# Moon hit strong enough to put it in a slow spin?

I’m building a world nearly equal to earth; i need a catastrophic event that make the moon start spinning breaking the tidal lock, a really slow spin, like 500 years for a full spin. i thought about a strong impact with great angle. It will be possible while retain its orbit mostly unchanged? Every scientific objection are welcomed

• Welcome to worldbuilding, please give a good read to our help center to understand what we expect from questions here. You are asking more than one question, while we prefer only one, and I think some of them have already been answered here.
– L.Dutch
Commented Nov 6, 2021 at 9:00
• Sorry, i’ll reformulate Commented Nov 6, 2021 at 9:15
• Does it really need to be catastrophic? Maybe you could have other large celestial objects fly by and give it a slow spin. Repeat for a 500 year spin. A moon of Jupiter or something spins because of other moons if I recall correctly. Commented Nov 6, 2021 at 13:09
• Well, it could in fact be something other than an impact, but i would settle for something spectacular, if not i could just assume that the moon of this planet isn’t yet totally locked with the planet rotation. But if the forces in plays are the same, as the first answer, the gravitational force of the external body would break apart the moon before make it spin... Commented Nov 6, 2021 at 13:21
• @DWKraus, black holes are stellar-mass objects, possibly heavier that the Sun, and one passing through the Solar System will wreak an immense havoc to planetary orbits. If you don't want Jupiter migrating inwards and ejecting the Earth out into interstellar space or flinging it into a deadly freezing orbit somewhere between Saturn and Uranus, better don't shoot black holes at our poor, barely dynamically stable Solar System! :) Commented Nov 7, 2021 at 3:22

A lunar day, equal to lunar orbital period, is ≈28 (Earth) days, adding a 1/500 yr^-1 to it corresponds to a relative change of (1/(500×365))/(1/28), which is about 150 ppm. Such a small deviation will likely be compensated by the orbital resonance attractor in the spin-orbit phase space, even given a low eccentricity of the Moon orbit. My feeling is that the Moon would return to the 1:1 resonance barely after 1-5 axial spins at the increased (or decreased) rotation rate. Since the Moon orbit eccentricity is very low (≈0.06), the resonant band of the spin-orbit phase space is quite narrow, and, as you likely know, separated from other resonant bands by chaotic bands. It is possible that the rotation speed will enter the a band of a chaotic regime, so that the rotation rate would not decrease smoothly back to where it were. The tidal heating will also vary then. In the final phase, the process shifts from the chaotic regime to librations of decreasing amplitude which may be protracted; surprisingly, this part is modeled by a dumped pendulum equations quite well.

The heat dissipated in the process could in principle start some volcanic activity on the Moon, and will certainly initiate outgassing in the heating rock, but I cannot speak to this, unfortunately. The excess energy, about 150 ppm relative, i.e. 1.5×10^-4 of the total rotational energy, is quite low. The largest unknown here is the time over which the energy dissipates. My feeling is the process should be quick, on the order of 10^2 to 10^3 years. Unfortunately, I'm not familiar with energy models when establishing an orbital resonance; I studied only the dynamics of it, where energy “just gets lost,” so I have no intuition how much heating this will cause, and what the heating profile over time would be.

Sorry that this is a little bit handwavy. This is rather just my thoughts about how complicated the situation is, and that its outcome may be predictable or not, depending on how far off 1:1 resonance the system will be thrown, i.e. whether it will reach the chaotic band in the phase space. The Moon will not necessarily disintegrate from a glancing blow, as @l-dutch helpfully estimated. Such a blow will impart both spin and orbital velocity change, and the exact figure will depend on the angle of impact and the mass and speed of the impactor. A head-on impact will change orbital velocity without affecting spin, which will also disturb the resonance. Any impact, central or glancing, actually will. The impact itself will also produce significant amount of heat in an instant, which should also be accounted for. An off-equator blow will also send the rotation axis tumbling, which will eventually stabilize in the presence of Sun's gravity, that also should not be discounted. Planetary dynamics is already horribly complex even when these effects are ignored. I'd turn to numeric modeling rather than trying to write and solve equations accounting for all factors; they aren't likely even solvable (welcome to the wonderful underworld of the systems of PDEs!). But an impact that throws the Moon out of resonance by just 150 ppm is not catastrophic at all for the Earth-Moon system, and things will “get back to normal” almost instantly on the astronomic timescale, although the new “normal” may end up a bit different, due to a shifted rotation axis of the Moon and a different eccentricity and, albeit very slightly, radius of its orbit.

As a wild guess, does The Universe Sandbox has a model of tidal resonance?

Since you have a wide literary licence, you may assume any sensible regime in the range that I tried to describe, even if rather qualitative. If you want lunar volcanism, it's possible. If you want the impact ejeca reaching the Earth, it's also possible. A recovery time of hundreds to tens of thousand years is reasonable. Finally, if you want the Moon to end up rotating on a tilted axis with precession after the event, it's not only possible but very likely. If you do not, that's also does not violate physics, just requires a more or less precise nearly-equatorial momentum transfer, which is also realistic, given the relatively low energy gain.

