Physics

Gravity

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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 $Q$

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