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Author Topic: Ratios of Planetary Mass & Surface Gravity  (Read 17102 times)

ROBERT

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Ratios of Planetary Mass & Surface Gravity
« on: 08/02/2006 15:33:38 »
All the ratios below are at least 99% accurate :-

SURFACE GRAVITY RATIOS :-
Mercury : Mars = 1 : 1
Uranus : Saturn = 1 : 1
Mercury/Mars : Uranus/Saturn = 1: 3
Uranus/Saturn : Jupiter = 4 : 9
Mercury/Mars : Jupiter = 1 : 7

(Isn�t it peculiar that the surface gravity of one planet
 is an exact multiple of the surface gravity of another planet ?).

PLANETARY MASS RATIOS :-
Mercury : Mars = 1 : 2
Venus : Uranus = 1 :18
Uranus : Saturn = 2 :13
Saturn : Jupiter = 3 : 10
Venus : Neptune = 1 :21

(Isn�t it peculiar that the mass of one planet
 is an exact multiple of the mass of another planet ?).

Are these exact ratios accidental coincidences,
 or is there a physical reason for this pattern of whole number ratios ?.

(This pattern is reminiscent of the masses of atomic nuclei).
« Last Edit: 27/03/2006 00:26:52 by daveshorts »


 

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #1 on: 10/02/2006 19:47:06 »
Not sure the surface gravity or mass ratios are despeately significant but the orbital periods are probably quite important

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ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #2 on: 16/02/2006 15:32:35 »
I am aware of the relationship between the orbital period of a planet and its orbital radius.
 However I do not see how Keplers laws explain the whole number ratios between the masses of the planets.

A possible explanation is that in the early solar system many small (mercury sized?) planetesimals formed initially, analogous to raindrops condensing from a cloud they were of equal size.

If present day planets are an amalgamation of these equal planetesimals, this would explain the whole number ratios between the masses of the planets: each is made up of a whole number of equally sized planetesimals.

I am interested in other possible explanations for the whole number ratios in planetary masses.
« Last Edit: 16/02/2006 15:33:00 by ROBERT »
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #3 on: 20/02/2006 13:12:23 »
The data I used for the above ratios is from a book entitled Patrick Moores Guide to the Stars and Planets, (p23), ISBN 0-540-08644-4.

             Planetary Mass (Earth=1)   | Surface Gravity (Earth=1)

Mercury       0.055      |   0.38
Venus         0.815      |   0.90
Earth         1      |   1
Mars         0.11       |   0.38
Jupiter         317.9      |   2.64
Saturn         95.2      |   1.16
Uranus         14.6      |   1.17
Neptune            17.2            |       1.2
« Last Edit: 20/02/2006 13:29:33 by ROBERT »
 

Offline daveshorts

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #4 on: 20/02/2006 16:07:27 »
You are doing a load of comparisons with numbers that are not quoted with much precision and only looking at the ones that produce interesting fractions.
I would have thought that if you got the figures to a few more decimal places the relationships are likely to break down.
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #5 on: 20/02/2006 16:19:40 »
This whole number relationship may have something to do with the Titus-Bode "law":
 another curious "coincidental" whole number relationship between the planets:-

""  The Titus-Bode Law
1. First discovered by German Johann Titus in 1766, this is an rough guide to the spacings of planets away from the Sun.
2. Another German, Johan Bode, elaborated on it and it is today called either Bode's Law or the Titus Bode
Law, although the term "law" is perhaps a bit too strong a word.
a. Start with this sequence of numbers: 0 3 6 12 24 48 96 192 384
Then add 4 to each and divide each by 10.
This gives the approximate distances of the major planets to the Sun:
.4 .7 1.0 1.6 2.8 5.2 10.0 19.6 39 in terms of astronomical units
Note that nothing was seen at 2.8 AU. The "celestial police" eventually discovered the asteroids there.
Also note that it breaks down after Uranus. Neptune is at 29 AU, not 39, but Pluto is at 39.
3. The Titus-Bode Law is an interesting mathematical curiousity, for which there is no known physical reason.
Since no one has been able to define a precise mechanism by which it might work, it is not widely
accepted today, and is seen rather as an interesting coincidence. However, some astronomers believe that
there may be some underlying reason, likely related to the interplay of gravitational fields of the planets and
Sun, that could give the Titus-Bode Law more credibility. But such a reason hasn't yet been found.""
« Last Edit: 20/02/2006 16:25:24 by ROBERT »
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #6 on: 24/02/2006 16:33:31 »
A possible explanation for the Titus-Bode law.

In Chladni figures on a circular plate, material accumulates at the nodes which can take the form of concentric circles.

Couldnt a similar process have occurred in the proto-planetary disc of gas & dust ?. Vibrations from a slowly rotating, (precessing ?), sun sending out waves into the proto-planetary disc. This would create nodes where material would accumulate as in Chladni figures. These concentric nodes would seed planet formation and become the orbits of the planets.

