Variables

G gravitational constant
r distance between the two bodies
v velocity
μ standard gravitational parameter
a semi-major axis
e orbital eccentricity

Type of Orbits

Circular
$$e=0$$

Elliptical
$$0<e<1$$

Parabolic
$$e=1$$

Hyperbolic
$$e>1$$

General formulas

Orbital period
$$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$

Escape velocity
$$\displaystyle v\geq {\sqrt {\frac {2GM}{r}}}$$

Specific potential energy
$$\epsilon_{p} = -\frac{GM}{r}$$

Specific kinetic energy
$$\displaystyle \epsilon _{k}={\frac {v^{2}}{2}}$$

Specific orbital energy
$$\displaystyle \epsilon =\epsilon _{k}+\epsilon _{p}={\frac {v^{2}}{2}}-{\frac {GM}{r}}$$

Elliptical orbits

Periapsis
$$r_p=\frac{p}{1+e}$$

Apoapsis
$$r_a=\frac{p}{1-e}$$

Velocity

$$v=\sqrt{\mu\left({2\over{r}}-{1\over{a}}\right)}$$