Planetary Orbital Radius in AU using Titius - Bode Law Calculator

The Titius-Bode law is a hypothesis that the bodies in some orbital systems, including the Sun's, observe a semi-regular pattern of distances. Often used in Physics and Astrophysics, it's particularly relevant in the study of our Solar System's structure and the prediction of planetary positions. This tutorial delves into this empirical rule's application in calculating a planet's orbital radius in Astronomical Units (AU) based on the planet's index.

Planetary Orbital Radius in AU using Titius - Bode Law Calculator
Titius - Bode Law Calculator Results
Planetary Orbital Radius (a)= AU

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Example Formula

The Titius-Bode Law can be formulated as follows:

a = 0.4 + 0.3 × 2n


  1. a represents the planet's mean distance from the Sun, measured in Astronomical Units (AU).
  2. n is the index of the planet. It is -∞ for Mercury, 0 for Venus, 1 for Earth, and so on.

Who wrote/refined the formula

The Titius-Bode law was first noted by Johann Daniel Titius in 1766 and then popularized by Johann Elert Bode in 1772. While this empirical rule is primarily used in Astrophysics for predicting the position of planets in our Solar System, it also finds relevance in celestial mechanics and planetary sciences.

Real Life Application

The Titius-Bode law was initially used to hypothesize the existence of a then-undiscovered planet between Mars and Jupiter. This area is now known to be the asteroid belt, but the discovery of the planet Uranus, which approximately fit the law's prediction, further validated its use in real-world astronomical predictions.

Key individuals in the discipline

Johann Daniel Titius and Johann Elert Bode are the key figures associated with the Titius-Bode Law. Titius, a German astronomer, introduced the formula in 1766, while Bode, another German astronomer, refined it and brought it to the forefront of astronomical research in 1772.

Interesting Facts

  1. The Titius-Bode law was used to predict the existence of a planet between Mars and Jupiter. The discovery of the asteroid belt in this region partially validated these predictions.
  2. The discovery of the planet Neptune, which does not conform to the Titius-Bode law, led many astronomers to abandon the law in the 19th century.
  3. Despite its limitations, the Titius-Bode law has been instrumental in guiding astronomers' search for new celestial bodies within our Solar System and beyond.


Although the Titius-Bode law has been met with skepticism due to its inability to accurately predict all planetary distances, it remains an intriguing tool in astrophysical studies. The historical use of this law to predict the locations of Uranus and the asteroid belt underscores its potential in guiding exploratory research into the cosmos.

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