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**Physics, Astronomy & Cosmology / Re: What spun-down the inner planets ?**

« **on:**26/09/2018 00:39:03 »

The time it takes for a body orbiting another body to tidally lock is found by the equation:

T = wa^6 mQ/(3GM^2 K R^3)

w is the starting angular velocity of the body's rotation

a is the semi-major axis of its orbit

Q is the dissipation factor

m the body's mass

G the universal gravitational constant

M the mass of tht body it is orbiting

K the "Love" number.

R the radius of the body.

Q and K are not well known except in the case of the Earth and Moon system. So for the sake of argument, we will assume they are the same for all three planets and the Sun.

Since we are comparing planets orbiting the Sun G and M will be the same.

If we assume that w starts out as the came for all three then the difference in tidal locking times can be simplified to the relationship of

a^6 m/R^3

It also turns out that the ratio of m/R^3 comes out to be fairly close to each other for all three planets. So in the end, the major deciding factor is a^6

Earth is 2.58 times further from the Sun than Mercury, so it would take nearly 300 times longer to tidal lock to the Sun.

The Earth is 1.38 times further than Venus and would take 7 time longer to lock. Assuming all other things are equal.

One thing to keep in mind is that tidal forces fall of by the cube of the distance. So even though the Moon's tidal effect of the Earth is ~ twice that of the Sun's, At the distance of Mercury, the Sun's tidal force has increased by a factor of 17, and be 8.5 times stronger than the Moon's effect on the Earth and at the distance of Venus it would be 1.3 times stronger than the Moon on the Earth.

But we don't know that all things started out equal or stayed that way. For example, the Earth is believed to have been struck by a Mars sized body in its past which initially formed the Moon, and likely spun the Earth up quite a bit. This would have given it a lot more rotational energy to shed.

Venus actually rotates slower than it orbits. This also may have been due to a collision; one that robbed it of spin rather than giving it more spin.

So without knowing the full history of each planet it is hard to say what all the influences were that contributed to their present rotations.

T = wa^6 mQ/(3GM^2 K R^3)

w is the starting angular velocity of the body's rotation

a is the semi-major axis of its orbit

Q is the dissipation factor

m the body's mass

G the universal gravitational constant

M the mass of tht body it is orbiting

K the "Love" number.

R the radius of the body.

Q and K are not well known except in the case of the Earth and Moon system. So for the sake of argument, we will assume they are the same for all three planets and the Sun.

Since we are comparing planets orbiting the Sun G and M will be the same.

If we assume that w starts out as the came for all three then the difference in tidal locking times can be simplified to the relationship of

a^6 m/R^3

It also turns out that the ratio of m/R^3 comes out to be fairly close to each other for all three planets. So in the end, the major deciding factor is a^6

Earth is 2.58 times further from the Sun than Mercury, so it would take nearly 300 times longer to tidal lock to the Sun.

The Earth is 1.38 times further than Venus and would take 7 time longer to lock. Assuming all other things are equal.

One thing to keep in mind is that tidal forces fall of by the cube of the distance. So even though the Moon's tidal effect of the Earth is ~ twice that of the Sun's, At the distance of Mercury, the Sun's tidal force has increased by a factor of 17, and be 8.5 times stronger than the Moon's effect on the Earth and at the distance of Venus it would be 1.3 times stronger than the Moon on the Earth.

But we don't know that all things started out equal or stayed that way. For example, the Earth is believed to have been struck by a Mars sized body in its past which initially formed the Moon, and likely spun the Earth up quite a bit. This would have given it a lot more rotational energy to shed.

Venus actually rotates slower than it orbits. This also may have been due to a collision; one that robbed it of spin rather than giving it more spin.

So without knowing the full history of each planet it is hard to say what all the influences were that contributed to their present rotations.

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