diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 3645164..5aeb648 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -586,9 +586,9 @@ $$\Sigma \vec{F}_c=m\vec{a}_c$$ ## 6.2 - Newton's law of gravitation 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: -$$F_G=G\frac{mM}{r^2}$$ +$$\vec{F}_G=G\frac{mM}{r^2}$$ -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. +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: $F_G \propto \frac{1}{r^2}$. The net gravitational force acting on an object is equal to the resultant vector formed by components of each force acting on it. @@ -599,8 +599,23 @@ A **force field** is a model representing a region of space where a mass or char The **gravitational field strength** at any point in the field represents the force per unit of mass experienced by any mass—it is constant for any mass at the same distance $r$. $$|\vec{g}|=G\frac{M}{r^2}$$ -Its units also make it equivalent to the acceleration experienced by that mass. -$$F_G=m\vec{g}$$ +Its units also make it equivalent to the acceleration experienced by that mass. On Earth, $\vec{g}=9.81 \text{ N/kg [down]}$. +$$\vec{g}=\frac{\vec{F}_G}{m}$$ + +!!! note + Only the distance between objects and the mass of the **body acting** on another affect gravitational field strength of the acting body. + +(Source: Kognity) + +Gravitational field lines equidistantly point radially to the centre of a mass to indicate strength—a greater density of field lines in a given area indicates greater strength. + +### Orbital motion + +In space, only gravity acts on **satellites**—objects that orbit around another object, effectively as if in constant free fall. As gravity is the only force, it is also the only force contributing to centripetal force. +$$\vec{F}_G=\Sigma\vec{F}_c$$ + +So the orbital speed of a satellite must be independent of its own mass, such that: +$$v=\sqrt{\frac{GM}{r}}$$ ## Resources