Law of Universal Gravitation

Newton discovered that Gravity attracts any two objects depending on their masses and their distance apart

${\vec{F}}_g=\frac{G{m}_1{m}_2}{r^2}$Gravitational Constant: $G=1.67\times 10^{-11}\frac{N{m}^2}{k{g}^2}$

Gravitational Fields

A collection of vectors that determines the magnitude and direction of gravitational force. $g=\frac{G{m}_1{m}_2}{r^2}$

Altitude

To get the altitude of a satellite: Subtract the orbital radius by the radius of the planet

Orbits & Satellites

Orbital Velocity $v$

$F_g=F_c$ $\frac{G{m}_1{m}_2}{r^2}=\frac{m_1{v}^2}{r}$ $\sqrt{\frac{Gm}{r}}=v$

Where $m$ is the mass of the planet the satellite is orbiting around Too much speed and it escapes the atmosphere, Too little speed and it will burn up or fall into earth.

Orbital Period $T$

$F_g=F_c$ $\frac{G{m}_1{m}_2}{r^2}=\frac{m_{1}4{\pi }^{2}r}{T^2}$ $4{\pi }^2{r}^3=G{m}_2{T}^2$ $\sqrt{\frac{4{\pi }^2{r}^3}{Gm}}=T$

Orbital Radius $r$

$\sqrt[3]{\frac{G{m}_2{T}^2}{4{\pi }^2}}=r$

Geosynchronous Orbit

When the orbital period of a satellite is equal to the period of rotation of a planet on its axis

Geostationary Orbit

When a satellite lies in the same plane as the equator