Actually it can't spin faster than its escape velocity because then it would fly apart. But it can spin right up to the point where its surface has low earth orbit velocity, for current Earth around 7 km / sec (escape velocity about 11.2 km / sec).
As it does that it goes through various transformations. First like this
Then like this, as it gets faster:
Ellipsoid rotating about its minor axis, the shortest of its three axes.
It turns out that there are two possible solutions, as the spin rate increases. You can get an oblate spheroid, or a triaxial ellipsoid - the solution "bifurcates". But the triaxial ellipsoid is the most stable of the two as Jacobi found out in his paper published in 1834 Figures of Equilibrium - Historical Account* - Chandrasekar which came as a surprise because until then everyone thought that rapidly spinning planets would be oblate spheroids.
This is an artist's impression of a dwarf planet in the Kuiper belt which is thought to be in the shape of a triaxial ellipsoid from its light curve:
Then in principle as it gets faster, it can be triangular or square or even pentagonal with rounded corners like this
LiveLeak.com - Spinning water droplets behave like black holes
Here the droplets are held together by surface tension. But apparently theoretically droplets held together by surface tension in zero g have the same shape as a planet or star held together by gravity. So this is experimental work that also confirms theoretical predictions for possible shapes of planets too. Paper here: Nonaxisymmetric Shapes of a Magnetically Levitated and Spinning Water Droplet
We don't know of any planets or stars shaped like this yet.
Then as it spins faster, it can turn into two spheres joined together. This is the scenario of a binary planet.
If two planets are gravitationally locked to each other, in the same way as Pluto and Charon, then tidal effects no longer matter.
They are just permanently distorted. You could in principle even have an Earth sized planet almost touching our Earth - even with a shared atmosphere and ocean.
(Image NASA) 'Double Earths' Could Be Fun Exoplanets To Hunt For -- If They Exist see: Can binary terrestrial planets exist?
This is explored fictionally in Robert Forward's "Rocheworld" which is an "overcontact binary"
Rocheworld
Though we don't know any Rocheworld planets yet, there are many contact binary asteroids. These are too small to be rounded under their own gravity, but are approximately the shape of an overcontact binary.
This is 216 Kleopatra
And comets also, this is 67P/Churyumov–Gerasimenko which is also approximately the shape of an overcontact binary
Also many contact binary stars are known, again including "overcontact binaries" also like these asteroids and comets, so close together that their atmospheres overlap - the first discovered W Ursae Majoris.
figure from: Chapter 19-7 and for another image see also Contact Binaries
As it spins even faster then in theory anyway, a planet or star can turn into three or even four spheres joined together to make an "overcontact ternary" or "overcontact quarternary" planet or star, or you could have a donut shaped planet too, though so far we haven't found anything like this:
See Viewpoint: The many shapes of spinning drops
This is an animation someone did of a thin torus, the "hoopworld"
But thin hoops like this are unstable and easily break up into droplets.
Thicker hoops like this visualization from io9 can be stable.
I shouldn't think there are many of these in our universe :). Needs very special conditions to form. But - not impossible apparently.
Here is a youtube video of a Moon of a donuut planet:
You can also get donut shaped solutions for end state of a collapsing gas cloud, which are stable, in principle. So, you could have young toroidal stars as the author suggests in this paper : General Relativisitic Sturcture of Star Toroidal Systems (1992).
Anders Sandberg's fun article explores many aspects of life on a donut shaped planet - and the orbits of satellites and moons around such a planet.
What would the Earth be like if it was the shape of a donut?
(see also Why are all planets round and not square or rectangular?)
As it does that it goes through various transformations. First like this
Then like this, as it gets faster:
Ellipsoid rotating about its minor axis, the shortest of its three axes.
It turns out that there are two possible solutions, as the spin rate increases. You can get an oblate spheroid, or a triaxial ellipsoid - the solution "bifurcates". But the triaxial ellipsoid is the most stable of the two as Jacobi found out in his paper published in 1834 Figures of Equilibrium - Historical Account* - Chandrasekar which came as a surprise because until then everyone thought that rapidly spinning planets would be oblate spheroids.
This is an artist's impression of a dwarf planet in the Kuiper belt which is thought to be in the shape of a triaxial ellipsoid from its light curve:
Then in principle as it gets faster, it can be triangular or square or even pentagonal with rounded corners like this
Here the droplets are held together by surface tension. But apparently theoretically droplets held together by surface tension in zero g have the same shape as a planet or star held together by gravity. So this is experimental work that also confirms theoretical predictions for possible shapes of planets too. Paper here: Nonaxisymmetric Shapes of a Magnetically Levitated and Spinning Water Droplet
We don't know of any planets or stars shaped like this yet.
Then as it spins faster, it can turn into two spheres joined together. This is the scenario of a binary planet.
GRAVITATIONALLY LOCKED BINARY PLANET
If two planets are gravitationally locked to each other, in the same way as Pluto and Charon, then tidal effects no longer matter.
They are just permanently distorted. You could in principle even have an Earth sized planet almost touching our Earth - even with a shared atmosphere and ocean.
This is explored fictionally in Robert Forward's "Rocheworld" which is an "overcontact binary"
Though we don't know any Rocheworld planets yet, there are many contact binary asteroids. These are too small to be rounded under their own gravity, but are approximately the shape of an overcontact binary.
This is 216 Kleopatra
And comets also, this is 67P/Churyumov–Gerasimenko which is also approximately the shape of an overcontact binary
Also many contact binary stars are known, again including "overcontact binaries" also like these asteroids and comets, so close together that their atmospheres overlap - the first discovered W Ursae Majoris.
As it spins even faster then in theory anyway, a planet or star can turn into three or even four spheres joined together to make an "overcontact ternary" or "overcontact quarternary" planet or star, or you could have a donut shaped planet too, though so far we haven't found anything like this:
This is an animation someone did of a thin torus, the "hoopworld"
But thin hoops like this are unstable and easily break up into droplets.
Thicker hoops like this visualization from io9 can be stable.
Here is a youtube video of a Moon of a donuut planet:
You can also get donut shaped solutions for end state of a collapsing gas cloud, which are stable, in principle. So, you could have young toroidal stars as the author suggests in this paper : General Relativisitic Sturcture of Star Toroidal Systems (1992).
Anders Sandberg's fun article explores many aspects of life on a donut shaped planet - and the orbits of satellites and moons around such a planet.
What would the Earth be like if it was the shape of a donut?
(see also Why are all planets round and not square or rectangular?)
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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