• wow, ok, this is really helpful! I guess i’m going to do some math, until i will eventually got bored! 😁 Commented Nov 7, 2021 at 12:42
• @MicheleFornasari Unfortunately, the math here is so complicated that it's more common to resort to computer simulations. Or, rather, supercomputer simulation, if you want to account for heat distribution inside the Moon while it regains its resonance—this one is certainly unsolvable analytically. What we study analytically is a general structure of spin-orbit phase space, which is a simplified version of your question. It does not answer, for example, how much heat in energy losses is generated by each of the two bodies, only the total lost energy, or tells anything about the relaxation time. Commented Nov 8, 2021 at 6:39
• @MicheleFornasari, I don't know how much background in math you have, but here's an introductory-level paper on types of orbital resonance and their phase space topologies. It's in fact even avoids PDEs, and is written in the ODE language, greatly simplified, but much easier to solve and feel the meaning of the equations. The exposition is well-paced and detailed: it's a seminar lecture, so you expect that attendees grok as you talk. Just in case, since you mentioned you wanted to do the math, it could be a good start: lpl.arizona.edu/~renu/malhotra_preprints/rio97.pdf Commented Nov 8, 2021 at 7:01
• WoW, this is really interesting! I fear that it would be far off my math capabilities, but i will surely try it! Thank you Commented Nov 8, 2021 at 11:46

The rotational kinetic energy of the moon is $$3 \cdot 10^{23}$$ J. In order to change the rotational speed of the moon, you will need to play with an energy of that order of magnitude.

The gravitational binding energy of the moon is instead $$1 \cdot 10^{29}$$ J, which is about 1 million times higher.

Therefore you can "safely" spin up the moon by grazing its surface with asteroid impacts.

• I followed your link for “Gravitational binding energy of the moon”, and it gives a different answer than you have posted. You have it at 7*10^22 J, but that Wolfram page says that it is 1.244*10^29 J. I suspect that you mistakenly read the moon’s mass, 7*10^22 kg as the binding energy. This would also resolve the mystery of how an intact body could have a higher rotational energy than its binding energy. Commented Nov 6, 2021 at 19:46
• @RBarryYoung thanks for finding the error, now corrected
– L.Dutch
Commented Nov 6, 2021 at 19:49
• I was wrong as well, and energy in Alpha is for 27 days period of rotation, for moon - that 3.071e23, and for 500 years per rotation change the energy still 6700 times less than it is now, so a delta of energy is 44e18 J, which can be considered as standing still impactor with a mass of 100 million tons (difference of speeds about 30km/s) Commented Nov 7, 2021 at 10:46

The Moon rotates around the common Earth-Moon barycenter in a given time T1, and it also revolves around its own axis in a time T2.

Being tidally locked just means that T1 = T2.

And one solution to make it not tidally locked would be to vary T2. This would require to either brake or increase the Moon's rotation.

A different - actually, exactly opposite - approach would be to vary T1 by altering the Moon's orbit. This you can do by crashing a very large comet against the Moon, thus increasing (or decreasing) its orbital speed. The Moon's rotation would remain unchanged, and therefore would fall out of sync with the new duration of the Lunar month.

To decrease the effects of the impact on the Moon's integrity you might imagine the comet having recently broken up in, say, a close encounter with Jupiter. The impact would take place on a very large portion of the Moon's surface (a more catastrophic version of this impact is depicted in Jack DeVitt's Moonfall.

Even in a non-completely-catastrophic scenario (say, something like Bob Shaw's The Ceres Solution) you would get lots of ejecta, a considerable portion of which would certainly re-enter Earth's atmosphere, as well as very probably triggering a Kessler chain reaction.

A less catastrophic scenario would have the Moon narrowly missed by a much larger celestial body than a comet: large enough to "pull" the Moon outwards in its orbit. This would inevitably gravitationally influence the Earth and its orbit also, so most timebases would need to be recalibrated.

Volcanic eruptions can release enough energy to be comparable to the kinetic energy of the moon's motion.

Perhaps a glancing hit by a massive meteor could have ripped off the surface of this moon, and the intense tectonic response could spew enough lava into space to make the moon spin? The moon might have a glowing spot for a hundred or so years before it settled down.

Our moon isn't tectonically active, but yours could be.

• A glancing blow could also mess with the gravitational bulb that takes form from gravity that is causing the tidal lock. If you hit that part, it could make the slowing down and it again being tidally locked take a long time. Commented Nov 6, 2021 at 13:19
• Yep, that’s what i was thinking about! it could be possible without destroying the moon, hurling it into deep space, or wiping clean earth surface with meteor shower? Commented Nov 6, 2021 at 13:44
• Yep. Rather than a single push over a few minutes it would be numerous volcanic pushes over decades or centuries. Commented Nov 6, 2021 at 14:15
• @Trioxidane, for calculations we model planets and moons as if they were made of a very viscous liquid, which they really are. Dispersing the “gravitational bulb,” as you aptly called it, will do very little, as a new one will form immediately, on the scale of hours to days. Also, it's not a stable feature, and is shifting as the Moon librates due to its orbit's eccentricity, dissipating energy and slowing it down, causing it to lose orbital velocity and recede from the Earth. Commented Nov 7, 2021 at 2:39