## newtonian gravity

how would you describe newtonian gravity as a vector field?
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 Recognitions: Gold Member Homework Help Science Advisor Well, as a simple case, suppose you've got a mass positioned at location $$\vec{x}_{0}=(x_{0},y_{0},z_{0})$$ with mass $m_{0}$ Then, for any spatial point $$(x,y,z)=\vec{x}\neq\vec{x}_{0}$$ that mass generates at that point a force per unit mass: $$\vec{f}(x,y,z)=-\frac{Gm_{0}}{||\vec{x}-\vec{x}_{0}||^{3}}(\vec{x}-\vec{x}_{0})$$ The force $\vec{F}$ acting upon an object of mass M situated at (x,y,z) is then found by multiplying f with M.
 Mentor Another form you sometimes see assumes that the mass is at the origin, and uses spherical coordinates: $$\vec F (r, \theta, \phi) = - \frac{G m_0}{r^2} \hat r$$ where $\hat r$ is the unit vector in the outward radial direction at that particular point.