# Talk:Celestial mechanics

The deleted discussions concern minor details on the two-body problem without importance for the understanding of the subject of this article. (Celestial Mechanics) I prefer not to overcrowd the article with many algebraic demonstrations.

## Corrections

Using heliocentric vectors, the **angular momentum of the planet** is given by:
\[ \frac{\mu^2}{m} \vec{r} \times \vec{v} \]
(where \(\mu\) is the reduced mass), not:
\[ m \vec{r} \times \vec{v} \].

The latter would be the angular momentum of the planet if the Sun were held fixed in space.

Also, the principal of conservation of energy (kinetic & potential) was certainly not known prior to 1740. Lagrange's *Mécanique Analytique* is generally acknowledged as the first appearance of the orbital conservation equation used this article.

Existing: "Another result found by Newton is that the mechanical energy is conserved."

Suggested: "A century after Newton, Joseph-Louis Lagrange showed that the mechanical energy is also conserved."