eggy/eifueo
1
1
Fork 1
Code Issues 2 Pull Requests Releases Wiki Activity

phys: orbital motion 1

Browse Source
This commit is contained in:
eggy 2020-11-21 13:07:53 -05:00
parent 7979f074fa
commit 09615316d6
1 changed files with 19 additions and 4 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

23
docs/sph3u7.md
View File

@ -586,9 +586,9 @@ $$\Sigma \vec{F}_c=m\vec{a}_c$$
## 6.2 - Newton's law of gravitation ## 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: 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. 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 $r$. 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 $r$.
$$|\vec{g}|=G\frac{M}{r^2}$$ $$|\vec{g}|=G\frac{M}{r^2}$$
Its units also make it equivalent to the acceleration experienced by that mass. Its units also make it equivalent to the acceleration experienced by that mass. On Earth, $\vec{g}=9.81 \text{ N/kg [down]}$.
$$F_G=m\vec{g}$$ $$\vec{g}=\frac{\vec{F}_G}{m}$$
!!! note
Only the distance between objects and the mass of the **body acting** on another affect gravitational field strength of the acting body.
<img src="/resources/images/grav-radial-lines.png" width=700>(Source: Kognity)</img>
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 ## Resources