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### Background

Gravity is fundamental to everything humans have experienced in (written) history

- Newton was the first person recorded in modern history to question why objects always fall towards the ground
- Used gravity to explain this phenomena
- Lead to the development of classical mechanics (later updated by Einstein)
- Note: classical mechanics applies to macroscopic objects that are traveling far slower than the speed of light

Importantly, we currently do not have a very good understanding of what is causing gravity

- Question: what is mass and why do bodies of mass “gravitate” towards each other?
- Answer: we dont know
- Comments/random thoughts: this is kind of like the opposite of diffusion (
**diffusion**= the tendency for particles to move from areas of high concentration gradients – i.e. – areas with a lot of particles, to areas of low concentration gradients – i.e. – areas with few particles)- Like diffusion, gravity seems to occur spontaneously, so maybe it is the result of something that can be described as “energetically favorable”
- Q: is there a “randomness” component to gravity like there is for the diffusion of particles?

Although we still dont exactly know *why* gravity exists, we are pretty good at describing *how *gravity behaves (in the context of systems that follow principles of classical mechanics)

### Newton’s Law of Gravitation

- Generally,
**gravity**is defined as the attractive force $\overrightarrow{F}_g$ between two objects with positive nonzero masses $m_1$ and $m_2$ whose centers of mass are separated by a distance vector $\overrightarrow{r}$- Note: Newton’s law is stated in the context of particles

- Equation for the gravitational force between two objects:

$\left\| \overrightarrow{F}_g \right\| = G \frac{m_1 m_2}{\left\| \overrightarrow{r} \right\|}$

- Variables:
- $\left\| \overrightarrow{F}_g \right\| = $ the magnitude of the gravitational force between object 1 and object 2 (SI units: Newton)
- $G =$ the graviational constant $ \approx 6.67 \cdot 10^{-11} \mathrm{N (\frac{m}{kg})^2}$
- $m_i$ = the mass of object $i$ (SI units: $\mathrm{kg}$)
- $\left\| \overrightarrow{r} \right\| =$ the length of the vector describing the distance between the two objects (SI units: $\mathrm{m}$)

- Also, assume $m_1$ is located at a point $P$ and $m_2$ is located at a point $Q$