The Exo-planetary System of 55 Cancri and the Titius-Bode Law

TL;DR

This paper examines the 55 Cancri exo-planetary system and finds that an exponential Titius-Bode law accurately fits the observed planets, allowing predictions of additional planets in the system.

Contribution

It demonstrates that a simple exponential Titius-Bode relation can model the 55 Cancri system and predicts two potential additional planets.

Findings

The exponential TB law fits the five observed planets well.

Predicts a planet at 2.0 AU with a 1130-day period.

Suggests a possible seventh planet at 15 AU with a 62-year period.

Abstract

The recent discovery of a fifth planet bound to 55 Cancri (Fischer et. al 2007) motivated us to investigate if this exo-planetary system fits some form of the Titius-Bode (TB) law. We found that a simple exponential TB relation reproduces very well the five observed major semi-axis, provided we assign the orbital n = 6 to the largest a. This way of counting leaves empty the position n = 5, a situation curiously reminiscent of TB law in our planetary system, before the discovery of Ceres. The application of an exponential TB relation to 55 Cancri allows us to predict the existence of a planet at a = 2.0 AU with a period of P = 1130 days located within the large gap between a = 0.781 AU (P = 260 days) and a = 5.77 AU (P = 5218 days). With less certainty, we also predict a seventh planet at a = 15 AU with P = 62 years.