User:OEP/Formulae

Universal gravitation constant:

${\displaystyle G=6.673\times 10^{-11}{\frac {N\cdot M^{2}}{kg^{2}}}}$

Force of gravity:

${\displaystyle F_{g}=G{\frac {m_{1}m_{2}}{r^{2}}}}$

Calculating g:

${\displaystyle g={\frac {GM}{R^{2}}}}$

Kepler's Laws:

1. All planets orbit in an ellipse
2. Equal areas over equal time intervals (conservation of angular momentum)
3. ${\displaystyle {\frac {T^{2}}{R^{3}}}=K}$

Gravitational potential energy:

${\displaystyle U=-{\frac {Gm_{1}m_{2}}{r}}}$

${\displaystyle \Delta U=-Gm_{1}m_{2}({\frac {1}{r_{f}}}-{\frac {1}{r_{i}}})}$

Energy over an orbit:

${\displaystyle E={\frac {GMm}{2a}}(ellipse)={\frac {GMm}{2r}}(circle)}$

Escape velocity:

${\displaystyle v_{esc}={\sqrt {\frac {2GM}{R}}}}$

Pressure function:

${\displaystyle \Delta P=\Delta P_{max}\sin {(kx-\omega t)}}$

${\displaystyle \Delta P_{max}=\rho v\omega s_{max}}$

Displacement function:

${\displaystyle s(x,t)=s_{max}\cos {(kx-\omega t)}}$

Intensity:

${\displaystyle {\frac {Power}{Area}}={\frac {1}{2}}\rho v(\omega s_{max})^{2}={\frac {\Delta P_{max}^{2}}{2\rho v}}}$

At a distance r...

${\displaystyle I={\frac {{\mathcal {P}}_{ave}}{4\pi r^{2}}}}$

Decibels:

${\displaystyle \mathrm {B} =10\log {\frac {I}{I_{0}}}}$  ${\displaystyle I_{0}=1.00\times 10^{-12}{\frac {W}{m^{2}}}}$

Doppler:

${\displaystyle f'=f\cdot {\frac {v+v_{obs}}{v-v_{source}}}}$