Catching a rogue planet

[jnb]

If rogue planets are as common as some people suggest, and some people suggest there may be more rogue planets than normal planets. Then what is the chance of a rogue planet passing through the solar system? If a rogue planet did pass through the solar system what would be the chance that it would be captured and enter a stable orbit and if a rogue planet had done that in the past then would we be able to tell that it had been a rogue planet in the past?

A question inspired by the observation that Uranus appears to have less internal heat than we would expect for its age.

[JulianO]

Rogue, or free floating planets are probably quite common. The way planets interact as they form, some of them will get ejected and cast loose.

The chance of one coming through our solar system is probably very very small. Mostly because space is very big, and planets are very tiny in relation to the separation. So the chance of a free planet encountering another system is pretty unlikely.

Also for a planet to be ejected from the solar system is has to be going faster than about 42 km/s, so at this speed it is unlikely to be caught by another system maybe just deflected a bit.

So being captured is pretty hard, it has to land in the right place,  and then would need some special interactions with Jupiter and the Sun to slow it down enough. Not impossible, but far more likely it was made in place.

[ronin]

If I recall the probability of 2 stars colliding is so small that it means that so far the universe has not been around long enough for the chance of it occuring once is still far too small. As that is 2 big stars in the universe then 1 planet ambling into or through ours is even smaller. Even when Andromeda and the Milky Way "collide" it is said no 2 stars will collide.

I suspect they have had to redetermine the number of rogue planets and as a finger in the air guees I would say 1 planet per star is a better guess. Guess based on most (all) stars will have a planetary system, and a solar system will eject what it needs to in order to maintain stability. It is said that there was likely a planet ejected from out system early on, then Jupiter and Saturn took up more stable orbits further out. We have 4 gas giants and presently seem stable. May change in a few million years I suppose.

problem is that we only have a sample of 1 to base ideas on - our solar system. And so far many ideas of planetary formation and systems have had to change in recent times.

I believe the reason they say there must be lots of rogue planets is that one (only one) observation of a star was made when the brightness dropped, this was in line with a planet passing in front of the star but not part of the star system and the chance of that occuring are very close to zero. So the idea that if correct there has to be lots of unattached planets out there.

[jnb]

Though while space is very big, it is also very old.

While a planet would need to achieve escape velocity from a star to escape (tautological and obvious) because each star will have its own proper motion that does not mean that it will pass through another star system above its escape velocity. For example the solar system is moving as a whole at about 20km s^-1 if a rogue planet were to come up behind us at 42 km s^-1 then it would be below the solar system's escape velocity.

A few back of envelope calculations

If stars are spaced at about 5ly then they are about 5 x 10¹³ km apart

If rogue planets move at that escape velocity that is about 10⁹ km yr^-1

So a rogue planet moves 5 ly in about 50000 years

If a star system is about 30AU across and spaced at about 5ly then each star system is an area of about 5 X 10¹⁹ km² in a cube with sides of about 10²⁷ km²

So if there is an average of one rogue planet per star then every 50 000 years there would be about a 10^-7 chance of a rogue planet passing through a planetary system

Or on average you would have to wait about 5 x 10¹¹ years to see a rogue pass through any one star system compared to about 5 x 10⁹ years as the age of the solar system.

So each star system would have a 1% chance of a "Nbiru" style event in its life but with the number of stars in the galaxy that still a high number

The observation about collisions being rare is true but that refers to a direct collision whereas this just needs gravtiational interaction.

NB I am not suggesting that Uranus was a rogue planet that's just the train of through that led to this.

[Knight of Clear Skies]

I don't think your maths is correct I'm afraid jnb, as you need to consider volume rather than area. That lengthens the odds considerably.

The chance of a rogue planet wandering through the inner solar system are extremely low, even over its lifetime. However, they would have been higher early in its history, when it was part of a dense open cluster. One possible explanation for the odd orbit of Sedna is that it is a captured body. There are also thought to be large numbers of interstellar comets, much larger than the population of rogue planets. To date we haven't observed any on a highly hyperbolic orbit that definitely came from beyond the Oort cloud, but there are a couple of odd ones that could have been captured. The jury is out.

