diff --git a/docs/user-guide/gravitational-harmonics/index.rst b/docs/user-guide/gravitational-harmonics/index.rst index 5cffea631..790339207 100644 --- a/docs/user-guide/gravitational-harmonics/index.rst +++ b/docs/user-guide/gravitational-harmonics/index.rst @@ -2,21 +2,37 @@ Gravitational Harmonics ########################## -Here, we show how to use Swiftest's Gravitational Harmonics capabilities. -Swiftest uses `SHTOOLS `__ to compute the gravitational harmonics coefficients for a given body and calculate it's associated acceleration kick. +Here, we show how to use Swiftest's Gravitational Harmonics capabilities. This is based on ``/spherical_harmonics_cb`` +in ``swiftest/examples``. Swiftest uses `SHTOOLS `__ to compute the gravitational +harmonics coefficients for a given body and calculate it's associated acceleration kick. The additional acceleration +kick is based on the gravitaional potential described `here `__. + +..math:: + + U(r) = \frac{GM}{r} \sum_{l=0}^{\infty} \sum_{m=-l}^{l} \left( \frac{R_0}{r} \right)^l C_{lm} Y_{lm} (\theta, \phi) \label{grav_pot} + +* Gravitational potential:math:`U` at a point:math:`\Vec{r}`;:math:`\theta` is the polar angle;:math:`\phi` is the azimuthal angle;:math:`R_0` is the central body +radius;:math:`G` is the gravitational constant;:math:`Y_{lm}` is the spherical harmonic function at degree:math:`l` and order:math:`m`;:math:`C_{lm}` is the corresponding coefficient. + + +Gravitational Harmonics coefficients +===================================== + +Swiftest adopts the :math:`4\pi` or geodesy normalization for the gravitational harmonics coefficients. The coefficients can be computed in a number of ways: - Using the axes measurements of the body ( :func:`clm_from_ellipsoid `) - Using a surface relief grid ( :func:`clm_from_relief `). - * This function is still in development and may not work as expected. + - This function is still in development and may not work as expected. - Manually entering the coefficients when adding the central body ( :func:`add_body `) -This is based on ``/spherical_harmonics_cb`` in ``swiftest/examples``. +Computing coefficients from axes measurements +=============================================== .. .. toctree:: .. :maxdepth: 2