Two-Body State Vector Propagator

Given an initial position vector r₀, velocity vector v₀, a central body's gravitational parameter μ, and a time-of-flight Δt, this tool propagates the body to time t₀+Δt using the analytical universal-variable method (Stumpff c/s functions + Newton iteration on the universal Kepler equation), which works for ALL conic-section orbit types (circle / ellipse / parabola / hyperbola) without branching.

It then derives the full set of classical orbital elements from the state vector:

• Specific mechanical energy ε = v²/2 − μ/r and angular momentum h = |r×v|
• Semi-major axis a (for bound orbits), eccentricity e (via the eccentricity vector), orbital period T
• Inclination i, RAAN Ω, argument of periapsis ω, true anomaly θ
• Periapsis / apoapsis radii

Different from kepler-orbit-solver, which takes a mean anomaly M + eccentricity e and solves for a single eccentric anomaly. This tool takes a STATE VECTOR and propagates it through time — the core of orbit determination. Inputs are in SI units (m, m/s, s); μ values are NASA/IAU standard. Formulas follow Vallado and Curtis.