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phys: clarify orbital radius and centre of mass

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eggy 2020-11-23 09:55:12 -05:00
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@ -588,7 +588,7 @@ $$\Sigma \vec{F}_c=m\vec{a}_c$$
All masses exert gravitational force on each other. The universal law of gravitation states that the gravitational force, $F_G$ between any two objects is attractive along the line joining them and equal to: All masses exert gravitational force on each other. The universal law of gravitation states that the gravitational force, $F_G$ between any two objects is attractive along the line joining them and equal to:
$$\vec{F}_G=G\frac{mM}{r^2}$$ $$\vec{F}_G=G\frac{mM}{r^2}$$
where $G=6.67×10^{-11} \text{ N}\cdot\text{m}^2\cdot\text{kg}^{-2}$ is Newton's constant of universal gravitation, $r$ is the distance between the objects' **centre of mass**, and $m$ and $M$ are the masses of the objects acted on and acting, respectively. This indicates that the force on a given mass is proportional to its distance: $F_G \propto \frac{1}{r^2}$. where $G=6.67×10^{-11} \text{ N}\cdot\text{m}^2\cdot\text{kg}^{-2}$ is Newton's constant of universal gravitation, the **orbital radius** $r$ is the distance between the objects' **centre of mass**, and $m$ and $M$ are the masses of the objects acted on and acting, respectively. This indicates that the force on a given mass is proportional to its distance: $F_G \propto \frac{1}{r^2}$.
The net gravitational force acting on an object is equal to the resultant vector formed by components of each force acting on it. The net gravitational force acting on an object is equal to the resultant vector formed by components of each force acting on it.
@ -603,7 +603,7 @@ Its units also make it equivalent to the acceleration experienced by that mass.
$$\vec{g}=\frac{\vec{F}_G}{m}$$ $$\vec{g}=\frac{\vec{F}_G}{m}$$
!!! note !!! note
Only the distance between objects and the mass of the **body acting** on another affect gravitational field strength of the acting body. Only the distance between the centre of mass of the objects and the mass of the **body acting** on another affect gravitational field strength of the acting body.
<img src="/resources/images/grav-radial-lines.png" width=700>(Source: Kognity)</img> <img src="/resources/images/grav-radial-lines.png" width=700>(Source: Kognity)</img>