Potential energy of radial planetary motion¶
The total mechanical energy of the planet can be viewed as the sum of the kinetic and potential energy. The potential energy is in turn the sum of the potential energy due to the gravitational interaction between the planet and the Sun, and the the energy of the tangential motion, which depends on the planet’s angular momentum.
Links:
Sivukhin, D.V. (1979). Obshchiy kurs fiziki [General course of Physics], vol. 1, p. 315.
- total_potential_energy¶
The total
potential_energyof the planet.- Symbol:
U_tot- Latex:
\(U_\text{tot}\)
- Dimension:
energy
- gravitational_potential_energy¶
The
potential_energyof the planet due to the gravitational interaction of the planet and the star.- Symbol:
U_gr- Latex:
\(U_\text{gr}\)
- Dimension:
energy
- angular_momentum¶
The
angular_momentumof the planet.- Symbol:
L- Latex:
\(L\)
- Dimension:
length**2*mass/time
- distance¶
The
euclidean_distancebetween the star and the planet.- Symbol:
d- Latex:
\(d\)
- Dimension:
length
- law¶
U_tot = U_gr + L^2 / (2 * m * d^2)- Latex:
- \[U_\text{tot} = U_\text{gr} + \frac{L^{2}}{2 m d^{2}}\]