# Will the earth and sun ever be tidally locked?

by ARAVIND113122
Tags: earth, locked, tidally
 P: 54 suppose there are two bodies,one revolving in an orbit around the other[like the earth moon system]Differences in orbital and axial rotation of a small body results in a torque applied on it by the larger body. This results in the smaller body being tidally locked. THEN WHY ISN'T THE EARTH TIDALLY LOCKED WITH THE SUN?WILL IT EVER BE?
 Emeritus Sci Advisor PF Gold P: 2,361 There hasn't been enough time. Even the Moon, which has ~twice the tidal effect on the Earth as the Sun does hasn't had enough time to tidally lock the Earth it.
P: 80
 Quote by Janus There hasn't been enough time. Even the Moon, which has ~twice the tidal effect on the Earth as the Sun does hasn't had enough time to tidally lock the Earth it.
what's this TIME got to do with the above question? really I can't understand it and could you please explain me in detail.

 P: 1,815 Will the earth and sun ever be tidally locked? As Janus says, the moon has ~twice the tidal effect as the sun, so it would seem unlikely until the moon's orbit moves far enough away from earth that the sun has a greater effect or that the period of lunar orbit equals one earth year.
P: 269
 Quote by Astro.padma what's this TIME got to do with the above question? really I can't understand it and could you please explain me in detail.
As time progresses the Earth's rotation is slowing. The Earth and the moon might eventually be tidally locked if the moon doesn't drift away far enough to let the suns tidal forces on the Earth over come it's tidal forces on the Earth. At which point the Earth will become tidally locked with the sun.
Emeritus
PF Gold
P: 2,361
 Quote by Astro.padma what's this TIME got to do with the above question? really I can't understand it and could you please explain me in detail.
You can estimate the time it would take for one body to tidal lock to another by the formula:

$$\frac{\omega a^6 I Q}{3GM^2k_2 R^5}$$

Tidal locking takes time to occur.

The factors include the initial rotation speed of the body, its distance from the other body, Its moment of Inertia, the Mass and radius of the body it is orbiting, plus a couple of coupling factors.

I mentioned the Moon because its tidal effect on the Earth is larger than the Sun's, so if not enough time has passed for the Moon to slow the Earth's rotation to match its orbit, then definitely not enough time has passed for the Sun the tidally lock the Earth to it.
 P: 841 Ummm...The moon is tidally locked. The above equation is a good one though.
 P: 54 Thank you very much!!!
Mentor
P: 15,170
 Quote by Travis_King Ummm...The moon is tidally locked.
You missed the point. While the Moon is tidally locked to the Earth, the Earth is not tidally locked to the Moon.
 P: 841 Not to sound rude, but: so? The earth-moon and earth-sun systems are independent (barring the rotational effects the moon has on the earth). There's no sense in comparing the two. Besides, the question is whether the Earth will become tidally locked to the Sun. In this case, the earth is the satellite and the sun is the primary. In the earth-moon, the earth is the primary and the moon is the satellite. The OP asked whether or not the earth will be tidally locked to the Sun, not the other way around.
P: 80
 Quote by Janus You can estimate the time it would take for one body to tidal lock to another by the formula: $$\frac{\omega a^6 I Q}{3GM^2k_2 R^5}$$ Tidal locking takes time to occur. The factors include the initial rotation speed of the body, its distance from the other body, Its moment of Inertia, the Mass and radius of the body it is orbiting, plus a couple of coupling factors. I mentioned the Moon because its tidal effect on the Earth is larger than the Sun's, so if not enough time has passed for the Moon to slow the Earth's rotation to match its orbit, then definitely not enough time has passed for the Sun the tidally lock the Earth to it.
K...Thanks for the reply but is this what you meant by the above? : The Moon's tidal effect on the Earth is larger than that of the Sun's. So only at that point of time, when the Moon's effect gets decreased, the Sun could tidally lock the Earth?
P: 80
 Quote by Janus $$\frac{\omega a^6 I Q}{3GM^2k_2 R^5}$$ I mentioned the Moon because its tidal effect on the Earth is larger than the Sun's, so if not enough time has passed for the Moon to slow the Earth's rotation to match its orbit, then definitely not enough time has passed for the Sun the tidally lock the Earth to it.
Sir..Why in this context is the Moon's effect superior to that of the sun? Why do you think that the time to be taken by the Sun to tidally lock would be longer than the time taken by the Moon??
Emeritus
PF Gold
P: 2,361
 Quote by Astro.padma Sir..Why in this context is the Moon's effect superior to that of the sun? Why do you think that the time to be taken by the Sun to tidally lock would be longer than the time taken by the Moon??
Tidal force is proportional to the mass exerting the force and inversely proportional to its distance. The moon is 1/27210884 the mass of the Sun, but it is 400 times closer. So the Sun's tidal force on the Earth is 27210884/400^3 = 0.4252 times that of the Moon.

It is This tidal force acting on the Earth which would cause it to lock with either the Earth or Moon. Since the Moon exerts the greater tidal force on the Earth, It would be the first to tidally lock the Earth to it.

Actually, if you look at the formula I gave for the time for tidal locking to occur, you will note that it increases by the distance between the bodies (a) to the power of 6, and decreases by the mass of the acting body by only the square of the mass.

So 400^6/27210884^2 = 5.53, meaning that it would take ~5.5 times longer for the Sun to lock the Earth to it than it would for the Moon to lock the Earth.
 P: 841 I see what you are saying. I stand corrected.
P: 80
 Quote by Janus So 400^6/27210884^2 = 5.53, meaning that it would take ~5.5 times longer for the Sun to lock the Earth to it than it would for the Moon to lock the Earth.
Oh K...now I got it :) but I really wonder why couldn't the Moon yet tidally lock the Earth?? Not Enough time or anything else?? If it is a matter of time, on what assumptions was the equation given by you framed? Ive tried to google it but couldn't find the answer.
 P: 841 The equation above describes the time required in those conditions to attain tidal locking. It's not a matter of assumptions, really. It's a matter of physics, and I'm sure the equations were derived painstakingly and are very long.
P: 80
 Quote by Travis_King The equation above describes the time required in those conditions to attain tidal locking.
If am not bugging you people, here what does it mean by "those conditions" ?

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