High School Is this a coincidence?... (distances between planets)

[Jan Naus]

I'm not a student or graduate in Astrophysics.. Wish i were though...

I was playing with distances between planets...
I found that Mars, Ceres, Jupiter and Saturn have somthing in common...
They are in a kind of ratio with another.. They all got a difference about 1,84 to 1,88x the distance from the previous planet, sub-planet.
On average 1,845x.
I thought this can be coincidential.
So i took the big moons of Jupiter and Saturn to do the same thing
jupiter; Io, Europa and Ganymede have a ratio of around 1,593
Saturn: Mimas, Enceladus, Thetys and Dione about 1,26
I found a few Exoplanets do have the same thing. Trappist-1, Teegarden's star, YZ Ceti, Lasseille 9352.
My question is why isn't this coincidential anymore, why is it that way.

 

[russ_watters]

Welcome to PF!

It's probably more than a coincidence but no real explanation has been found:

https://en.wikipedia.org/wiki/Titius–Bode_law

 

[sbrothy]

Fractals immediately came to my mind, but that is probably too simple and/or nebulous an "explanation".

Stumbled over this one though:

ON THE ORIGIN OF THE GRAVITATIONAL QUANTIZATION: THE TITIUS–BODE LAW.

EDIT: Not to explain anything mind. It just looked like fun. They're probably not the first to relate the smallest and the largest to eek out some explanation.

 

[sophiecentaur]

They are in a kind of ratio with another.

Kepler noticed this, a while ago and was quantified more accurately by the Titus Bode law (above) A solitary planet will have an orbit which can 'easily' be calculated, according to its orbital Energy (Net Kinetic and Potential) but when a second planet is added, the interaction between the planets becomes the 'Three Body Problem' and there's no analytical (formula) solution to the two orbits. For more planets it gets worse and worse. The fractal idea is attractive with the predicted chaotic motion. Interaction between planets can cause resonances which can throw orbits wildly out and that spoils formation of a 'stable' setup' and the resulting eccentric orbits can take the object out of the system. Only certain spacings can give (almost) stability and systems can settle into the spacing we recognise. I guess there's an argument that rogue planets would have been thrown out of the system a long time ago and we are left with the present situation which 'looks special'.

There's a similar argument to explain the formation of an original planetary disc out of a random ball of dust etc. Orbits out of the planetary plane would have normalised to within the disc; the only thing that would need to be conserved would have been net angular momentum of the original piece of a nebula from which the Sun formed. Looks pretty special until this idea is applied and a disc is what you'd expect. (Similar thing with galaxy formation; the older galaxies tend to have settled into spirasl whereas the newer ones are still elliptical shapes.

I can't remember where I read this but it's thought that members of the Asteroid belt are held in a similar orbital position but. due to the presence of massive 'shepherding' effect of Jupiter the asteroids maintain their mean orbital radii (roughly). The occasional asteroid gets thrown out due to collisions or near collisions and can get a more eccentric orbit and then collide with planets. The jostling around of the asteroids is causing them to break up and (I heard) so the size of potentially colliding asteroids is actually reducing. So one day, (far future of course) Earth will no longer have the risk of massive collisions. The centre of mass of the total number of asteroids will still be kept in the existing orbital band, due to Jupiter, in particular.

 

[Hornbein]

I'm not a student or graduate in Astrophysics.. Wish i were though...

I was playing with distances between planets...
I found that Mars, Ceres, Jupiter and Saturn have somthing in common...
They are in a kind of ratio with another.. They all got a difference about 1,84 to 1,88x the distance from the previous planet, sub-planet.
On average 1,845x.
I thought this can be coincidential.
So i took the big moons of Jupiter and Saturn to do the same thing
sterium.

jupiter; Io, Europa and Ganymede have a ratio of around 1,593

Saturn: Mimas, Enceladus, Thetys and Dione about 1,26

I found a few Exoplanets do have the same thing. Trappist-1, Teegarden's star, YZ Ceti, Lasseille 9352.

My question is why isn't this coincidential anymore, why is it that way.

This is similar to the discoveries of Kepler published in 1596 in his Mysterium Cosmographicum.

 

[DaveC426913]

HD 110067 is six planets that are all in harmonic orbits - simple ratios of their orbital periods.

This happens because they tug on each other until they achieve a certain amount of stability (otherwise they just keep getting tugged).

It's to the only system, just the most spectacular.

I suspect that the orbital periods is the primary cause, which would drive the planets toh simple ratios of orbital radii.

 

[sophiecentaur]

I suspect that the orbital periods is the primary cause, which would drive the planets toh simple ratios of orbital radii.

The ratios are only approximate, though. Sneaky.

 

[DaveC426913]

The ratios are only approximate, though. Sneaky.

True. I put that down, at least partially, to the fact that at any given time, they may be in transition. For all we know, in ten million years, they will have settled into more harmonic states (or less).

I don't think the states are all that robust; they might easily be perturbed by, say, a Jovian mass migating inward, as it seems such bodies are wont to do. Harmonic orbits might be no more stable than, say, Lagrange points. Bodies might drift in, stay for a while, then drift away again.

But I should probably not be filling the OP's head with unevidenced speculation.