as a vector field?



#2
Aug1607, 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. 


#3
Aug1607, 07:58 PM

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P: 11,875

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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