Skip to content
This repository was archived by the owner on Aug 28, 2024. It is now read-only.

Commit

Permalink
Testing math and rearranging
Browse files Browse the repository at this point in the history
  • Loading branch information
anand43 committed Mar 1, 2024
1 parent ff5338c commit 8448c4b
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions docs/user-guide/gravitational-harmonics/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -7,18 +7,18 @@ in ``swiftest/examples``. Swiftest uses `SHTOOLS <https://shtools.github.io/SHTO
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 <https://sseh.uchicago.edu/doc/Weiczorek_2015.pdf>`__.

..math::
.. 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 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.
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 <swiftest.shgrav.clm_from_ellipsoid>`)
Expand Down

0 comments on commit 8448c4b

Please sign in to comment.