# Collisions of celestial objects

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.

• Why are you interested in it? Simply, to know what you are thinking. Nov 19, 2014 at 14:46

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.

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:

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

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.