Changes
Page history
Update Gravitational Potential including indirect terms
authored
Apr 28, 2021
by
Elena Lega
Show whitespace changes
Inline
Side-by-side
Code-equations/Gravitational-Potential-including-indirect-terms.md
View page @
dee9c5cb
The gravitational potential entering in the source terms of the Navier-Stokes equations is the sum of multiple terms:
The gravitational potential entering in the source terms of the Navier-Stokes equations is the sum of multiple terms:
1.
##The potential from the central massive body (primary of mass $
`M_*`
$):
##
The potential from the central massive body (primary of mass $`M_*`$):
$
`\Phi_*=-{{ G M_*} \over {r}}`
$
$
`\Phi_*=-{{ G M_*} \over {r}}`
$
2.
##The potential form the planets of mass $m_p$.
##
The potential form the planets of mass $m_p$.
Below we consider the case of one single planet, easily extended to multiple planets.
Below we consider the case of one single planet, easily extended to multiple planets.
-
In the 3 Dimensional case
-
In the 3 Dimensional case
we use a cubic-potential of the form:
we use a cubic-potential of the form:
...
@@ -54,7 +54,7 @@ To select this choice for a simulation in the config file:
...
@@ -54,7 +54,7 @@ To select this choice for a simulation in the config file:
}
}
```
```
3.
##The indirect terms
##
The indirect terms
This term in the potential accounts for the acceleration of the primary
This term in the potential accounts for the acceleration of the primary
...
...
...
...