astroforge.force_models.F_geo_ITRS#

astroforge.force_models.F_geo_ITRS(x)[source]#

Compute Earth’s gravitational potential for a position in ITRS coordinates using an 8x8 spherical harmonics model.

Parameters:: x (NDArray[np.float64]) – ITRS position vector at which geo potential should computed, should have shape (3, ) and be in units of km
Returns:: acc – Acceleration due to Earth’s gravitational potential, has shape (3, ) and is in units of km / s²
Return type:: NDArray[np.float64]

Examples

We know the acceleration due to gravity at the surface of the Earth is approximately 9.81 \(m/s^2\). We can use this function to compute an even more accurate vector of acceleration using an 8x8 spherical harmonic model of Earth’s gravitational potential.

>>> x = np.array([af.R_earth, 0.0, 0.0])
array([6378.137,    0.   ,    0.   ])
>>> F_geo_ITRS(x)
array([-9.81427717e-03, -6.14784939e-08,  3.15547395e-08])

Indeed, the strongest component of Earth’s gravity points toward the middle of the Earth with an approximate magnitude of 9.81 x 10^-3 km / s². The other terms are significantly smaller, but may be consequential for precisely propagating an orbit.

astroforge.force_models.F_geo_ITRS#

This Page