When two planets collide what is their terminal velocity?

[pavelcherepan]

So was Theia a trojan planet before hand or not IYO?

 

Based on what I read it most certainly was.

[Robittybob1]

 

Based on what I read it most certainly was.

So where would it get that extra velocity from? Could the GIT be made to work if the only extra speed Theia had was due to the gravitational attraction of the Earth? If it is already co-orbiting with the Earth it average distance to the Sun is the Earth radius so it shouldn't be falling toward the sun as comets and Near Earth Objects do.

If it caught up with the Earth from behind, as the Earth is orbiting the Sun, and the Earth pulled it in faster it could hit the Earth off center and flick matter during impact in the right direction of rotation to form the Moon.

Edited April 4, 2015 by Robittybob1

[pavelcherepan]

So where would it get that extra velocity from? Could the GIT be made to work if the only extra speed Theia had was due to the gravitational attraction of the Earth? If it is already co-orbiting with the Earth it average distance to the Sun is the Earth radius so it shouldn't be falling toward the sun as comets and Near Earth Objects do.

If it caught up with the Earth from behind, as the Earth is orbiting the Sun, and the Earth pulled it in faster it could hit the Earth off center and flick matter during impact in the right direction of rotation.

 

It's been assumed that Theia's orbit has been perturbed by interaction with Venus and Jupiter (which had much more eccentric orbit back then).

[Robittybob1]

 

It's been assumed that Theia's orbit has been perturbed by interaction with Venus and Jupiter (which had much more eccentric orbit back then).

Venus maybe.

[Robittybob1]

So was Theia a trojan planet before hand or not IYO?

So does it get enough velocity?

[pavelcherepan]

Enough for what?

[Robittybob1]

Enough for what?

To get a Giant Impact collision of course. I had already calculated the speed an object hit earth would get from infinity (hope I did it right) but how did that speed compare to a planet that just coming in from the L3 position (furthest point)?

[pavelcherepan]

To get a Giant Impact collision of course. I had already calculated the speed an object hit earth would get from infinity (hope I did it right) but how did that speed compare to a planet that just coming in from the L3 position (furthest point)?

 

I really have no idea what you're talking about. There's no specific limit of velocity for the Giant Impact and the number of [latex]v_{\infty} = 4\, km/s[/latex] was taken from the simulation of GI so there's no need to prove it recursively.

 

What does L3 Lagrangian point have to do with it? Anyway, if a planet is coming from L3 for some reason and if [latex]v_{\infty}[/latex] is still 4km/s then impact speed will be exactly the same based on this:

 

[latex] v^2 = v_{esc}^2 + v_\infty^2 [/latex]

 

[latex]v_{esc}[/latex] and [latex]v_{\infty}[/latex] will be the same and so the impact velocity will be exactly the same.

 

But then again, L3 point in Sun-Earth system is widely unstable and no sizable body could've formed there.

Edited April 5, 2015 by pavelcherepan

[Robittybob1]

 

I really have no idea what you're talking about. There's no specific limit of velocity for the Giant Impact and the number of [latex]v_{\infty} = 4\, km/s[/latex] was taken from the simulation of GI so there's no need to prove that it will be enough.

 

What does L3 Lagrangian point have to do with it? Anyway, if a planet is coming from L3 for some reason and if [latex]v_{\infty}[/latex] is still 4km/s then impact speed will be exactly the same based on this:

 

[latex] v^2 = v_{esc}^2 + v_\infty^2 [/latex]

 

[latex]v_{esc}[/latex] and [latex]v_{\infty}[/latex] will be the same and so the impact velocity will be exactly the same.

Well you agreed it was a trojan planet, so there are limited places it could have come from if that was the case, and none of them have anything to do with "infinity". The L3 is a postion co-orbiting with the Earth on opposites sides of the Sun (300 million km). OK it is a long way around the orbit but if it was perturbed by Venus and if it got out of the balanced situation it could begin a journey being pulled toward the Earth, slowly at first but after sometime it would impact.

