https://en.wikipedia.org/wiki/Orbital_elements
https://en.wikipedia.org/wiki/Eccentric_anomaly
https://en.wikipedia.org/wiki/Mean_anomaly
https://en.wikipedia.org/wiki/Standard_gravitational_parameter
https://en.wikipedia.org/wiki/Longitude_of_the_periapsis
https://en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes
https://en.wikipedia.org/wiki/Conic_section#Conic_parameters
https://astronomy.stackexchange.com/questions/632/determining-effect-of-small-variable-force-on-planetary-perihelion-precession
https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity
https://en.wikipedia.org/wiki/Laplace%E2%80%93Runge%E2%80%93Lenz_vector#Evolution_under_perturbed_potentials
$m$ = meter
$kg$ = kilogram
$s$ = second
$G$ = gravitational constant
${G} = {{{6.673848\cdot{10^{-11}}}} \cdot {{\frac{{m}^{3}}{{{kg}} \cdot {{{s}^{2}}}}}}}$
$Mass$ = mass
${Mass_{parent}}$ = parent mass
$\mu$ = gravitational parameter
${\mu} = {{{G}} {{\left({{Mass} + {{Mass_{parent}}}}\right)}}}$
$L$ = angular momentum
$e$ = eccentricity
$l$ = semi-latus rectum
${l} = {{\frac{1}{G}} {{L}^{2}}}$
$i$ = inclination
$\Omega$ = longitude of ascending node
$\omega$ = argument of periapsis
$a$ = semi-major axis
$b$ = semi-minor axis
${b} = {\sqrt{{{a}} {{l}}}}$
${b} = {{{a}} {{\sqrt{{1}{-{{e}^{2}}}}}}}$
${l} = {{{a}} {{\left({{1}{-{{e}^{2}}}}\right)}}}$
$\vec{A}$ = semi-major axis vector
${\vec{A}} = {\left[\begin{array}{c} {{a}} {{\left({{{{\cos\left( \Omega\right)}} {{\cos\left( \omega\right)}}}{-{{{\sin\left( \Omega\right)}} {{\sin\left( \omega\right)}} {{\cos\left( i\right)}}}}}\right)}}\\ {{a}} {{\left({{{{\sin\left( \Omega\right)}} {{\cos\left( \omega\right)}}} + {{{\cos\left( \Omega\right)}} {{\sin\left( \omega\right)}} {{\cos\left( i\right)}}}}\right)}}\\ {{a}} {{\sin\left( \omega\right)}} {{\sin\left( i\right)}}\end{array}\right]}$
$\vec{B}$ = semi-minor axis vector
${\vec{B}} = {\left[\begin{array}{c} {-{b}} {{\left({{{{\cos\left( \Omega\right)}} {{\sin\left( \omega\right)}}} + {{{\sin\left( \Omega\right)}} {{\cos\left( \omega\right)}} {{\cos\left( i\right)}}}}\right)}}\\ {{b}} {{\left({{ {-{\sin\left( \Omega\right)}} {{\sin\left( \omega\right)}}} + {{{\cos\left( \Omega\right)}} {{\cos\left( \omega\right)}} {{\cos\left( i\right)}}}}\right)}}\\ {{b}} {{\cos\left( \omega\right)}} {{\sin\left( i\right)}}\end{array}\right]}$
$T$ = orbital period
${T} = {{{2}} {{π}} \cdot {{\sqrt{{\frac{1}{\mu}} {{a}^{3}}}}}}$ : Kepler's 3rd law
${a} = {\sqrt[3]{\frac{{{\mu}} \cdot {{{T}^{2}}}}{{{4}} {{{π}^{2}}}}}}$
$\vec{r}$ = position
$d$ = distance to parent
$E$ = eccentric anomaly
${\cos\left( E\right)} = {{\frac{1}{e}}{\left({{1}{-{{\frac{1}{a}} {d}}}}\right)}}$
${M_0}$ = mean anomaly at epoch
$t$ = time
${t_0}$ = epoch
$n$ = mean motion
${n} = {{\frac{1}{T}} {{{2}} {{π}}}}$
$\theta$ = angle of orbit (better name?)
${\theta} = {{{n}} {{\left({{t}{-{{t_0}}}}\right)}}}$
$M$ mean anomaly
${M} = {{{M_0}} + {{{n}} {{\left({{t}{-{{t_0}}}}\right)}}}}$
${M} = {{E}{-{{{e}} {{\sin\left( E\right)}}}}}$
This equation relates E to M, and the previous relates M to t, so from these two you can calculate E based on t. Also notice that all arguments of $\vec{A}$ and $\vec{B}$ are not determined by time.
${\vec{r}} = {{{{\left({{\cos\left( E\right)}{-{e}}}\right)}} {{\vec{A}}}} + {{{\sin\left( E\right)}} {{\vec{B}}}}}$