JPL Horizons Ephemeris Integration:
NASA's Eyes uses accurate orbital state vectors derived from the Jet Propulsion Laboratory (JPL) DE440/DE441 planetary ephemeris. State vectors are integrated using high-order numerical relativistic ODE solvers accounting for mutual N-body planetary perturbations, solar oblateness ($J_2$), and general relativity.
Vis-Viva Equation: $v = \sqrt{GM_\odot \left( rac{2}{r} - rac{1}{a}
ight)}$
Kepler's 3rd Law: $T^2 = a^3$ ($T$ in yr, $a$ in AU)
Perihelion / Aphelion: $r_p = a(1-e), \quad r_a = a(1+e)$
Lagrange Point $L_2$: $r_{L2} pprox R\left( rac{M_2}{3M_1}
ight)^{1/3} pprox 1.5 ext{M km}$