BODE'S LAW

Previous year papers questions related to Bode’s Law

1. Write a note on Bode’s law of Planetary position.                                  (2009-10,5 marks)

2. Define and state the Bode’s law with all its mathematical calculations? (2016-17, 15 mar)

3. What is Bode’s law? Which planet do not fit in Bode’s law and why? (2017-18,10 marks)

BODE’S LAW

The Titius-Bode Law is rough rule that predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was formulated as a mathematical expression by J.E. Bode in 1778.The hypothesis correctly predicted the orbits of Ceres (in the asteroid belt) and Uranus, but failed as a predictor of Neptune's orbit.

The law relates the mean distances of the planets from the sun to a simple mathematics progression of numbers. It relates the semi major axis a of each planet outward from Sun :

  a = 4 + x

where x = 0,

3,

6,

12,

24,

48,

96,

192,

384

With the exception of the first two, the others are simple twice the value of the preceding number.

Add 4 to each number:

4

7

10

16

28

52

100

196

388

Then divide by 10:

0.4	0.7	1.0	1.6	2.8	5.2	10.0	19.6	38.8

The resulting sequence is very close to the distribution of mean distances of the planets from the Sun:

Body	Actual distance (A.U.)	Bode's Law prediction
Mercury	0.39	0.4
Venus	0.72	0.7
Earth	1.00	1.0
Mars	1.52	1.6
Asteroid Belt	2.7	2.8
Jupiter	5.20	5.2
Saturn	9.54	10.0
Uranus	19.19	19.6
Neptune	30.1	38.8
Pluto	39.5	77.2

       

When it was initially published, it was found that this law correctly predicts the distances of all known planets from Mercury to Saturn. It also correctly predicted the (then unknown) locations of the asteroid belt and Uranus, but not for Neptune or Pluto .It is now thought to be a mathematical coincidence rather than an actual physical law since it fails to apply to the outermost planets in our solar system. It is suggested that this relation is a mathematical result of orbital resonances and gravitational interactions within multi-body planetary systems.

           The Titius-Bode relation plotted against the actual distances of planets from the Sun.