def from_apses(
body: Body,
periapsis: Quantity,
apoapsis: Quantity,
sea_level: bool = False,
) -> Orbit:
periapsis = body.adjust_height(periapsis, sea_level)
apoapsis = body.adjust_height(apoapsis, sea_level)
assert 0 * METERS <= periapsis <= apoapsis
# E = -mu/2a = -mu/(A + P)
energy = -body.mu / (periapsis + apoapsis)
return Orbit(body, periapsis, energy)
def flyby(
body: Body,
periapsis: Quantity,
scattering_angle: float,
sea_level: bool = False,
) -> Orbit:
periapsis = body.adjust_height(periapsis, sea_level)
# alpha = 2 arccos(-1/e) - pi ==> cos((alpha + pi)/2) = -1/e
# ==> e = -1/cos((alpha+pi)/2) = 1/cos((alpha-pi)/2)
eccentricity = 1 / math.cos((scattering_angle - math.pi) / 2)
# pe = a(1-e) = -mu/2E * (1-e) ==> E = (e-1) * mu / (2 * pe)
energy = (eccentricity - 1) * body.mu / 2 / periapsis
return Orbit(body, periapsis, energy)
def radial_trajectory(body: Body,
max_height: Quantity,
sea_level: bool = False) -> Orbit:
max_height = body.adjust_height(max_height, sea_level)
energy = -body.mu / max_height
return Orbit(body, 0 * METERS, energy)
