Computes Keplerian orbital elements from the terminal state.

Functions¶

orbit_diagnostics¶

Calculate orbital elements at engine cutoff.

def orbit_diagnostics(
    *, 
    y: Array, 
    earth: EarthParams
) -> tuple[float, float, float, float, float, float]:

Returns: 1. eps - Specific orbital energy [J/kg] 2. h_ang - Specific angular momentum [m²/s] 3. a - Semi-major axis [m] 4. e - Eccentricity 5. r_apo - Apoapsis radius [m] 6. r_peri - Periapsis radius [m]

Equations¶

Eq. 18 - Specific energy: $$ \varepsilon = \frac{v^2}{2} - \frac{\mu}{r} $$

Eq. 19 - Specific angular momentum: $$ h = r \cdot v \cdot \cos\gamma $$

Eq. 20 - Eccentricity: $$ e = \sqrt{1 + \frac{2\varepsilon h^2}{\mu^2}} $$

Eq. 21 - Semi-major axis: $$ a = -\frac{\mu}{2\varepsilon} $$

Implementation¶

def orbit_diagnostics(*, y: Array, earth: EarthParams):
    r = y[_R]
    v = y[_V]
    gamma = y[_GAMMA]
    mu = earth.mu

    # [Eq. 18]
    eps = 0.5 * v * v - mu / r

    # [Eq. 19]
    h_ang = r * v * jnp.cos(gamma)

    # [Eq. 20]
    e = jnp.sqrt(jnp.maximum(0.0, 1.0 + (2.0 * eps * h_ang * h_ang) / (mu * mu)))

    # [Eq. 21]
    a = -mu / (2.0 * eps)

    r_apo = a * (1.0 + e)
    r_peri = a * (1.0 - e)

    return eps, h_ang, a, e, r_apo, r_peri