I don't believe the impact speed is the same for all starting positions especial from a Lagrangian point.

http://en.wikipedia.org/wiki/Lagrangian_point

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

Well you agreed it was a trojan planet, so there are limited places it could have come from it that was the case, and none of them have anything to do with infinity. L3 is a postion co-orbiting with the Earth on opposites sides of the Sun. OK it is a long way around the orbit but if it was perturbed by Venus and if it got out of the balanced situation it could begin being pulled toward the Earth, slowly at first but after sometime it would impact.

I don't believe the impact speed is the same for all starting positions.

 

Trojan planets, asteroids etc can only form in L4 and L5 for Sun-Earth system, all other L-points are unstable for various reasons. And the term "Trojans" only refers to objects at L4 and L5 points.

 

 

 

It is common to find objects at or orbiting the L₄ and L₅ points of natural orbital systems. These are commonly called "trojans";

 

And here's why there can't be anything in L3:

 

 

 

Sun–Earth L₃ was a popular place to put a "Counter-Earth" in pulp science fiction and comic books. Once space-based observation became possible via satellites^[14] and probes, it was shown to hold no such object. The Sun–Earth L₃ is unstable and could not contain an object, large or small, for very long. This is because the gravitational forces of the other planets are stronger than that of Earth (Venus, for example, comes within 0.3 AU of this L₃ every 20 months).

 

OK?

 

 

 

I don't believe the impact speed is the same for all starting positions.

 

What you believe is irrelevant. Probably you don't understand what hyperbolic trajectory is and what velocity at infinity is. So please read up on the relevant entry in Wikipedia or in the following link <Basics of Space Flight>.

[Robittybob1]

 

Trojan planets, asteroids etc can only form in L4 and L5 for Sun-Earth system, all other L-points are unstable for various reasons. And the term "Trojans" only refers to objects at L4 and L5 points.

 

 

And here's why there can't be anything in L3:

 

 

OK?

 

Doesn't that prove my point for we are saying soon after forming at the L3 it became unstable and later impacted the Earth.

Once I do the calculation you will see (and believe) that a planet coming from L3 will impact slower than from infinity.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

Doesn't that prove my point for we are saying soon after forming at the L3 it became unstable and later impacted the Earth.

It most certainly doesn't. The L3 point is unstable and there's not enough time for a planet the size of Mars to form before it's kicked out of the orbit.

 

Did you even read the sources I quoted?

Edited April 5, 2015 by pavelcherepan

[Robittybob1]

It most certainly doesn't. The L3 point is unstable and there's not enough time for a planet the size of Mars to form before it's kicked out of the orbit.

 

Did you even read the sources I quoted?

So where do you get that time limit from?

I might have read them had you not been so condescending. How long do you think it would take to pull a planet around from the Earth's L3 position?

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

So where do you get that time limit from?

I might have read them had you not been so condescending.

 

I wasn't being condescending. I said that what you believe matters not if it disagrees with physics and mind you, we're not even in Speculations, we're in Classical Physics forums.

 

If you think otherwise please find any study that proves that Theia could've formed in L3 or any physics-based proof for that and I will happily discuss that with you.

 

So where do you get that time limit from?

 

Estimation. At present Venus creates major disturbance at L3 every 20'ish months. Back during the formation of Solar system Venus would be smaller, but the Earth would be smaller too and also there's be plenty of various planetesimals wondering around that would disturb the L3 objects too. I can't estimate how long exactly the object can stay stable in that point at that stage but even if we take the best-case scenario and say that it could stay there for a 100,000 years (which is enormous overestimation), but formation of a Mars-sized planet takes in excess of ten millions years which is two orders of magnitude longer that our gross overestimate for L3 stability.

 

Maybe something did form there, but definitely not Theia.

Edited April 5, 2015 by pavelcherepan

[Robittybob1]

 

I wasn't being condescending. I said that what you believe matters not if it disagrees with physics and mind you, we're not even in Speculations, we're in Classical Physics forums.

 

If you think otherwise please find any study that proves that Theia could've formed in L3 or any physics-based proof for that and I will happily discuss that with you.

