An amazing formula

[Krupin]

I have discovered a fundamentally new type of relationship of planetary orbits, which can be expressed by the following formula:
$$ \sqrt{{\left( \frac{({R_1}+{R_2})}{2R_1}\right)}^3}$$
Substituting in this formula values of orbital radius of the Earth R1=1a.u. (by definition) and R2=0,723 – orbital radius of the Venus, we get 4 / 5 - relations tiny integers. If we substitute values R1=5,203 and R2=0,723 (the Jupiter and the Venus), we get 3 / 7. Substituting values R1=9,539 (the Saturn) and R2=30,06 (the Neptune), we obtain 2.99 , which close to integer - 3. This golden formula works not only for the planets, but also for satellites of giant planets.

 

[D H]

Numerology = pseudoscience, at best. I'll let the pseudoscience moderators decide if this is just cess.

 

[James R]

It looks a bit like Kepler's third law, which says that the square of the orbital period of a planet is proportional to the cube of the orbital distance:

$$T^2 = kr^3$$

The orbital period of a plant is therefore proportional to its orbital radius to the power of 1.5:

$$T = k'\sqrt{r^3}$$

The ratio of the periods of two planets is:

$$\frac{T_1}{T_2} = \sqrt{\left(\frac{r_1}{r_2}\right)^3}$$

which is similar to the formula you have given.

Have you calculated the value of your formula for every pair of planets? How do the others look?

Also, how did you come upon your formula? Trial and error?

 

[AlphaNumeric]

Many of the planets form some kind of orbital resonance with one another and likewise for Jupiter's larger moons. The fact you can come up with some formula which outputs pairs of small integers doesn't mean much, you have no predictive power. For instance, knowing the positions of Mercury, Venus and Earth doesn't tell you the position of Mars. No doubt you can find plenty of pairings which have small integer ratios but you'll be able to find ones which don't come close to small ratios or you have to say "Well that's close to 3/7". For instance, you have 2.99 in your original post, which you take to be 3. What if it isn't? What if its actually 298/101? That is obviously not a pair of small integers but it's close. If you allow 'Oh it's close enough, call it 3/1' then you render your work worthless because there's LOADS of 'small integer rations' close to pretty much any number.

 

[Krupin]

System Kepler-11 has an interesting pattern. Let's say, between the outermost planet and one of the internal appeals asteroid. Then the asteroid and the outermost planet are in orbital resonance. These resonances 2 : 3 ; 3 : 5 ; 4 : 9 ; 1 : 2 ; 7 : 9. The first three resonances are such that the denominator is odd, and the numerator = (denominator + 1) / 2. There is a missing 4: 7. There it may exist another planet.