Function lupnt::AccelerationRelativisticNBody

Function Documentation

Vec3 lupnt::AccelerationRelativisticNBody(const Vec3 &r_sc, const Vec3 &v_sc, const std::vector<Vec3> &r_bodies, const std::vector<Vec3> &v_bodies, const std::vector<Real> &mu_bodies, Real c_light = C, Real beta = 1.0, Real gamma = 1.0)

Relativistic n-body point-mass perturbative acceleration of the spacecraft, from Moyer (2000), “Formulation for Observed and Computed

Values of Deep Space Network Data Types for Navigation” (JPL Pub 00-7), Eq. (4-26), with the leading Newtonian point-mass term (the “1” in the first brace) removed so it can be ADDED to the Newtonian gravity already computed.

Body indices i, j, k, l in Eq. (4-26) refer to the spacecraft (i) and the massive perturbing bodies (j, k, l). All positions/velocities/GMs must be referred to the same (Solar-System barycentric) inertial origin, in one coherent unit system. Body accelerations use the Newtonian value (terms of order 1/c^4 are dropped, per Moyer p. 4-21). beta = gamma = 1 recovers general relativity.

Parameters:

  • r_sc, v_sc – Spacecraft (SSB-referenced) position and velocity

  • r_bodies – SSB-referenced positions of the massive bodies

  • v_bodies – SSB-referenced velocities of the massive bodies

  • mu_bodies – Gravitational parameters of the massive bodies

  • c_light – Speed of light (same coherent units)

  • beta, gamma – PPN parameters (1 for general relativity)

Returns:

Post-Newtonian relativistic perturbative acceleration