 

 

Estimation. At present Venus creates major disturbance at L3 every 20'ish months. Back during the formation of Solar system Venus would be smaller, but the Earth would be smaller too and also there's be plenty of various planetesimals wondering around that would disturb the L3 objects too. I can't estimate how long exactly the object can stay stable in that point at that stage but even if we take the best-case scenario and say that it could stay there for a 100,000 years (which is enormous overestimation), but formation of a Mars-sized planet takes in excess of ten millions years which is two orders of magnitude longer that our gross overestimate for L3 stability.

 

Maybe something did form there, but definitely not Theia.

I sense a bit of guessing here. I can't see a planet forming at L4 or L5. I know objects get lodged there but do they form there? There is more chance of a planet forming at L3 even if it is ultimately unstable. 100,000 years maybe enough time. I'd like to see some figures.

 

Even so if a planet did form at L4 or L5 and became unstable and drawn to the Earth it would not impact at a speed similar to an object coming in from infinity. I read about that yesterday that it was easier to send a spacecraft to a trojan at the L4 or L5 position, so presumably to reverse applies if an object comes in from the same location. Earth has a trojan at the L4 Lagrangian Point.

http://en.wikipedia.org/wiki/2010_TK7

 

 

Accessibility from Earth[edit]

Position of 2010 TK7 relative to Earth in 2011

Because Earth trojans share Earth's orbit and have little gravity of their own, it can sometimes be less energetically costly to reach them than the Moon, even though they are dozens of times more distant. However, 2010 TK7 is not an energetically attractive target for a space mission because of its orbital inclination:[8] It moves so far above and below Earth's orbit that the required change in velocity for a spacecraft to match its trajectory coming from Earth's would be 9.4 km/s, whereas some other near-Earth asteroids require less than 4 km/s.[4]

 

OK let's put some figures on our hunches shall we?

http://en.wikipedia.org/wiki/Nebular_hypothesis

 

The protoplanetary disk is an accretion disk that feeds the central star. Initially very hot, the disk later cools in what is known as the T tauri star stage; here, formation of small dust grains made of rocks and ice is possible. The grains eventually may coagulate into kilometer-sized planetesimals. If the disk is massive enough, the runaway accretions begin, resulting in the rapid—100,000 to 300,000 years—formation of Moon- to Mars-sized planetary embryos. Near the star, the planetary embryos go through a stage of violent mergers, producing a few terrestrial planets.

 

This is the bit that made me feel anti -

 

Probably you don't understand what hyperbolic trajectory is and what velocity at infinity is. So please read up on the relevant entry in Wikipedia or in the following link <Basics of Space Flight>.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

OK let's put some figures on our hunches shall we?

 

I've done that before and I'm happy to do so now. I have yet to see any figures from you, though.

 

From the paper <Terrestrial planet formation>

 

Page 9:

 

At 1 AU from the Sun, assuming [latex]\Sigma_{solid} \sim 4\, g/cm^2[/latex] when oligarchic growth ceased, gives [latex]t_{late} \sim 2 \times 10^8 [/latex]

years.

 

Page 17:

 

The final stage of terrestrial-planet formation involved a few tens to a few hundred embryos moving on crossing orbits, and lasted [latex]\sim 10^8[/latex] years according to data from radioactive isotopes.

 

And these describe the final stages of formation after planetesimals have been formed so my initial estimate was even off by an order of magnitude. In the same paper you can read up how stable were orbits in the system based on N-body simulation. 100,000 years in L3 would not happen and even if it did it's 2-3 orders of magnitude smaller than required for Mars-sized body.

 

 

 

Even so if a planet did form at L4 or L5 and became unstable and drawn to the Earth it would not impact at a speed similar to an object coming in from infinity.

 

So you still haven't read the links I gave you on orbital mechanics. Really there's no point discussing it unless you understand what [latex]v_{\infty}[/latex] refers to.

 

Here is a quote from NASA site for Theia formation:

 

 

 

"Their computer models show that Theia could have grown large enough to produce the Moon if it formed in the L4 or L5 regions, where the balance of forces allowed enough material to accumulate," says Kaiser. "Later, Theia would have been nudged out of L4 or L5 by the increasing gravity of other developing planets like Venus and sent on a collision course with Earth."