If the vibration from the sun driving this process was not SHM but complex, (e.g. rotation & precession), then this could explain the varying masses of the planets, as complex vibrations would create concentric nodes of varying width thus determining the eventual size of the planets.

[This could be the answer to my original question about the peculiar ratios of planetary masses].

Should I expect a telephone call from Stockholm  :),
Or is this hypothesis impossible ?.

« Last Edit: 24/02/2006 16:41:17 by ROBERT »
 

Offline Dr B

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #7 on: 24/02/2006 16:44:11 »
A quick look at the data given by other sources show that the relationship mentioned is all in the rounding.  It would, however, have been fascinating if true!

Dr B
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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #8 on: 27/02/2006 12:55:25 »
quote:
Originally posted by ROBERT

All the ratios below are at least 99% accurate :-

SURFACE GRAVITY RATIOS :-
Mercury : Mars = 1 : 1
Uranus : Saturn = 1 : 1
Mercury/Mars : Uranus/Saturn = 1: 3
Uranus/Saturn : Jupiter = 4 : 9
Mercury/Mars : Jupiter = 1 : 7

(Isnt it peculiar that the surface gravity of one planet
 is an exact multiple of the surface gravity of another planet ?).

PLANETARY MASS RATIOS :-
Mercury : Mars = 1 : 2
Venus : Uranus = 1 :18
Uranus : Saturn = 2 :13
Saturn : Jupiter = 3 : 10
Venus : Neptune = 1 :21

(Isnt it peculiar that the mass of one planet
 is an exact multiple of the mass of another planet ?).

Are these exact ratios accidental coincidences,
 or is there a physical reason for this pattern of whole number ratios ?.

(This pattern is reminiscent of the masses of atomic nuclei).




Maybe I'm missing something here, but I don't see how 13 is an exact multiple of 2 nor 10 an exact multiple of 3.
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #9 on: 01/03/2006 12:34:05 »
They are all whole number ratios, Dr Beaver, some of which are multiples, 1:2, 1:3, 1:7, 1:18, 1:21.etc
 It is peculiar that the masses of the planets should be related by whole number ratios: it seems the masses of planets are not continuously variable.
« Last Edit: 01/03/2006 12:50:50 by ROBERT »
 

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #10 on: 01/03/2006 14:28:51 »
It was the way it was phrased as "exact multiples" that confused me.
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #11 on: 07/04/2006 15:53:41 »
For the uninitiated here is a diagram of Chladni patterns on a disc

Fine sand sprinkled on the disc forms patterns (nodes) consisting of diametric lines and concentric circles when the disc is vibrated, (here with a violin bow).
On this uniform disc the concentric circles are equally spaced.
The protoplanetary disc would not have been uniform; its density would have diminished towards its edge and consequently any nodes (orbits) would become increasingly far apart, (as in Titus-Bode).
« Last Edit: 07/04/2006 15:57:51 by ROBERT »
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #12 on: 18/04/2006 16:47:09 »
This is an extract from Wikipedia which I found today:-

"  'Near' mean motion resonances

Other near resonances exist among the moons including:

Saturn system

(5:3) Rhea-Dione
Uranus system

(3:1) Umbriel-Miranda
(5:3) Umbriel-Ariel
(2:1) Titania-Umbriel
(3:2) Oberon-Titania
The absence of (precise) resonances in the Uranus system, given their abundance in the Saturn and Jupiter systems is actually a bit of enigma.

One can claim 'near' resonances among the Planets e.g.

(2:1) Neptune-Uranus
(3:1) Uranus-Saturn
(5:2) Jupiter-Saturn
(see Titius-Bode law).
However, in spite of efforts, no significance has been identified so far for these near commensurabilities."

http://en.wikipedia.org/wiki/Orbital_resonance
« Last Edit: 18/04/2006 16:53:56 by ROBERT »
 

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #13 on: 11/05/2006 16:47:03 »
If
the planets formed like this, on a
proto-planetary disc of gas & dust in the same manner as  
Chladni figures on a circular plate,
wouldn't they all have the same period?

It seems like they would all take the same amount of time to revolve around the sun.  Its not they could slow down, or they would get sucked into the sun.  Simple Newtonian physics.
 

ROBERT

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Re: Ratios of Planetary Mass & Surface Gravity
« Reply #14 on: 13/05/2006 11:19:37 »
All parts of the proto-planetary disc were not rotating at the same speed:
 it had a vortex motion similar to a spiral galaxy.
 This motion would have produced planets which have different periods.
http://en.wikipedia.org/wiki/Spiral_galaxy
« Last Edit: 13/05/2006 11:23:44 by ROBERT »
 

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Re: Ratios of Planetary Mass & Surface Gravity
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