How would the solar system capture an extra solar planet ?

[supag33k]

How would the solar system capture an extra solar planet ??

Hello! - my first post here...and an informative site to be sure!

I have checked the archives here and checked additional online resources, the point of my question being...

How would the solar system capture an extra solar planet..??

- I admit that I am formulating something to work in creative writing sense ...but don't let that stop anyone contributing...

Essentially I would like someone with real physics knowledge to look it over please...

The understanding I have so far, as a set of two main alternatives listed below. I know the chances are vanishing small to non existent - just want to get my head around the dynamics of it all - is that over several years either could occur...

1. Bad news generally, and for us on Earth especially if...

a. Incoming Exta Solar planet [ES for short] is much larger than Jupiter, and comes inside the orbit of pluto.
b. Incoming ES is larger than Earth and comes inside the orbit of Mars.
c. Incoming ES comes in on a collision trajectory - or head on approach...unlikely given the galactic orbital plane constraints.
d. Incoming ES actually impacts with our sun Sol and cause a major flare/nova event.
e. Incoming ES has orbiting moons that it could conceivably shed during ES capture by our solar system.

I understand in real life the likely outcome - however remote - is as above...as the constraints for point 2 below are most likely impossible..

2. Good news, and the point of my writing to try and verify, if...

a. Incoming ES is between 3 and 4 Earth masses, orbital velocity of 30km per sec.
b. closes on a trailing trajectory gradually overtaking the solar system, the incoming trajectory inclination is about 25 degrees.
c. For calc purposes the solar system is essentially the Sun and Jupiter...and possibly Saturn, so really a major body calculation.
d. On entry to the solar system, the ES misses Pluto, Uranus and Neptune.
e. The incoming ES at closest trailing approach to Saturn approaches with 40 Million km over the south pole on a converging approach, this flattens the inclination to 15 degrees, sheds 4 km sec, and vectors the ES on a trailing approach to Jupiter.
f. The orbital real estate between Mars and Jupiter in our system is not actually "dynamically full" ie Jupiter moved out to it's present position and/or planetary formation is not allowed, but planteray capture via major body deceleration of an ES object still may be valid..??
g. The incoming ES approaches Jupiter on a trailing approach at 24km sec and closest approach is 60 million km - due to Jupiter's much greater mass -
the inclination drops to 5 degrees, and the orbital speed drops to 20km sec.
h. The incoming ES drops into a "standard orbit" with 0.1 eccentricity about 440 million km from the sun, between Mars and Jupiter. My own rough estimates show that this is possible, and that bodes law also works at this point.
i. Possibly tidal heating is a problem on approach of the ES to a Jovian but the Roche limits are never reached...

- obviously the major players have to be in the correct locations otherwise...potentially a big crunch somewhere...

sorry for the longish post ..

But as folks can see I have done serious thinking already!

cheers,

supa

 

[chroot]

What mechanism do you propose that could cause this planet to come flying through interstellar space in the first place?

- Warren

 

[supag33k]

What mechanism do you propose that could cause this planet to come flying through interstellar space in the first place?

- Warren

A good point and something I should have mentioned...I have the ES planet as having been ejected from another star system undergoing a change from sole star to binary millions of years in the past.

The originating system also has a high angular moment relative to the galactic main streamstream of stars, a cosmic jaywalker in other words...

Plus the new binary system member is a red dwarf that ejects the ES object, effectively drops the ES object back to a speed only slightly faster than the bulk of the stars...ie co-rotates..

Also the entry to our solar system would take decades..indeed I am relying on it to do so in my creative work... :)

 

[russ_watters]

There was a Sky and Telescope article about a month ago about how the Earth recently captured a second moon...for about four orbits. It requires perturbations from other massive bodies for the capture to happen. A close encounter with Jupiter would probably suffice, though it could just knock Jupiter out of orbit if it were similar mass.

 

[supag33k]

...
...
A close encounter with Jupiter would probably suffice, though it could just knock Jupiter out of orbit if it were similar mass.

Yep, hence my earlier comment about a ES larger than Jupiter coming into the outermost limits of Pluto's orbit being bad news..so no BD [brown dwarves] in this story!

Jupiter is about 300 Earth masses, and the fictional ES is 3 to 4 Earth masses.

I have the fictional ES doing a reverse of the "grand tour" of the solar system on it's way to entering orbit between 2.8 and 3.0 AU - which apparently is also a bode's law point. Almost like a incoming ES doing a couple of Holman transfers as it encounters the Jovian planets.

