What orbit do exoplanets follow?

What orbit do exoplanets follow?

A  recent report involved the dis-covery of a new planetary system, more than two thousand light years from the Earth. Apart from the oddities of the individual planets, like PH3c, which had a highly inconsistent orbit, what is striking about this planetary system is the ratios of their orbital time periods.

According to Joseph Schmitt, a very quirky feature of this peculiar trio, is that the outer planets period is 1.91 times longer than that of the middle planet and the middle planets ‘year’ is 1.91 times longer than the inner planet PH3b!

Kepler’s third law of planetary motion, namely the squares of orbital periods are proportional to the cubes of their distances (of the planets) from their parent star
(indeed this law is truly universal, valid ubiquitously!), then implies that the ratios of the distances of the trio, is about 1.6. The outer planet is 1.6 times farther (from the parent star) than the middle planet which in turn is 1.6 times further away than the inner planet.

Our own solar system’s planets have a well-known regularity of this sort, known as the ‘Titius-Bode Law’. Again, it is to be noted that in our solar system, the ratio of the periods of Mars and Earth is close to 1.9 and that of the Neptune and Uranus is again close to 1.95!

Indeed most of the other consecutive planetary periods have a ratio around two! Now let us come to the Titius-Bode law, which was first enunciated by Johann Bode, although it was actually discovered by another German, Johann Titius in 1766! The two discovered an apparently coincidental arithmetic relationship involving distances of the planets from the Sun. One AU is the earth’s distance from the Sun. So Mars is about 1.6 AU (note again the factor 1.6!), Venus 0.7, Mercury 0.4, and so on. Note that the ratio of Earth to Mercury orbital distances is about 2.5, i.e. 1.6 squared, just like the inner and outer planets of this exotic new planetary system.

Moreover 1.6 is close to the well-known golden ratio. It occurs in so many different situations and circumstances, ranging from petal arrangements in flora of all kinds (like sunflower), aquatic creatures like Nautilus, in the nano world, in structures of gigantic spiral galaxies as well as being involved in architecture of all cultures (Greek, Byzantine and Islamic)! The Titius-Bode Law can be formulated in terms of involving powers of this ratio. We have seen some examples. If this is valid in other planetary systems, it may shed light on the type of quantitative theoretical models forming such systems.

Again, in our solar system, we have phenomena like orbital resonances where two bodies have periods of revolution that are in a simple whole number ratio, allowing each body to have a regularity recurring gravitational effect on each other. In this regard, we have the well-known phenomenon of Kirkwood gaps, where there are relatively empty regions in the distribution of asteroids that correspond to orbital resonance with Jupiter whose strong gravitational influence would have perturbed and shifted the minor bodies to other orbits.

Perhaps, with more detailed research, several other planetary systems may reveal several such similar traits.  


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