Gravity¶

Point-Mass Gravity¶

Point-mass gravity computes the Newtonian gravitational acceleration. For the central body at the origin (Earth two-body), use the convenience function accel_gravity:

import jax.numpy as jnp
from astrojax.orbit_dynamics import accel_gravity, accel_point_mass
from astrojax.constants import GM_SUN

r = jnp.array([6878e3, 0.0, 0.0])  # LEO position [m]
a = accel_gravity(r)  # Earth two-body acceleration [m/s^2]

For third-body perturbations, accel_point_mass handles the indirect acceleration term when the attracting body is not at the origin:

where \(\mathbf{d} = \mathbf{r} - \mathbf{r}_{\text{body}}\).

Spherical Harmonic Gravity¶

For accurate orbit propagation in LEO, point-mass gravity is insufficient. The GravityModel class loads spherical harmonic gravity field models (Stokes coefficients \(C_{nm}\), \(S_{nm}\)) from standard ICGEM GFC format files:

from astrojax.orbit_dynamics import GravityModel, accel_gravity_spherical_harmonics

# Load a packaged model
model = GravityModel.from_type("JGM3")  # 70x70, also: "EGM2008_360", "GGM05S"

The acceleration function uses the V/W matrix recursion from Montenbruck & Gill (2012, p. 56-68) to evaluate the gravity field at a given position. The position must be provided in the ECI frame along with the ECI-to-ECEF rotation matrix:

import jax.numpy as jnp
from astrojax.frames import rotation_eci_to_ecef
from astrojax.eop import zero_eop
from astrojax import Epoch

eop = zero_eop()
epc = Epoch(2024, 6, 15, 12, 0, 0)
r_eci = jnp.array([6878e3, 0.0, 0.0])
R = rotation_eci_to_ecef(eop, epc)

# Evaluate to degree and order 20
a = accel_gravity_spherical_harmonics(r_eci, R, model, n_max=20, m_max=20)

Three packaged gravity models are available:

Models can also be loaded from custom GFC files using GravityModel.from_file("path/to/model.gfc").

To reduce computation time, truncate a model to a lower degree/order:

model = GravityModel.from_type("EGM2008_360")
model.set_max_degree_order(20, 20)  # Truncate to 20x20