One of the real questions is how far an ES would have get inside a jovian gravity well to drop several km per second??

Also I think it more plausible for a couple of favourable gravitation encounters with Saturn and Jupiter to account for better e and inclination values...but hey someone with the real maths can tell me I am wrong...!

The method as I understand it - I have it down as a trailing approach that closes about 13km per second nett, and sheds several degress of inclination. For speed the ES would approach at 26km sec versus Jupiters 13km per sec, accelerate in the gravity well to 30Km sec before the long climb out of the gravity well reduces the speed to around 20km sec and changes the ES's course by around 30 deg co-planar [this is where my maths fails me...groan ]

Just enough to set the ES in a good orbit. Also I reckon the any large body at this point providing the e values are not too radical [ < .15] would tend to settle down in inclination and e due to the dampening effect of Jupiter.

From what I can tell there is no critical resonances at about 3AU [+/- .2 AU]with Jupiter?

Also the modest e and minimal inclination at 3 AU should see the inner planets not affected...though there is a twist - as in all good works!

Though a hint of course...a smaller mass trailing the larger ES into our solar system would be more adversely affected by orbital encounters with Jovian planets...if my understanding of the mass squared and distance squared rules are correct.

 

[tony873004]

There was a Sky and Telescope article about a month ago about how the Earth recently captured a second moon...for about four orbits. It requires perturbations from other massive bodies for the capture to happen. A close encounter with Jupiter would probably suffice, though it could just knock Jupiter out of orbit if it were similar mass.

Do you happen to know what issue of S&T that was? I'd like to read it. I did a simulation of this object. Screen shots:
http://orbitsimulator.com/gravity/images/newMoon1.GIF
http://orbitsimulator.com/gravity/images/newMoon2.GIF

More info from my website:
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1182030550

Here's another simulation where the Sun captures Sedna after a Brown Dwarf passes close to the Sun. S&T magazine also had a short article on this:
http://www.orbitsimulator.com/gravity/articles/sedna.html

There are many ways the Sun could capture an interstellar object. The odds are very low, but it could happen. Think of a capture as an ejection in reverse. If you want to capture a planet into a round stable orbit inbetween Mars and Jupiter, first imagine an object in this stable orbit. What would it take to eject it? If its orbit is stable, not much. Another interstellar massive object could pass through the solar system, making a close pass to this planet and ejecting it. So the reverse of that would be that two interstellar planets, completely unrelated, pass through the solar system at the same time, make a close encounter to each other at the position of the desired stable orbit, exchanging energy, causing one to be inserted into a round stable orbit while the other one continues on a hyperbolic trajectory out of the solar system. Possible? Yes! Probable? I doubt this has ever happened anywhere in the galaxy.

If you are willing to settle for a non-stable orbit, the possibilities grow. A non-stable orbit means that the object will probably one day be ejected. The reverse of this is that the object gets captured into an unstable orbit.

Another method is for a binary planet to encounter the solar system. As they pass through, they get split apart, leaving one in solar orbit while the other one continues on a hyperbolic trajectory to infinity. Some theorize that this is how Neptune captured Triton.

 

[supag33k]

Hello Tony,

Thank you for your interesting reply.

It is starting to sound like a series of encounters would be more plausible from a science and literary sense for my ES object...basically a keyhole approach initally in the past that sets the ES up for a Jupiter encounter in our times.

I downloaded your excellent simulator and fiddled abit with various parameters, though at this stage I can get the ES object at 3 AU and give it the correct 20 km/sec, inclination, and e, but it shoots off into interstellar space...?

I have taken to backing up the default gsim so that I don't pollute/change it with my efforts...

Also is there a way of slowing the simulation speed down at all..??

I can see where a large object can eject a planet from a stable orbit easily enough, it is the orbital physics of a so called "dynamically full or nearly full solar system" when an ES object of terrestrial size is added to the mix that is interesting!

I must confess that I am time poor at the moment due to work and study commitments.

The first main question I have please is that if a 3 Earth mass planet approaches a jovian on a trailing vector, does it shed velocity or does it gain velocity?

The second main question is that if a 3 eMass is at 3AU at 20km sec with little e [ < .015] and inclination [< 5 degrees] - will it go into orbit around the sun..?

- I understand that there is a series of dynamic rules for a smaller body and a larger orbiting planet??...

1. Head on encounter..ie smaller body is in front of the planet's orbital direction:
a. if head on encounter, speed can be variable, and no angular difference..then an impact.
b. if head on encounter, high speed and big angular difference, then the smaller object's speed is increased and it is ejected.
c. if head on encounter, moderate speed, and modest angular difference, then a retrograde orbit or boosted to cometary orbit with big e values.
d. e and inclination can be highly variable.