Edited April 5, 2015 by pavelcherepan

[Robittybob1]

Show me a reference that says anything about the L3 lagrangian point please. All those other references seem so far off the topic.

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/lagpt.html

 

The Lagrange points L1, L2 and L3 would not appear to be so useful because they are unstable equilibrium points. Like balancing a pencil on its point, keeping a satellite there is theoretically possible, but any perturbing influence will drive it out of equilibrium. However, in practice these Lagrange points have proven to be very useful indeed since a spacecraft can be made to execute a small orbit about one of these Lagrange points with a very small expenditure of energy. They have provided useful places to "park" a spacecraft for observations. These orbits around L1 and L2 are often called "halo orbits". L3 is on the opposite side of the Earth from the Moon, so is not so easy to use.

 

Still doesn't say it is impossible.

Obviously a spacecraft parked at L3 becomes very difficult to communicate with having the Sun in the way.

Some references of the instability on the L3 position hint it is due to the influence of the Moon on the Earth -Moon system. So what about when the Moon wasn't there. Was that a period of increased stability?

 

Also in the planet building scenarios I work with the terrestrial planets formed prior to the Sun going main sequence hence the physical size of the protosun would be considerably larger for a while. I'd say that increased the stability too.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

Show me a reference that says anything about the L3 lagrangian point please. All those other references seem so far off the topic.

 

Robbitybob1, I would show you references to L3 if there were any models that presumed that Theia could form there, but there are none. Any why in the world do I have to provide references to support your position? Shouldn't you do it?

 

I'd really love to see one or all of the following from you:

 

1) Link or quote from any reference that suggests that Theia could've formed at L3 Lagrangian point.

2) Link or quote that suggests that 10⁵ years is enough to form a Mars-sized planet

3) Calculation that proves that object coming from L3 would impact proto-Earth at higher velocity than object coming from L4 or L5 with same initial velocity.

 

Unless I see any of those, what you're doing here is soapboxing and as long as I keep providing you with proper evidence and you just keep saying random stuff without any sort of proof there's nothing to discuss here, is it? Ciao!

[Robittybob1]

 

Robbitybob1, I would show you references to L3 if there were any models that presumed that Theia could form there, but there are none. Any why in the world do I have to provide references to support your position? Shouldn't you do it?

 

I'd really love to see one or all of the following from you:

 

1) Link or quote from any reference that suggests that Theia could've formed at L3 Lagrangian point.

2) Link or quote that suggests that 10⁵ years is enough to form a Mars-sized planet

3) Calculation that proves that object coming from L3 would impact proto-Earth at higher velocity than object coming from L4 or L5 with same initial velocity.

 

Unless I see any of those, what you're doing here is soapboxing and as long as I keep providing you with proper evidence and you just keep saying random stuff without any sort of proof there's nothing to discuss here, is it? Ciao!

1. Nothing says it couldn't

2. I have already given you a reference to 2 above. http://www.scienceforums.net/topic/88421-when-two-planets-collide-what-is-their-terminal-velocity/page-2#entry861986

3. I will do 3 when I get back to the office where I have a sheet set up with the calculations. Initial speed in these cases approximates zero (just off balance and that is all). I am very surprised that that is not just standard physics to you.

 

So far you have just linked to papers that don't even mention Lagrangian Points so what are you talking about.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

1. Nothing says it couldn't

2. I have already given you a reference to 2 above. http://www.scienceforums.net/topic/88421-when-two-planets-collide-what-is-their-terminal-velocity/page-2#entry861986

3. I will do 3 when I get back to the office where I have a sheet set up with the calculations. Initial speed in these cases approximates zero (just off balance and that is all). I am very surprised that that is not just standard physics to you.

 

1. Is a logical fallacy. The fact that nothing says it couldn't doesn't mean it could.

2. I see no proof here at all. Just same logical fallacies as above.

3. I'm waiting.

 

 

So far you have just linked to papers that don't even mention Lagrangian Points so what are you talking about.

 

Wrong. What about quote from post #41? Did you even read it?

