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Message started by frankuitaalst on 01/06/13 at 03:25:52

Title: If Earth had rings
Post by frankuitaalst on 01/06/13 at 03:25:52

Could Earth support rings such as Saturn does ? How wide could they be ?
The sim hereunder puts 139 in a circular orbit around Earth roughly between 80.000 and 250.000 km's.

Title: If Earth had rings
Post by frankuitaalst on 01/06/13 at 03:34:03

Running the above sim for ca. 30 years gives the following output processed with the GSimviewer .
X-axis shows the Sma of the test particles . The Y-axis shows the eccentricity .

Particles seem to become unstable ( gaining eccentricity ) at about 180.000 km . This is about 1/2 the distance to the moon . This corresponds with roughly a 3:1 resonence with our moon.
The violet peak at the right may be a 2:1 resonance .
The green peaks at 150.000 km correspond with a 4:1 resonance .

So , if we assume the eccentricty build op to be representative for stability , rings might be unstable above 150.000 km .
I didn't find any quick references about stability of sattelites around Earth

Title: If Earth had rings
Post by frankuitaalst on 01/06/13 at 06:25:45

If we limit the distance of the rings to Sma = 150.000 kms we get a "stable" system .
The system was run over 150 years .
Here's the output of the Gsimviewer .
The eccentricity doesn't seem to rise to more than 0.06 .

Title: Re: If Earth had rings
Post by frankuitaalst on 01/06/13 at 06:29:25

If we represent the evolution of inclination over these 150 years we get a surprising result :
The inclination of some parts of the rings rises above 30 , although the moons inclination is only 5 .
So there must be some "pumping" action .  

Title: Re: If Earth had rings
Post by frankuitaalst on 01/06/13 at 06:35:05

A weird phenomenon seems to be working here .
I don't know if I can post the file I prepared ( because of the 1.5 MB it contains ) .
If we plot the time evolution of inclination a kind of wave goes through the ring which pumps of the particles to higher inclinations and then reduces the inclination again .
I don't know how to explain this phenomenon exactly .

Title: Re: If Earth had rings
Post by EDG on 01/06/13 at 08:58:19

Your 'weird phenomenon' isn't related to gravsim rounding/truncation errors is it? I found something similar in the kirkwood gap simulations that I ran a few years ago ( see http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1223831545 )

Title: Re: If Earth had rings
Post by frankuitaalst on 01/06/13 at 09:19:19


EDG wrote:
Your 'weird phenomenon' isn't related to gravsim rounding/truncation errors is it? I found something similar in the kirkwood gap simulations that I ran a few years ago ( see http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1223831545 )

I'm sure it isn't an artifact of rounding or truncation . It must be the result of gravitational interaction with the moon.

Title: Re: If Earth had rings
Post by Tony on 01/06/13 at 10:47:48

Don't forget Kozai  ;)

Title: Re: If Earth had rings
Post by frankuitaalst on 01/06/13 at 11:25:29

Thanks Tony for remembering our mysterious Friend  :). However , I don't fully understand what's happeninig because the test particles start at zero eccentricity and low inclination ( 0 ) . I thought Kozai exchanges eccentricity for inclination and vice versa.
I've run another simulation afterwards and put the particles in the inclination of the moon , taking into account the Omega and omega .
To my surprise the inclination also rises in this case to 36 after 250 years ,wheras the eccentricity stays as low as less than 0.1 . Weird Kozai ?

Title: Re: If Earth had rings
Post by EDG on 01/06/13 at 13:35:20

Do you have the sun in the model too? Maybe it's a solar influence?

Title: Re: If Earth had rings
Post by frankuitaalst on 01/06/13 at 13:53:09


EDG wrote:
Do you have the sun in the model too? Maybe it's a solar influence?

Yes , all the planets are in the system simulated .
What's bothering  me is that the eccentricies are moderate ( Moon= ca. 0.06 ) but inclination rises as high as 36 .
Maybe it is indeed a Kozai of complex form ( Sun , Earth, Moon , ...Jupiter ..) .
Normal Kozai formulas (3 body restriced body system ) don't apply in this situation .

Title: Re: If Earth had rings
Post by EDG on 01/06/13 at 15:16:09

I'd suggest that you try removing all other bodies except the earth and moon - let's see what it looks like without any other influences. Then try adding the sun, and see what happens. Solar tides are pretty significant, and the earth/moon system is inclined relative to the ecliptic, so I'm thinking that may be affecting things here.

Title: Re: If Earth had rings
Post by frankuitaalst on 01/07/13 at 11:29:11


EDG wrote:
I'd suggest that you try removing all other bodies except the earth and moon - let's see what it looks like without any other influences. Then try adding the sun, and see what happens. Solar tides are pretty significant, and the earth/moon system is inclined relative to the ecliptic, so I'm thinking that may be affecting things here.


I've made a new simulation with the following change : I set the inclination of our moon to zero and started the sim again.
All 150 bodies become quit now . Their inclination is kept very small .
So I think the inclination of our moon is the culprit .
It is worthwile mentioning that it doesn't matter what initial inclination the rings have : setting their inclination to zero or let them match he inclination of our moon doesn't prevent them to gain inclination so they are evolving to a "cloud" instead of a plane ring .  
BTW : I haven't checked the inclination of moons systems of the gas giants . If the inclination of these systems is not zero one could also expect wavelike structures or changing inclinations of some moons .

Title: Re: If Earth had rings
Post by frankuitaalst on 01/07/13 at 12:13:40

I've found this link , mentioning also instability features of a ring structure due to moon - sun perturbations . The first paragraphs deal with oblatness issues , which were not taken into account of course in the sims above .
http://www.astroscience.org/abdul-ahad/earth-ring-dynamics.htm

Title: Re: If Earth had rings
Post by JDoolin on 01/13/13 at 18:12:29

Speaking of rings, and maybe this should actually start a new topic...  Has anybody ever seen a derivation of the Roche Limit?  

I've got some ideas how to do it; basically adding the centripital acceleration due to orbital radius, the gravitational acceleration due to the mass of the moon, and the gravitational acceleration due to the mass of the planet, and figuring out when the sum is zero.  

However, I wondered if there were any other effects that I should be taking into account.  

Title: Re: If Earth had rings
Post by Tony on 01/13/13 at 21:40:51

You need to find out the distance at which the tidal force trying to rip the object apart is greater than the object's gravity that is holding it together.  Wikipedia has a nice article on how to do it:
http://en.wikipedia.org/wiki/Roche_limit#Derivation_of_the_formula_2

Title: Re: If Earth had rings
Post by frankuitaalst on 01/16/13 at 13:38:12

As mentionned above Earth Rings don't stay in their original plane . Hereunder is an animation which shows the inclination evolation in time as a function of distance from Earth .
The timespan is about 350 years .
Originally all particles were set at moons inclination ( 5) . Moreover the LAN was set to the LAN of the moon .
Due to perturbations the inclintions rise  . It's no wonder that particles further away exhibit stronger perturbations .

Title: Re: If Earth had rings
Post by frankuitaalst on 01/16/13 at 13:44:32

What's more : even the LAN ( longitude  of ascending node ) doesn't stay synchronised with the LAN of the moon .
THe mmon itself has a LAN oscillation of about 18.6 years .
The animation herunder shows the LAN variation in time . Originally all partickes had a LAN of about 355 .

If we combine all parameters it may be obvious that a ring structure around Earth evolves very quickly to a wavy cloud like structure .

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