2. Trailing encounter with jovian, ie trails the jovian on an overtaking trajectory:
a. high speed, and no angular difference..then impact...
b. high speed and modest angular difference, plus modest e and inclination..then deflection [30 to 60 degress] and speed reduction [??]
c. Polar approaches on trailing vector should flatten out e values...and conversely head on encounter including going over one of the jovian's poles should increase the e markedly.


Please advise if I have this down right or am I off at an "orbital dynamics tangent" ??, and thanks once again!

supa

 

[tony873004]

...Also is there a way of slowing the simulation speed down at all..??

Most people want to know how to speed it up, so you're probably doing something wrong. Try this:

• Open the simulation called "onlyplanets.gsim".
• menu Objects> Create Objects
• Choose 3 AU for semi-major axis
• Specify a mass
• Leave all other inputs at their default values (unless you want to tinker with inclination, eccentricity and the other elements).
• Press "Create". It will compute the speed for you.

It is important to note that just because your planet seems to make a few stable-looking orbits, that is not a guarantee that it will remain stable forever. One of the methods for determining stability used by the exo-solar planet group on the "Systemic" web page is to see if the semi-major axis of your planet remains steady, or if it changes over the course of 100 years. If it varies by more than 1 percent, then they consider it unstable, even though you could potentially run your simulation for thousands of years with no sign of instability.

As an example, start with the simulation "onlyplanets.gsim". Edit Venus. Make its mass 2 Jupiter masses. Increase the time step to 1024 seconds. Sit back and watch. Everything remains normal for more than 100,000 years, with no sign of instability detected anywhere. Then, in a period of only a few hundred years, the eccentricity of Mars grows until it is ejected from the solar system. If you try this, it will take about 12 hours to complete the simulation at this time step if you turn off the plotting so the computer is only crunching numbers.

 

[supag33k]

Most people want to know how to speed it up, so you're probably doing something wrong. Try this:

• Open the simulation called "onlyplanets.gsim".
• menu Objects> Create Objects
• Choose 3 AU for semi-major axis
• Specify a mass
• Leave all other inputs at their default values (unless you want to tinker with inclination, eccentricity and the other elements).
• Press "Create". It will compute the speed for you.

It is important to note that just because your planet seems to make a few stable-looking orbits, that is not a guarantee that it will remain stable forever. One of the methods for determining stability used by the exo-solar planet group on the "Systemic" web page is to see if the semi-major axis of your planet remains steady, or if it changes over the course of 100 years. If it varies by more than 1 percent, then they consider it unstable, even though you could potentially run your simulation for thousands of years with no sign of instability.

As an example, start with the simulation "onlyplanets.gsim". Edit Venus. Make its mass 2 Jupiter masses. Increase the time step to 1024 seconds. Sit back and watch. Everything remains normal for more than 100,000 years, with no sign of instability detected anywhere. Then, in a period of only a few hundred years, the eccentricity of Mars grows until it is ejected from the solar system. If you try this, it will take about 12 hours to complete the simulation at this time step if you turn off the plotting so the computer is only crunching numbers.

Thanks for the help!

Okay so I have 3 Earth masses at 3 AU - and it initally looks reasonally stable!

The e values are a bit higher than Mars [.04 to 0.5], but Mars itself remains stable, though the inclination creeps up all the time [1.7 and climbing very slowly]

-Possibly it looks like it is still too close to Jupiter to be stable at 3AU for millions of years...the inclination does not appear to be "closed loop" yet.

I'll try bringing the SMA down to 2.5 AU and *maybe* still be okay with the inner planets...possibly lowering the rate the inclination climbs.

Does the Simulator mention elapsed time anywhere at all?

So how do I increase the time step? - and also turn off plotting?

EDIT - oops I found all that under View, dashboard elements.. ;)

Then I'll test some more -especially the inner jovian model !

 

[Hurkyl]

As an example, start with the simulation "onlyplanets.gsim". Edit Venus. Make its mass 2 Jupiter masses. Increase the time step to 1024 seconds. Sit back and watch. Everything remains normal for more than 100,000 years, with no sign of instability detected anywhere. Then, in a period of only a few hundred years, the eccentricity of Mars grows until it is ejected from the solar system. If you try this, it will take about 12 hours to complete the simulation at this time step if you turn off the plotting so the computer is only crunching numbers.

2^35 iterations is a lot; do we know that this isn't just a numerical instability?

