Mercury's Tidal Lock & Eccentric Orbit Explained

[pixel01]

Mercury is very close to the sun and I think it has been tidal locked, but for its eccentric orbit it can not be faced one half to the sun. Am I right? If it is not locked, what is the scenario that Mercury will have in the future?

 

[Vanadium 50]

Mercury is in a 3:2 tidal lock. That is, it rotates 3 times for every 2 revolutions.

 

[pixel01]

Mercury is in a 3:2 tidal lock. That is, it rotates 3 times for every 2 revolutions.

Thanks, so will ever Mercury be 100% locked?

 

[negitron]

Nope, it's a spin-orbit resonance. It will maintain that rate indefinitely, all else remaining unchanged.

 

[fleem]

Thanks, so will ever Mercury be 100% locked?

Yes, given enough time. Any wobbling or non-synchronous spin will cause tides which deform the planet, which wastes energy (or adds energy in the case of retrograde spin) until the spin synchronizes with the orbit.

 

[pixel01]

Yes, given enough time. Any wobbling or non-synchronous spin will cause tides which deform the planet, which wastes energy (or adds energy in the case of retrograde spin) until the spin synchronizes with the orbit.

Can you imagine the scenario then? I mean with the eccentric orbit, Mercury can never face only one half to the Sun unless its orbit be changed.

 

[Phrak]

Can you imagine the scenario then? I mean with the eccentric orbit, Mercury can never face only one half to the Sun unless its orbit be changed.

Now that's interesting. Imagine a 1:1 tidal locked Mercury. Energy is still dissipated in tidal distortion from the eccentric orbit. What happens to the orbit of this hypothetical Mercury?

 

[pixel01]

Now that's interesting. Imagine a 1:1 tidal locked Mercury. Energy is still dissipated in tidal distortion from the eccentric orbit. What happens to the orbit of this hypothetical Mercury?

I think once the orbit is still eccentric, Mercury can never be 1/1 locked because the difference in angular velocity between the nearest and the farthest points in orbit is too much so the rotation can not adapt to.

I do not know if given enough time, Mercury one day will be locked 1/1 with its orbit of no eccentricity

 

[fleem]

Now that's interesting. Imagine a 1:1 tidal locked Mercury. Energy is still dissipated in tidal distortion from the eccentric orbit. What happens to the orbit of this hypothetical Mercury?

The energy of that tidal deformation has to come from some where, of course, and the only places it can come from are the spin of the sun, spin or wobble of the planet, and the orbit of the planet. So all of those things are affected. The final result is a tidal locked planet with circular orbit in the same plane as the parent's spin (or in some cases, a planet that crashes into its parent), because only then are there no more tides. The orbit can also expand or shrink, in the process, depending on the direction of spin of the sun/parent. For example, current theory is that the moon was once a lot closer to the Earth, and the Earth spun faster. You can picture how this happens by imagining the tidal bulge of the Earth (the one that is caused by the moon) slightly leading (because of the spin of the Earth) the orbital angle of the moon--which would accelerate the moon and slow down the spin of the Earth.

 

[Vanadium 50]

Yes, given enough time.

Are you sure? There's a huge potential barrier the system has to climb out of to move from a 3:2 to a 1:1 resonance.

 

[fleem]

Are you sure? There's a huge potential barrier the system has to climb out of to move from a 3:2 to a 1:1 resonance.

Pretty sure--and I think the proof is in the pudding that we see 1:1 tidally locked satellites that were, presumably, at some time in the past locked at 3:2 (because no orbit is perfectly circular). The explanation is that no matter how solid and elongated Mercury is, there will still be some energy wasted in tidal deformation for both the Sun and Mercury, and that energy must come from the Sun's spin, mercury's spin, and/or Mercury's orbit--thus changing one or more of those things. What will happen is that first Mercury's orbit will become more circular because of the Sun's bulge giving Mercury more orbital energy when Mercury is closer to the sun, and then once the orbit is more circular Mercury will be able to hop out of that 3:2 metastable state into the 1:1 state. Of course, in the mean time other heavenly bodies might upset things further and prevent it from happening before Mercury or the solar system is destroyed by cataclysm.

 

[Vanadium 50]

Pretty sure--and I think the proof is in the pudding that we see 1:1 tidally locked satellites that were, presumably, at some time in the past locked at 3:2 (because no orbit is perfectly circular).

The fact that at one point their history they were in a 3:2 phase doesn't mean they were locked in this phase. To be locked, perturbations around the resonance condition need to tend to return the system to the resonance condition. You can think of it in analogy to potential energy: you have a global minimum at 1:1. You may or may not have a local minimum at 3:2. And it's possible that something in the local minimum can't get through the potential barrier to get to the global minimum.

 

[LURCH]

Keep in mind that the Moon is not in a cirular orbit, either. The Moon is tidally locked to the Earth, but its eliptical orbit means that it doesn't exactly show one side all the time; it "rocks" from side to side very slightly (as seen from earth, of course).

 

[pixel01]

Keep in mind that the Moon is not in a cirular orbit, either. The Moon is tidally locked to the Earth, but its eliptical orbit means that it doesn't exactly show one side all the time; it "rocks" from side to side very slightly (as seen from earth, of course).

I think the difference here is the eccentricity of Mercury is much larger than the moon's so its rotation can not adapt.

I don't know if we can mathematically calculate the rotation of a planet when it is locked by the sun if we know the eccentricity and revolution cycle.

 

[Vanadium 50]

The Moon is tidally locked to the Earth, but its eliptical orbit means that it doesn't exactly show one side all the time; it "rocks" from side to side very slightly (as seen from earth, of course).

It's called libration. In the analogy I used, it's a perturbation about the "potential minimum" of a 1:1 lock. In the 3:2 lock case, like Mercury, the perturbations end up returning the system to 3:2. In a different configuration - perhaps with a less rigid body - the perturbation would be amplified and the system would eventually "fall" into a 1:1 lock.

 

[fleem]

I don't know if we can mathematically calculate the rotation of a planet when it is locked by the sun if we know the eccentricity and revolution cycle.

Right! Those moving tidal bulges (which vary with Mercury's distance) make it a many-body problem, so only simulation will work. But let me reiterate: Mercury's orbit will become more and more circular because its orbit is not retrograde with the sun's spin, and a much more circular orbit will eventually let it fall out of the 3:2 metastate. True, it might take a while, but its inevitable (or cataclysm makes the whole thing moot).

 

[D H]

Mercury's orbit will become more and more circular because its orbit is not retrograde with the sun's spin, and a much more circular orbit will eventually let it fall out of the 3:2 metastate. True, it might take a while, but its inevitable (or cataclysm makes the whole thing moot).

Far from inevitable; you are ignoring Jupiter.

For example, see J. Laskar & M. Gastineau, "Existence of collisional trajectories of Mercury, Mars and Venus with the Earth", Nature 459, 817-819 (11 June 2009)

At the time this post was written, this letter does not require a subscription at Nature. http://www.nature.com/nature/journal/v459/n7248/full/nature08096.html

 

[fleem]

Far from inevitable; you are ignoring Jupiter.

I mention it in a previous post, but don't bother to dwell on it in every post, because the discussion is leaning more in the realm of the theory, itself.

 

[Borek]

Moon is tidally locked to the Earth, but its eliptical orbit means that it doesn't exactly show one side all the time; it "rocks" from side to side very slightly (as seen from earth, of course).

 

[fleem]

Disclaimer: persons susceptible to motion sickness should NOT watch Borek's animated GIF for more than five seconds.

 

[LURCH]

What are you talkin' about? That GIF rocks!