Close encounters of the massive kind

[Nereid]

From the apparent stability of the orbits of the planets in our solar system (let's leave out EKB objects, for now), what limits can we put on past close encounters with massive, compact objects, such as stars, rogue Jupiters, and black holes?

For simplicity, assume an asymptotic closing speed of ~<100 km/s. Also assume any episodes of bombardment have zero effect (e.g. perturbations of Oort cloud comets, and subsequent collisions with any planets, do not result in changed planetary orbits).

 

[WarrenPlatts]

Well, I just stuck a twin Sun in UB313's orbit using GravitySimulator (onlyplanets.gsim), 0 eccentricity, 0 inclination, timestep 65336 seconds. Nothing much has happened after 600 years--wait Pluto's flying off! and Neptune's leaving its orbit!

 

[tony873004]

For simplicity, assume an asymptotic closing speed of ~<100 km/s.

100 km/s is very fast. Encounter speeds are more likely to be around 20 km/s. Slower speeds produce more dramatic results too.

Even objects as large as Jupiter or small brown dwarfs won't do much to the planets' orbits, even it it passes directly through the planetary region unless it passes very close to a planet or to the Sun. Passing close to the Sun would produce the most dramatic changes since it's perturbing our solar system's anchor. This would give it the ability to severly disrupt Neptune's orbit without passing anywhere near Neptune.

 

[WarrenPlatts]

I've let it run for over 12 hours now. Simulation time 120,000 years. Pluto is 1/2 ly away. Neptune's orbit still averages about 30 AU, but it's crazily chaotic, and having effects on Uranus which in turn slightly affects Saturn. The orbital paths of Neptune and Uranus at times slightly overlaps. Eventually, a very close encounter between Neptune and Uranus will cause something bad to happen. Inner solar system OK so far. Earth distance .99 AU, Venus .7 AU.

 

[tony873004]

What value did you use for the twin Sun's semi-major axis?

 

[WarrenPlatts]

An article by David Levy in the Sunday paper said 10 billion miles, so I entered 107.5 AU.

Still looks about the same after 165,000 years. I'm also running my escaped moon of Venus simulation with a time step of only 1024 seconds (17 minutes), so they're sharing processing time. I'm just going to let them crank for about a month and see what happens. . . .

 

[tony873004]

If you're doing long-term simulations, you can use the "Don't Plot" mode to freeze the graphics and the simulations run much faster. It's the P button on the Graphics Options window.

 

[WarrenPlatts]

Interesting. When I pause the solar system model and just run the Venus model with the plot off, it screeeeaams--almost 30 times faster than when the plot is on. But when I run both at once, even with the plot off, it doesn't run nearly as fast because the solar system model hogs about 80% of the processing power as viewed on the task manager.

I wish there was a way to manually allocate processing power. . . .

 

[WarrenPlatts]

Solar Twin simulation year 464997, Neptune getting more erratic diving to within 20 AU of Sun, and strongly interacting with Uranus. Saturn orbit starting to be affected. The twin star seems to be sucking angular momentum from the system.

 

[tony873004]

The twin star would be part of the system, so angular momentum should be conserved. Although it could be transferred from the planets to the twin star. But the twin star is over 1000 times as massive as the planets combined, so it contains the vast majority of the angular momentum in the whole system. Pluto took a little angular momentum with it when it left the system.

Keep in mind, at time step 65K planets that are destined to collide with each other will probably simply pass through each other since each planet moves more than its own diameter per time step. This also makes close encounters between the planets inaccurate. But the results you have so far are pretty much what I would expect, with planets' orbits crossing each other. But their ultimate fates, collisions or ejections, which may take millions of years to play out, will not be accurately simulated at that time step.

 

[WarrenPlatts]

Actually, when I wasn't looking, it must of been around simulation time of around 480,000 years, Neptune was ejected at least 45 km/s! When I looked, it was 4.5 light years away!

Interesting point about collisions. I was wondering about that. Collisions were what I really wanted to study with the Escaped Moon Of Venus (EMOV) scenario. So, the moon I have has twice the mass of Mercury, and a diameter of 6,223 km, and Venus is moving at 35 km/s (quick question: to figure out absolute speed, you add up the squares of all three velocity components and the take the square root of the sum, right?), then a distance of 6,223 km will be covered in 178 seconds, which implies that my time step is too fast by a factor of 5.7. Dang! Which means I have to start over with a time step of 128 seconds. Or do you think maybe it would be even better to go with 64 seconds? Actually, just fiddling with it for a bit here, with the plot off, at 64 s time step they do one revolution in about 6 seconds real time, and it's only 1/3 of moon diameter per time step, guaranteeing a hit if they get close enough. So I'll try that.

Thanks for your input, Tony.

 

[tony873004]

That's too fast for Neptune. That speed is probably due to error from too large of a time step.

The absolute speed is computed for you. It is the one labeled simply Velocity. Thinking about it, it would probably be more correct to call it speed since no direction vector is given.

The next two, Tangental and Radial are the two components of Velocity. Velocity = SQRT (tangental^2 + radial^2).

1/3 of a moon diameter is not a guarantee of a hit if the objects are destined to skim each other, but at least the odds are heavily on your side that you will properly register a collision.

 

[WarrenPlatts]

Wow, our plan worked. In the EMOV simulation a collision occurred around 7,000 years. The very first time I ran EMOV it caused a collision. Everytime after that there was no collision after 10 to 100 thousands of years because I had the time step set too high. Will restart the simulation at timestep = 64 s again to see if the collision can be replicated again.

Let's hope the Earth never loses its Moon!

 

[tony873004]

If Earth ever loses the Moon, a collision is almost inevitable.

Have you tried using the Auto Save feature? This way if the collision happens while you are not watching, you can go back and find it.

Basically, Auto Save (in the File menu) saves your simulation at specified time intervals. You specify the interval, and a maximum number of saves. This is to prevent you from filling your hard drive by accidently asking for 1 save per second on a multi-million year simulation.

It's best to save your original simulation file in a new folder so you don't clutter up your main simulations folder. It will make lots of .gsim files. Although they're only text files, and hence rather small compared to pictures, audio, or video, after you've found the one that contains the collision, you may want to delete the others.

If you come back to find a collision has occurred, just open the simulation saved at the halfway point and see if the collision has occurred yet. If not, pick a new halfway point and keep zeroing in on it.

 

[WarrenPlatts]

Cool, I was going to ask you if there was a way to save the output in order to replay the tape.

Thanks again, Tony