### Quantum Planets

G. C. Johnson

Bohr's observation that the electron's angular momentum occurs in integer increments of $\large \hbar$ is independent of the atomic number, Z.  That is, for any quantum state, N, the electron's velocity increases by the factor Z, and the shell radius decreases by the factor 1/Z, leaving the angular momentum unchanged.

This leads to the conjecture that quantum angular momentum might represent the preferred states of any orbital system in which negative potential energy is inversely proportional to radius.

The following quantum numbers for the planets in the solar system appear to validate the above conjecture.

### Quantum numbers for the planets

Mercury:  N = 3
Venus:     N = 4
Earth:      N = 5
Mars:       N = 6
Ceres:      N = 8
Jupiter:    N = 11
Saturn:    N = 15
Uranus:   N = 21
Neptune: N = 26

### Specific Angular Momentum

Specific angular momentum, (Orbital angular momentum divided by the planet's mass.), occurs in integer increments of 1.3038 au2/y.

$\large L/m = 1.3038 N \sim au^{2}/y$

$\large R= 0.043N^{2}\sim au$

### Orbital Period

Orbital periods increase with N3.

$P = 0.00891 N^{3}\sim y$