Physics grav. & elec. potential and potential energy

Change in Ep from Vg

\Delta E_{p}=m\Delta V_{g}

Force and Ep

F=\frac{\Delta E_{p}}{\Delta r}

Circular orbits

g=\frac{v^2}{R}

mg=\frac{mv^2}{R}

v=\sqrt{gR}

Orbital speed and period

v=\frac{2\pi r}{T}

T=\sqrt{\frac{4\pi^2r^3}{GM}}

\frac{T^2}{r^2}=\frac{4\pi^2}{GM} = constant

Energy of a satellite

E_{k}=\frac12\frac{GMm}{r}

E_{T}=-\frac12\frac{GMm}{r}=\frac12E_{p}=-E_{k}

Escape speed

v=v_{esc}=\sqrt{\frac{2GM}{R}}=\sqrt{2gR}

Electric potential energy Ep in terms of electric potential V

E_{p}=qV_{e}

Work in electric fields

W=\frac{kQq}{r} (Infinity to r)

W=q\Delta V (any two points)

W=qE\Delta r

Electric potential at a point from two charges

V_{e}=\frac{kq_1}{r_1}+\frac{kq_2}{r_2}