# I Orbit invariant under reflection about apsidal vectors

1. Mar 21, 2016

### Happiness

The book argues that since substituting $\theta$ by $-\theta$ leaves the orbit equation (3.34) unchanged, the orbit is therefore invariant under reflection about the apsidal vectors (Fig 3.12).

If substituting $\theta$ by $-\theta$ leaves the orbit equation (3.34) unchanged, then there exists a plane of symmetry (where $\theta=0$) in the orbit. How does the book reach the conclusion of invariance under reflection about the apsidal vectors?

2. Mar 26, 2016