It seems that collisions between stars are not that uncommon in open and globular clusters, they are known as Blue Stragglers. Outside these environments collisions are extremely rare - I think I read somewhere that the expected number in a Milky Way/Andromeda merger is about one, but I can't find a cite for that now. 

[JulianO]

I think most eject planets will be very small. We've only seen the big ones, because they are the only ones we stand a chance of detecting.

Simulations of planetary formation show a lot of stuff getting ejected or thrown into the sun. Similarly Jupiter has cleared out large numbers of asteroids, sending them into the sun or outer space. 

I think I'm right that you need a 3 body interaction to eject something typically, and I think the same would be true of capture. So the planet would have to interact with Jupiter or similar to be captured into a stable orbit around the sun.

Taking 30AU encompasses the outer planets, and a small object passing beyond the orbit of Uranus would be pretty hard to spot, and fairly unlikely to interact. A volume of a sphere of 5 AU diameter might be better for our own system, as that brings it within the range of Jupiter.

[jnb]

I don't think your maths is correct I'm afraid jnb, as you need to consider volume rather than area. That lengthens the odds considerably.

The chance of a rogue planet wandering through the inner solar system are extremely low, even over its lifetime. However, they would have been higher early in its history, when it was part of a dense open cluster. One possible explanation for the odd orbit of Sedna is that it is a captured body. There are also thought to be large numbers of interstellar comets, much larger than the population of rogue planets. To date we haven't observed any on a highly hyperbolic orbit that definitely came from beyond the Oort cloud, but there are a couple of odd ones that could have been captured. The jury is out.

It seems that collisions between stars are not that uncommon in open and globular clusters, they are known as Blue Stragglers. Outside these environments collisions are extremely rare - I think I read somewhere that the expected number in a Milky Way/Andromeda merger is about one, but I can't find a cite for that now. 

That calculation has considered volume but expressed as ratios of area X time, the time being the time a rogue takes to move the typical distance between stars. A quick dimensional analysis shows that will spit out a time which is the average time between the rogues crossing a given star system.

[Cath]

I suppose it's possible that a planet was flung out from our own system a couple of billion years ago, not totally but rather onto a very large elliptical orbit, enough for it reach the Oort cloud with ease. In which case it could be making it's way back towards the inner system as we speak. Not sure what the time scale would be for such an event.

edit: Thinking about it now, it would have made it's way back long before now.

[Knight of Clear Skies]

That calculation has considered volume but expressed as ratios of area X time, the time being the time a rogue takes to move the typical distance between stars. A quick dimensional analysis shows that will spit out a time which is the average time between the rogues crossing a given star system.

Sorry, I misread that.

[rwg]

While a planet would need to achieve escape velocity from a star to escape (tautological and obvious) because each star will have its own proper motion that does not mean that it will pass through another star system above its escape velocity. For example the solar system is moving as a whole at about 20km s^-1 if a rogue planet were to come up behind us at 42 km s^-1 then it would be below the solar system's escape velocity.

What you're forgetting is that while the relative speed may be below escape velocity when the planet is far outside the solar system, as it falls in towards the star it will speed up and always be above escape velocity. You need an interaction with a 3rd massive body (ie Jupiter, Saturn, etc) while the planet is within the star's gravity well for a capture to happen.

Robin

[jnb]

What you're forgetting is that while the relative speed may be below escape velocity when the planet is far outside the solar system, as it falls in towards the star it will speed up and always be above escape velocity. You need an interaction with a 3rd massive body (ie Jupiter, Saturn, etc) while the planet is within the star's gravity well for a capture to happen.

