Functions
template<typename Scalar>
Vec3< Scalar >	acceleration (const Vec3< Scalar > &r_ecef, double mu=constants::earth::mu, double J2_coeff=constants::earth::J2, double R_eq=constants::earth::R_eq)
	J2 gravitational acceleration (oblate Earth).
template<typename Scalar>
Scalar	potential (const Vec3< Scalar > &r_ecef, double mu=constants::earth::mu, double J2_coeff=constants::earth::J2, double R_eq=constants::earth::R_eq)
	J2 gravitational potential.

Function Documentation

◆ acceleration()

template<typename Scalar>

Vec3< Scalar > vulcan::gravity::j2::acceleration	(	const Vec3< Scalar > &	r_ecef,
		double	mu = constants::earth::mu,
		double	J2_coeff = constants::earth::J2,
		double	R_eq = constants::earth::R_eq )

J2 gravitational acceleration (oblate Earth).

Accounts for Earth's equatorial bulge. The J2 term is the dominant perturbation for low and medium Earth orbits.

Mathematical form: a_x = -μx/r³ · [1 - 1.5·J2·(R_eq/r)²·(5(z/r)² - 1)] a_y = -μy/r³ · [1 - 1.5·J2·(R_eq/r)²·(5(z/r)² - 1)] a_z = -μz/r³ · [1 - 1.5·J2·(R_eq/r)²·(5(z/r)² - 3)]

Template Parameters

Scalar double or casadi::MX

Parameters

r_ecef	Position in ECEF frame [m]
mu	Gravitational parameter [m³/s²]
J2_coeff	J2 zonal harmonic coefficient
R_eq	Equatorial radius [m]

Returns: Gravitational acceleration in ECEF [m/s²]

◆ potential()

template<typename Scalar>

Scalar vulcan::gravity::j2::potential	(	const Vec3< Scalar > &	r_ecef,
		double	mu = constants::earth::mu,
		double	J2_coeff = constants::earth::J2,
		double	R_eq = constants::earth::R_eq )

J2 gravitational potential.

U = -μ/r · [1 - J2·(R_eq/r)²·P₂(sin φ)]

where P₂(x) = (3x² - 1)/2 is the Legendre polynomial of degree 2.