 

 

 

"Their computer models show that Theia could have grown large enough to produce the Moon if it formed in the L4 or L5 regions, where the balance of forces allowed enough material to accumulate," says Kaiser. "Later, Theia would have been nudged out of L4 or L5 by the increasing gravity of other developing planets like Venus and sent on a collision course with Earth."

[Robittybob1]

 

1. Is a logical fallacy. The fact that nothing says it couldn't doesn't mean it could.

2. I see no proof here at all. Just same logical fallacies as above.

3. I'm waiting.

 

 

 

Wrong. What about quote from post #41? Did you even read it?

 

Of course I read that, and I found it interesting but I noted they didn't say why or if they hadn't considered L3, except of course logically if they did send a probe to L3 they can't communicate with it, as it is behind the Sun, and it is also a long way out to there, so it is technically difficult, so I don't blame them checking out the closer regions first.

 

Call 1 a "logical fallacy" but it is also a fact. If there is no reason to discount it why discount it. They are looking at L4 and L5 points because they are possible, but still without proof that Theia came from there either.

It is the Easter break here so it will be a couple of days before I'm back in my office.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

Call 1 a "logical fallacy" but it is also a fact.

 

Argument from ignorance (argumentum ad ignorantiam) - " assuming that a claim is true because it has not been or cannot be proven false, or vice versa."

 

and you should look at the following too:

 

onus probandi incumbit ei qui dicit, non ei qui negat - "the burden of proof is on the person who makes the claim, not on the person who denies"

 

 

 

If there is no reason to discount it why discount it. They are looking at L4 and L5 points because they are possible, but still without proof that Theia came from there either.

 

No reason to discount it but no reason to accept it either. And in order to be accepted it should come with some proof, which you have none of.

Edited April 5, 2015 by pavelcherepan

[Robittybob1]

 

Argument from ignorance (argumentum ad ignorantiam) - " assuming that a claim is true because it has not been or cannot be proven false, or vice versa."

 

and you should look at the following too:

 

onus probandi incumbit ei qui dicit, non ei qui negat - "the burden of proof is on the person who makes the claim, not on the person who denies"

 

 

No reason to discount it but no reason to accept it either. And in order to be accepted it should come with some proof, which you have none of.

I felt it was you who made the claim first, I'm sure I have always left my statements as possibilities. I have never claimed it was true. The "fact" being that it is possible.

Like if I say it is possible that Theia formed at L3 and you say that is "impossible". It is you making the claim not me.

That is why I have asked you prove that it is impossible.

Edited April 5, 2015 by Robittybob1

[pavelcherepan]

Like if I say it is possible that Theia formed at L3 and you say that is "impossible". It is you making the claim not me.

That is why I have asked you prove that it is impossible.

 

I have indeed made such claim, you got me there, but then again, I made a claim and provided evidence that it is highly unlikely in posts #35, 39 and 41.

 

 

 

I can't see a planet forming at L4 or L5. I know objects get lodged there but do they form there? There is more chance of a planet forming at L3 even if it is ultimately unstable.

 

Where's the proof?

 

 

 

100,000 years maybe enough time.

 

Where's the proof?

 

 

 

Even so if a planet did form at L4 or L5 and became unstable and drawn to the Earth it would not impact at a speed similar to an object coming in from infinity.

 

Proof?

[Robittybob1]

 

I have indeed made such claim, you got me there, but then again, I made a claim and provided evidence that it is highly unlikely in posts #35, 39 and 41.

 

 

Where's the proof?

 

 

Where's the proof?

 

 

Proof?

unlikely - no all you showed it was unstable. Look at it this way if Theia was at L3 and Earth opposite the Sun both planets are at the L3 Lagrangian point of the other. Earth formed even though it was at the L3 of the other planet, so either way it is possible, but unstable but even then how long would it take to come around behind the Earth it is a total of 942500 km around one half of the orbit

and if it started off at 1 km/year it will still take a while to impact even if in the final stages it is moving at 7 km/sec.

So it is building up mass and speed on its journey too. No one says the Earth and Theia were fully formed planets at the time of collision.