ssapy_toolkit.Orbital_Mechanics.misc

Functions

bi_elliptic_transfer_delta_v(r1, r2, rb, mu)	Return (dv1, dv2, dv3, total_dv) for bi-elliptic transfer via intermediate apoapsis rb
circular_velocity(mu, r)	Circular orbital velocity: v = sqrt(mu / r)
eccentricity_vector(r_vec, v_vec, mu)	Eccentricity vector: e_vec = (v x h)/mu - r/|r|
escape_velocity(mu, r)	Escape velocity: v_e = sqrt(2*mu / r)
hohmann_transfer_delta_v(r1, r2, mu)	Return (dv1, dv2, total_dv) for Hohmann transfer between circular orbits r1 and r2
kepler_E_from_M(M, e[, tol, max_iter])	Solve Kepler's equation M = E - e*sin(E) for E (elliptical)
kepler_E_from_M_from_nu(nu, e)	Compute eccentric anomaly E from true anomaly nu for elliptical orbits
orbital_elements_from_state(r_vec, v_vec, mu)	Compute classical orbital elements from state vectors.
orbital_period(a, mu)	Orbital period for ellipse: T = 2*pi*sqrt(a^3/mu)
plane_change_delta_v(v, i1, i2)	Delta-v for plane change at speed v from inclination i1 to i2: dv = 2*v*sin(|i2-i1|/2)
specific_angular_momentum(r_vec, v_vec)	Specific angular momentum vector: h = r x v
specific_orbital_energy(mu, r, v)	Specific orbital energy: epsilon = v^2/2 - mu/r
sphere_of_influence_radius(a, m_secondary, ...)	Sphere of influence radius: r_SOI = a*(m_secondary/m_primary)^(2/5)
vis_viva(mu, r, a)	Vis-viva equation: v^2 = mu * (2/r - 1/a)

ssapy_toolkit.Orbital_Mechanics.misc.bi_elliptic_transfer_delta_v(r1: float, r2: float, rb: float, mu: float) → Tuple[float, float, float, float]

Return (dv1, dv2, dv3, total_dv) for bi-elliptic transfer via intermediate apoapsis rb

ssapy_toolkit.Orbital_Mechanics.misc.circular_velocity(mu: float, r: float) → float

Circular orbital velocity: v = sqrt(mu / r)

ssapy_toolkit.Orbital_Mechanics.misc.eccentricity_vector(r_vec: ndarray, v_vec: ndarray, mu: float) → ndarray

Eccentricity vector: e_vec = (v x h)/mu - r/|r|

ssapy_toolkit.Orbital_Mechanics.misc.escape_velocity(mu: float, r: float) → float

Escape velocity: v_e = sqrt(2*mu / r)

ssapy_toolkit.Orbital_Mechanics.misc.hohmann_transfer_delta_v(r1: float, r2: float, mu: float) → Tuple[float, float, float]

Return (dv1, dv2, total_dv) for Hohmann transfer between circular orbits r1 and r2

ssapy_toolkit.Orbital_Mechanics.misc.kepler_E_from_M(M: float, e: float, tol: float = 1e-08, max_iter: int = 100) → float

Solve Kepler’s equation M = E - e*sin(E) for E (elliptical)

ssapy_toolkit.Orbital_Mechanics.misc.kepler_E_from_M_from_nu(nu: float, e: float) → float

Compute eccentric anomaly E from true anomaly nu for elliptical orbits

ssapy_toolkit.Orbital_Mechanics.misc.orbital_elements_from_state(r_vec: ndarray, v_vec: ndarray, mu: float)

Compute classical orbital elements from state vectors. Returns (a, e, i, RAAN, arg_periapsis, true_anomaly, mean_anomaly) a: semi-major axis (m) e: eccentricity (scalar) i: inclination (rad) RAAN: right ascension of ascending node (rad) arg_periapsis: argument of periapsis (rad) true_anomaly: (rad) mean_anomaly: (rad)

ssapy_toolkit.Orbital_Mechanics.misc.orbital_period(a: float, mu: float) → float | None

Orbital period for ellipse: T = 2*pi*sqrt(a^3/mu)

ssapy_toolkit.Orbital_Mechanics.misc.plane_change_delta_v(v: float, i1: float, i2: float) → float

Delta-v for plane change at speed v from inclination i1 to i2: dv = 2*v*sin(|i2-i1|/2)

ssapy_toolkit.Orbital_Mechanics.misc.specific_angular_momentum(r_vec: ndarray, v_vec: ndarray) → ndarray

Specific angular momentum vector: h = r x v

ssapy_toolkit.Orbital_Mechanics.misc.specific_orbital_energy(mu: float, r: float, v: float) → float

Specific orbital energy: epsilon = v^2/2 - mu/r

ssapy_toolkit.Orbital_Mechanics.misc.sphere_of_influence_radius(a: float, m_secondary: float, m_primary: float) → float

Sphere of influence radius: r_SOI = a*(m_secondary/m_primary)^(2/5)

ssapy_toolkit.Orbital_Mechanics.misc.vis_viva(mu: float, r: float, a: float) → float

Vis-viva equation: v^2 = mu * (2/r - 1/a)