Robin

That wouldn't have any net effect. The acceleration of a rogue falling in toward a star would on average be exactly matched by the deceleration as it left it's original system. e.g. we would not be considering a rogue approaching a star and accelerating from 40km s^-1 , instead it would have left its original system at 40km s^-1 decelerating due to gravity of the original system so it's speed relative to that system might only be 30km s^-1. But different proper motions means that speed might only be 10km s^-1 compared to another star so the acceleration would not be sufficient to get back to escape velocity.

What I haven't considered at all is how likely it is that such an object might be captured due to any required three body interaction.

[rwg]

That wouldn't have any net effect. The acceleration of a rogue falling in toward a star would on average be exactly matched by the deceleration as it left it's original system. e.g. we would not be considering a rogue approaching a star and accelerating from 40km s^-1 , instead it would have left its original system at 40km s^-1 decelerating due to gravity of the original system so it's speed relative to that system might only be 30km s^-1. But different proper motions means that speed might only be 10km s^-1 compared to another star so the acceleration would not be sufficient to get back to escape velocity.

No, sorry, that's not true, the acceleration into the second system is very important, and it's actually the initial system you can ignore. Consider it this way...

• Assume the rogue planet has escaped and is floating in deep space with some velocity.
• Now think of everything in the frame of reference of the second solar system (the one that the planet encounters). We're well below relativistic speeds, so no problem in working in that frame of reference
• In that frame of reference, long before the encounter, the rogue planet must have a velocity *towards* the second solar system, otherwise it won't encounter it at all
• Now, escape velocity is just the velocity where kinetic energy is higher than gravitational binding energy - when there's enough kinetic energy to escape the gravity well.
• The planet starts well outside the gravity well, with some velocity towards the solar system, so it has some kinetic energy when distant from the target solar system
• As it falls into the gravity well of the target system its kinetic energy will increase (gravitational energy converted to kinetic - no loss of energy)
• Since the kinetic energy started as >0 when distant and we have added the lost gravitational energy to it, the rogue planet always has kinetic energy higher than the gravitational binding energy during its encounter with the second solar system - by the law of conservation of energy it always has enough energy to get back out to the point it started from with the same kinetic energy it had there

So, the speed of passage of a rogue planet through a solar system will always be above the escape velocity for that solar system (unless there is a further interaction with a 3rd massive body in the system)

cheers,

Robin

[jnb]

Yes you're right - my mistake!

Though that doesn't change the chance of encountering a rogue merely the chance of capturing a rogue, a calculation which is beyond the size of any backs of envelopes I have to hand.

[rwg]

How about considering the chance of the rogue planet encountering the gravity well of a gas giant when 'in system'? - This would give a higher bound as not all encounters with a gas giant would lead to captures, but all captures would require interaction with a gas giant.

For instance, work out the cross sectional area of the zone where Jupiter's gravity dominates the Sun's gravity and use that as your interaction target...

cheers,

Robin

[jnb]

Good idea.

So GM(s)m r(j)^-1 = GM(j)m r( c)^-1

r(j) - jupiter orbit radius (about 5AU)

M(s) ~ 2 x 10³⁰Kg

M(j) ~ 2 x 10²⁷Kg

r( c) - Distance from Jupiter at which Jupiter's gravitational potential dominates the suns gravitational potential

r( c) = r(jupiter) x M(j) / M(s) ~ 0.005AU

That doesn't seem right, an object would have to be less than 1 million km from Jupiter for Jupiter to have a signifcant effect?

If those numbers are right then the chance of capturing an object passing through the solar system is about 10^-8

Again that seems suspiciously low, consider how many Oort cloud comets are captured into periodic orbits.

[rwg]

Ah, but if you look at the point where the force of gravity due to the sun is the same as due to Jupiter (distance to Lagrangian point L1), you have to use R^2, not R, so it comes out as 0.07AU.

Jupiter will have an effect beyond this radius, it just becomes less, so therefore the chance of it being just the right effect to capture drops off. Lots of unknown constants of proportionality in this approach that a) we have no idea how to calculate and b ) could be large...

cheers,

Robin