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Two Earth-like planets collide at a (relatively slow) speed of about 1,000 kph. For all questions regarding the size and composition of these planets, just think about Earth - and these two planets are moving towards each other at the same speed.

1) First, they would begin to rip each other apart due to roche limits.

2) Then the two planets (what remained of them, that hadnt been ripped apart) would connect with each other.

3) Eventually, they would merge together and form one larger planet.

My question is, roughly what kind of time span would there be between stages 2 and 3? Stage 2 being the planets connecting with each other, and Stage 3 being one single spherical planet. So I want to know roughly how quickly gravity would act upon these two planets whilst it is forming them into one (mostly) spherical planet.

Are we talking hours/days or are we talking years/centuries?

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    $\begingroup$ I would be curious to understand how you would go and arrange for two planets to collide at such a ridiculously low speed. Very curious. I just don't see how this could be possible. (Hint: when the planets are 100,000 km apart they are well within each other's gravitational field. What speed does an object get falling in Earth's gravitational field from 100,000 km?) $\endgroup$ – AlexP Jul 29 at 15:09
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    $\begingroup$ technically the moment they collide they are one large planet. There's a long step in the middle, where the Earth is a giant ball of magma and debris circling the sun for a few million years. $\endgroup$ – Trevor Jul 29 at 15:09
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    $\begingroup$ For reference purposes a fall to an Earth with no atmosphere would take about 4,000 meters (4km) to reach 1000 kph. It's only the air resistance that stops this in real life and in your scenario air resistance will be irrelevant. $\endgroup$ – StephenG Jul 29 at 16:55
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    $\begingroup$ Unless you've got alien engineers slowly lowering one planet onto the other, the minimum impact velocity for two Earth-like planets colliding is around 60,000 km/h. $\endgroup$ – Mark Jul 30 at 2:30
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    $\begingroup$ Hey Mark - can you tell us how you came to that conclusion? Not contesting it, was wondering how you figured that out for my own curiosity. $\endgroup$ – cyber101 Jul 30 at 5:45
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We're talking hours to days.

A good deal of work has been done on protoplanet-protoplanet collisions, mainly focused on testing the Giant Impact Hypothesis for the formation of the Moon. A number of fluid simulations (many smoothed-particle hydrodynamics) have been performed, for varying angles of attack and initial relative velocities (see e.g. Canup 2012, Eiland et al. 2013).

The takeaway from those simulations is that the planets initially coalesce within half a day to a day. However, the resulting body isn't round; it's somewhat elliptical, even a bit pointy at the ends. Some models have tails of matter (typically one or two) attached at the ends, which, though tenuous, may form another body, i.e. the Moon. By the end of about 24 hours, there is a clear central body surrounded by this excess material, but it may take up to a month for it to regain its spherical shape - a key characteristic of a planet.

Other things to consider:

  • It may take time for the interior of the planet to become differentiated, i.e. for it to take on a traditional planet-like structure. Even after coalescence, the cores may still be separated.
  • Glancing, indirect collisions tend to produce more ellipsoidal shapes than direct collisions, even if there's a merger.
  • There will still be debris orbiting for quite some time after the merger - again, perhaps weeks or months.
  • The final body will remain quite hot for some time, with surface temperatures of perhaps up to 6000 K in the day or so immediately following the collision.
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    $\begingroup$ Thank you for the answer - this is fascinating - I was imagining such a large collision to take longer, but to have two planets merge into one within a matter of hours is incredible - it would be no-doubt awesome to see such an event. $\endgroup$ – Jimmery Jul 30 at 10:13
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    $\begingroup$ @Jimmery You'd be struck blind. The energies involved... in 1 hour the sun puts out 10^30 J. The collision of two Earths has about 10^33 J of kinetic energy. That kind of energy is going to emit some really, really bright light. $\endgroup$ – Yakk Jul 30 at 14:55
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    $\begingroup$ @Yakk Better pack some really good sun-glasses then ;) $\endgroup$ – IMSoP Jul 30 at 15:06
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Please check out this link in case you find it interesting. It's about how the moon formed from a similar impact.

In the link above, it is assumed that there was an explosive collision (moderate at celestial standards) between Earth and Theia at an oblique angle. Despite such a collision, it is thought that it took surprisingly little time to form the moon, whereas it took around 0.1 billion years for Earth to form. A corresponding collision between your two planets would likely take longer, as the creation of the Earth itself (normally) took hundreds of millions of years.

A point about Roche limits: Roche limit takes effect 2.5 radii away from the larger planet. If these planets are equal in mass, they would merge into a central mass between them. This would basically be the same as forming a brand new planet from scratch.

Edit: I forgot to give you an actual answer - sorry lol. With little-to-no actual science to back this up (we don't know much about the formation of planets) I'm going to say between 0.5-1 billion Earth years IF both planets completely shatter into debris and then coalesce to form another planet. If they merge perfectly the way you described, could take 100,000 years, as the commenters suggested. That's assuming that these two planets don't just turn into an asteroid belt or something, and that nothing else gets in the way. I'm also not accounting for bombardment of debris from the collision of these two planets, or the possibility of smaller moons forming.

I'd also like to point out that the probability of 2 celestial objects 'only' crashing into each other at 1000 km/h wouldn't be much of a collision. Is this being done deliberately? If not, incredible luck.

Helpful links:

https://en.wikipedia.org/wiki/History_of_Earth#Solar_System_formation http://abyss.uoregon.edu/~js/glossary/roche_limit.html

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    $\begingroup$ It's not 0.1 billion years to form the Moon, it's 0.1 billion years to produce Earth-Theia collision. Moon had formed astonishingly fast after the collision: "The material in orbits around the Earth quickly coalesced into the Moon (possibly within less than a month, but in no more than a century)" $\endgroup$ – Alexander Jul 29 at 16:39
  • $\begingroup$ After such a collision the result will certainly be hot enough to melt rock. How long that takes to cool enough to form a rocky surface cool enough for liquid water is above my pay grade. But it will certainly be more than the time scale the OP suggested. Maybe 100,000 years is starting to get there. $\endgroup$ – puppetsock Jul 29 at 17:49
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    $\begingroup$ @cyber101 Thanks for this answer - the idea of two planets ripping apart and forming a new one in the middle of them is really awe inspiring! $\endgroup$ – Jimmery Jul 30 at 10:16

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