 

[tony873004]

The e values are a bit higher than Mars [.04 to 0.5], but Mars itself remains stable, though the inclination creeps up all the time [1.7 and climbing very slowly]

You will probably find that the inclinations don't creep up forever. The rate will slow, it will reach a peak, then it will decrease. Inclination is an oscillating orbital element. In fact, you can plot this using the "Output File" available in the File menu. (The beta version is much nicer in this department. It is available on my web site's forum.) This will make a text file for you that outputs the orbital elements of each object at an interval specified by you. Then you can open this text file in Excel or Microsoft Works spreadsheet and graph the inclination. You'll see something that looks somewhat sinusoidal. In fact, if you compare your graph to one made from secular perturbation theory (page 305 of Solar System Dynamics by C.D. Murray and S.F. Dermott, as well as other references), you'll find that they resemble each other for about 1 million years. After that, they begin to diverge. They still show the same trends, but they get out of sync and don't mirror each other any longer.

I'm glad you found the features you were looking for. The F8 and F9 buttons are the shortcut to opening all of them at once. One lines them up horizontally across your screen, the other vertically.

2^35 iterations is a lot; do we know that this isn't just a numerical instability?

That's a good point. It's about 34 billion iterations, or about 2^~31 or ~32. Even after that many iterations, a few hundred years prior to Mars' ejection, the solar system looks completely normal. All the planets are still orbiting the Sun in their present-day orbits.

But after that many iterations, a conclusion such as "Mars gets ejected on May 4, 107481" would be useless. If the same simulation was run at a different time step, Mars gets ejected on a different date, indicating that numiceral error is definitely present. But after many different trials at different time steps, a trend becomes clear: Mars gets ejected after a period of time in the high tens of thousands of years to the low 100,000s.

Realistically, I would expect that Mars is rolling the dice with each orbit, so it may be more correct to say that with each orbit (~2 years), Mars is taking a 1 out of 50,000 chance that this will be the orbit that begins the quick process that leads to its ejection. So under slightly different starting conditions, there's a small chance that it won't even last 1000 years, and a small chance that it will last over 200,000 years, with something in the high 10s to low 100s being the most probable.

 

[supag33k]

Okay so I worked out that 3 Earth masses and 3AU is not a good combination - as the inclination for the ES never recovers and it gets ejected after about 6000 years and the rest of the inner system is ruined also.

Then I have another attempt at 2.2 Earth masses at 2.75AU...so far stable beyond 60,000 years.

Tony - you are correct as mentioned on the inclination. It trades between Mars and the ES, + 4 degrees inclination for Mars, +2 degrees inclination for the ES, with the SMA and the e for both bodies intact...mars e goes fro .09 to .12 but still good..

I'll look into the beta as the logging and point in time stuff was one of my next questions...;)

There are some minute inclination changes of 1 degree for Earth but the rest looks okay...certainly a space going race would have a long time to resolve problems...hopefully..

This at least is start - so now I just have to get the orbital dynamics of the capture correct.

 

[tony873004]

This at least is start - so now I just have to get the orbital dynamics of the capture correct.

The easiest way to do this is to set your desired orbit, choose menu Time>Backwards, then wait until the object gets ejected. (This assumes that its orbit is unstable in the long-term). Then choose menu Time>Forward, save the simulation, and watch your object get captured. In the example I give above of a 2 Jupiter massed Venus, if you run time backwards after Mars' ejection, you get to watch Mars get captured, and then settle into a circular orbit which remains stable for 100,000 years.

 

[tony873004]

I found my simulations of the Venus with 2 Jupiter masses. Let me make some corrections to what I said earlier.

Everything appears normal up until about 223,000 years, after which point Mars' eccentricity starts rapidly growing. Within a few thousand years, it is a Venus, Earth, and Jupiter crosser. It spends 60,000 years in this risky orbit until it is boosted onto an escape trajectory.

If you want to try it yourself, here's a zip file that contains multiple gsim files of this simulation, saved every few thousand years: http://orbitsimulator.com/gravity/simulations/Venus2MJ.zip

This is run at a timestep of 8K seconds. Keep in mind that different time steps will give you different timetables of these events, an artifact of making many iterations in a highly chaotic system. This means the exact answer is useless, and a more general answer that Mars lasts less than a few hundred thousand years would be the best you could conclude.

 

[russ_watters]

Do you happen to know what issue of S&T that was? I'd like to read it. I did a simulation of this object. Screen shots:

It's just a 1/3 page blurb in the July issue.