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## Main Question or Discussion Point

Quick question, do bigger planet spin faster?

- Thread starter valdar
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Quick question, do bigger planet spin faster?

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Look up the data.

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Nabeshin

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In general, I don't think there's any relation.Quick question, do bigger planet spin faster?

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Chronos

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You must look at planet formation to understand this issue. The short answer is yes.

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mgb_phys

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Mercury 10.9

Venus 6.5

Earth 1670

Mars 867

Jupiter 45600

Saturn 37000

Uranus 10900

Neptune 8460

Pluto 47

You would expect small planets to spin faster - from conservation of angular momentum

But larger planets were formed from larger clouds of stuff.

As stuff contracted, then because of conservation of angular momentum it speeded up, the bigger/faster the original cloud the faster it ended up. Of course if you took the existing planets and made each of them smaller - they would speed up even more.

Then there are effects that have happened since. Mercury's rotation is slowed by tidal friction with the sun so has a very slow speed (long day), the Earth's is slowed a little by friction with the moon.

Uranus probably got hit by something in the past - which is why it has a weird axis tilt.

Mars might also have been affected by whatever caused the asteroid belt.

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Mercury 10.9

Venus 6.5

Earth 1670

Mars 867

Jupiter 45600

Saturn 37000

Uranus 10900

Neptune 8460

Pluto 47

You would expect small planets to spin faster - from conservation of angular momentum

But larger planets were formed from larger clouds of stuff.

As stuff contracted, then because of conservation of angular momentum it speeded up, the bigger/faster the original cloud the faster it ended up. Of course if you took the existing planets and made each of them smaller - they would speed up even more.

Then there are effects that have happened since. Mercury's rotation is slowed by tidal friction with the sun so has a very slow speed (long day), the Earth's is slowed a little by friction with the moon.

Uranus probably got hit by something in the past - which is why it has a weird axis tilt.

Mars might also have been affected by whatever caused the asteroid belt.

Very interesting. Thank you for providing this

- #8

stevebd1

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A good way of comparing spin in stars is to compare angular momentum and mass in geometric units where-

[tex]a=J/mc[/tex]

[tex]M=Gm/c^2[/tex]

where

[tex]J=vmr\,k[/tex]

where [itex]a[/itex] is the spin parameter in metres, v is the equatorial rotation velocity, m is mass, r is the equatorial radius and k is the moment of inertia coefficient (0.4 for an idealized sphere of uniform density).

a/M produces a unitless figure between 0 and 1, the higher the number, the higher the spin. For the Sun (k=0.06), a/M=~0.188, for a 2.2 sol neutron star with a frequency of 1500 Hz (k=0.35), a/M=~0.488.

This doesn't appear so straightforward with planets as M works out considerably smaller than [itex]a[/itex] but there should still be a way of comparing spin geometrically.

EDIT:

In the case of planets, you could probably get away with just considering the results of [itex]a[/itex] which is considered to be the amount of angular momentum per unit of mass (sometimes expressed as J/M). In this case, Jupiter is the clear winner and Mercury has the least 'spin' per unit of mass.

[tex]a=J/mc[/tex]

[tex]M=Gm/c^2[/tex]

where

[tex]J=vmr\,k[/tex]

where [itex]a[/itex] is the spin parameter in metres, v is the equatorial rotation velocity, m is mass, r is the equatorial radius and k is the moment of inertia coefficient (0.4 for an idealized sphere of uniform density).

a/M produces a unitless figure between 0 and 1, the higher the number, the higher the spin. For the Sun (k=0.06), a/M=~0.188, for a 2.2 sol neutron star with a frequency of 1500 Hz (k=0.35), a/M=~0.488.

This doesn't appear so straightforward with planets as M works out considerably smaller than [itex]a[/itex] but there should still be a way of comparing spin geometrically.

EDIT:

In the case of planets, you could probably get away with just considering the results of [itex]a[/itex] which is considered to be the amount of angular momentum per unit of mass (sometimes expressed as J/M). In this case, Jupiter is the clear winner and Mercury has the least 'spin' per unit of mass.

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