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When massive, spherical celestial objects collide, how long does it take for the objects to coalesce into a new, larger, spherical entity under the influence of gravity?

Examples of the above:-

  • Collision of 2 stars

  • Collision of 2 rogue planets

Or one a bit closer to home... the Giant Impact Hypothesis i.e. how long did it take, after the collision of Theia and 'Pre-Earth', for the current planet Earth (in terms of size, not atmosphere, water etc.) to form?

Mathematical reasoning, external sources etc. are welcomed.

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  • $\begingroup$ Why are you interested in it? Simply, to know what you are thinking. $\endgroup$ – Immortal Player Nov 19 '14 at 14:46
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Neutron stars are a special case.

When the neutron stars collide a black hole is formed within milliseconds.

A gamma ray burst of less than 2 seconds is expected to be observable from a great distant, as well as gravitational waves.

About 1% of a solar mass is expected to be ejected and include heavy elements.

On June 3rd 2013 the Swift gamma ray telescope detected a candidate for such a collision.

See Astrophysics: Radioactive glow as a smoking gun and references cited therein for more information.

For other objects that are massive enough to acheive hydrostatic equilibrium, in other words at least a planet as opposed to a dwarf planet, equilibrium would be restored on a dynamic timescale:

$T = \sqrt{\frac{R^3}{GM}}$

See also: http://www.astro.umd.edu/~miller/teaching/astr320/lecture17.pdf

In the below reference, collision of two Jupiter size planets under various scenerios, for example at a velocity of 20 km/s and an offset from head-on collison of 1.5 Jupiter radii is simulated. After initial contact, the planets more or less bounce off each other, and collide for a second time after about 55 hours. "Approximately 15 hours later the planets merge, and have more or less stabilized after an additional 50 hours." See page 59 and Fig. 24 for this example.

http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=2517816&fileOId=2517841

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  • $\begingroup$ I think that this is quite far from answering the question, but the reference is cool! Note that it says 1% of a solar mass, not of the total mass. $\endgroup$ – DarioP Nov 19 '14 at 16:44
  • $\begingroup$ @DarioP thanks, I edited it to "1% of a solar mass", and right I am only addressing the neutron star portion of the question, no attempt to answer the planetary aspect $\endgroup$ – DavePhD Nov 19 '14 at 16:53
  • $\begingroup$ Neutron star part is interesting! but what about the 'normal' case where the combined mass would not be enough to form a black hole? $\endgroup$ – Phizzy Nov 19 '14 at 19:48
  • $\begingroup$ @user45874 I was only intending to answer the neutron star subquestion, but I added to the answer since no one else was answering. My answer might be inaccurate as the case approaches being a dwarf planet, but I think it is accurate for stars and giant planets. $\endgroup$ – DavePhD Nov 20 '14 at 15:04
  • $\begingroup$ I thought about answering this in terms of the dynamical timescale, but that is just a lower limit for the time something takes to settle after a collision. In realistic systems, pressure, turbulence etc. wil lengthen this and not negligibly. I don't think there is a simple answer - each situation and collision will be different. $\endgroup$ – Rob Jeffries Nov 20 '14 at 19:23

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