User:OEP/Formulae

Universal Gravitation
Universal gravitation constant:
 * $$G = 6.673 \times 10^{-11}\frac{N \cdot M^2}{kg^2}$$

Force of gravity:
 * $$F_g = G\frac{m_1 m_2}{r^2}$$

Calculating g:
 * $$g = \frac{GM}{R^2}$$

Kepler's Laws: Gravitational potential energy:
 * 1) All planets orbit in an ellipse
 * 2) Equal areas over equal time intervals (conservation of angular momentum)
 * 3) $$\frac{T^2}{R^3} = K$$
 * $$U = -\frac{G m_1 m_2}{r}$$
 * $$\Delta U = -G m_1 m_2(\frac{1}{r_f} - \frac{1}{r_i})$$

Energy over an orbit:
 * $$E = \frac{GMm}{2a} (ellipse) = \frac{GMm}{2r} (circle)$$

Escape velocity:
 * $$v_{esc} = \sqrt{\frac{2GM}{R}}$$

Sound
Pressure function:
 * $$\Delta P = \Delta P_{max}\sin{(kx - \omega t)}$$
 * $$\Delta P_{max} = \rho v \omega s_{max}$$

Displacement function:
 * $$s(x,t) = s_{max}\cos{(kx - \omega t)}$$

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

At a distance r...
 * $$I = \frac{\mathcal{P}_{ave}}{4 \pi r^2}$$

Decibels:
 * $$\Beta = 10\log{\frac{I}{I_0}}$$ $$I_0 = 1.00 \times 10^{-12}\frac{W}{m^2}$$

Doppler:
 * $$f' = f \cdot \frac{v + v_{obs}}{v - v_{source}}$$