Physics to Scale

1. Introduction

 

Planetology has reached a status of understanding of knowledge regarding the description and interactions that we hardly expect any basic effects to be unknown thus far. If it comes to the question of long-term stability chaos theory took over scientific sovereignty pushing the whole planetary system in a turmoil. In consequence of this modern approach, accurate descriptions became outdated and the stability is gone, since long term the shape and radii of the path of the planets and their inclinations become unpredictable.

 

At present theory, the distance of the planets almost appear random. It is only an empirical formula which predicts the distance of the planets from the sun. In the 18th century the German astronomer Johann Daniel Titius developed a simple mathematical formula that was later published by Johann Elert Bode which approximates the distances of the planets solely from the number of their order. The formula became famous as it predicted a planet in the distance populated by the asteroids actually and the dwarf planet Pluto orbiting beyond the planets known at that point in time. Two drawbacks darken the value of the formula. First, so far no theoretical basis could uncover the physics behind the formula and secondly in the distance of the planet Neptune the formula does not predict a planet at all.

 

Distance scale

Distances of the planets to the sun in a logarithmic plot

 

Dots: actual values

 

Crosses: Titius Bode sequence

 

Line: Least square fit to actual values

 

Relation between mass and length

Log plot of characteristic lengths versus mass. Broken line shows the linear slope of a least square fit.

Exponent for sequences of pla- netary distances

 The relationship of planetary distances follows a slope of 0.5 as indicated by the upper broken line. The lower broken line reflects a second characteristic slope of 0.3 specific for densely populated planetary systems.