# Tides on a Super Close In Moon

I have a moon covered in liquid water that orbits a super-Earth very closely. As you might imagine, the tides are incredibly strong on this moon. However, it is tidally locked and so does not experience tides like Earth does but, I'm unsure about one aspect of this.

Would the extreme tides cause the water to permanently drain around the side of the moon (forming a ring of land that wrapped around the world) and raise sea levels around where the Prime Meridian and equator meet, as well as on the opposite side of the moon?

The planet is 2.55 times the mass of Earth while the moon in 0.107 Earth masses and orbits at a distance of 82,300 km.

• @JBH - Your physics is wrong. Look at this diagram - proxy.duckduckgo.com/iu/… – chasly - supports Monica Mar 23 '19 at 10:06
• @JBH - The contra-bulge has nothing to do with the Sun 'pulling in the opposite direction'. It makes no difference whether the Sun and Moon are lined up on the same side or opposite sides of the Earth. Both bulges will still be there. Note: I used to work at an Oceanographic Institute. I worked in the computing department but I know enough of oceanography to have some idea what I'm talking about. – chasly - supports Monica Mar 23 '19 at 15:06
• @JBH - Here is a diagram that shows both Sun and Moon effects. You can see that in both cases (spring and neap) the Sun and Moon each produce a bulge on both sides of Earth. proxy.duckduckgo.com/iu/… – chasly - supports Monica Mar 23 '19 at 15:14
• @299 Neandertal Variants - I suggest you add a science-based, or better still a hard-science tag. Otherwise you will get people answering by intuition instead of science. – chasly - supports Monica Mar 23 '19 at 15:17
• @JBH - I don't claim to be qualified in oceanography. I do claim to have discussed the phenomenon of tides with highly qualified oceanographers. At the time of writing, the OP hasn't specified hard-science and in any case mine was a comment, not an answer so I don't have to back it up with equations. I believe the burden of proof is on you. I'm simply questioning your assertions - you seem to be basing them on intuition rather than physics. – chasly - supports Monica Mar 23 '19 at 17:09

From some helpful posts on our sister site, Physics.SE...

There is no tidal bulge.1 This was one of Newton's few mistakes. Newton did get the tidal forcing function correct, but the response to that forcing in the oceans: completely wrong. … What Newton got wrong, Laplace got right. Laplace's dynamic theory of the tides accounts for the problems mentioned above. It explains why it's always high tide somewhere in the North Sea (and Patagonia, and the coast of New Zealand, and a few other places on the Earth where tides are just completely whacko). … The vertical component is the driving force behind the response of the Earth as a whole to these tidal forces. This question isn't about the Earth tides. The question is about the oceanic tides, and there it's the horizontal component that is the driving force. … Oceanographers still teach Newton's equilibrium tide theory for a number of reasons. It does give a proper picture of the tidal forcing function. Moreover, many students do not understand how many places can have two tides a day. For that matter, most oceanography instructors and textbook authors don't understand! Many oceanographers and their texts still hold that the inner bulge is a consequence of gravity but the other bulge is a consequence of a so-called centrifugal force. This drives geophysicists and geodocists absolutely nuts. That's starting to change; in the last ten years or so, some oceanography texts have finally started teaching that the only force that is needed to explain the tides is gravitation. (Source)

In reality the "tidal bulge" model is very inaccurate for explaining how the oceans rise and fall. It is more accurate to consider the oceans as a very complex driven oscillator, where the water is slowly sloshing around. The periodic minor variations in gravity caused by the moon contribute energy to the sloshing, but the actual shape and timing of the sloshes is much more influenced by coastlines than than by the moon itself. (Source)

What this means is that the tidal bulge experienced by Earth isn't simply caused by the gravitational pull of the moon. In fact, the tidal pull of the moon at any given moment isn't even a fraction of what's causing the bulge. So, what does "oscillator" mean?

Grab a half-cup full of water in your hand and shake it in the same way you would if you were trying to mix your favorite flavor into it. The water "oscillates" around the interior of the cup. And once you get the "oscillation" going, you don't need to put as much energy into it because the momentum of the water is doing most of the work.

This is really important, because that bulge isn't due to the water being "squeezed" from the poles. That's not how gravity works. It's due to the mass of water "oscillating," which you can see in your cup. The water moves from the center to the outer edges. When you're dealing with a sphere, the only place the water can go is the equator (simplistically).

What adds to this oscillation? We already know the first two of the following bullets, but there's two more.

• The momentum of the water.
• The moon's gravity.
• The Earth's rotation.
• The sun's gravity.

Like the moon's gravity, at any given moment the rotation of the Earth isn't adding much. The Earth's rotation isn't pushing the water along (like a pump) any more than the moon's gravity or Sol's gravity are substantially lifting the water up (like a vacuum, or another pump). These three forces: Earth's rotation, Sol's gravity, and Luna's gravity, are the gentle energy that slowly got the water moving over a bazillion years. But the energy now is principally the momentum of the water itself.

And that momentum is centrifugal (as is Earth's rotation), which is why you see two bulges on Earth.

Earth rotates 365ish times in a single year. Your planet rotates but once. Worse, your moon is only 10.7% the mass (and, give-or-take, the size) of Earth. This means less rotational and centrifugal force contributing to the "oscillation."

Next, you're tidally locked, which (for the benefit of all readers) is a fancy way of saying the same face of the moon is always facing toward your planet. That means there is no gravitational component due to the planet contributing to the "oscillation."

You do have a sun, and you've told us nothing about it. We don't know the orbital period of your moon around its planet, the orbital period of the planet around the sun, or the distance of the sun from the planet. There will be a small contributor to the oscillation due to the sun.

Finally, let's talk about the effects of local gravity. You haven't given us enough information to calculate the gravity of either the moon or the planet (you need the radius of both). This means my next statement is inaccurate, let me show you why.

• The ratio of gravity between Luna (1.62 m/s²) and Earth (9.807 m/s²) is 0.165:1 or 16.5%.
• The ratio of mass between Luna (7.34767309 × 1022 kg) and Earth (5.972 × 1024 kg) is 0.0123:1 or 1.2%.

That's an order-of-magnitude difference between the two ratios. So, let's calculate the ratio of mass in your situation and multiply by 10 and call it good.

• 1:238.3178 or 23,831.78%.

Your planet is exerting 1,444X the gravitational influence on your moon's oceans than Luna is on Earth's oceans.

And when you start plugging all those numbers into Laplace's equations, what you soon discover is there are no tides (excluding the small component from the sun, which is seriously overwhelmed by the planet) because everything is static.

Conclusion

• Insignificant centrifugal force.
• Insignificant rotational influence.
• Minor solar gravity influence.
• Massive planetary gravity influence.
• Tidally locked.

Fundamentally, no oscillation — no tides. This means you would not see a bulge of water on the back side of the moon. You would see a serious bulge on the planet-side of the moon. Considering how static everything is and how massive the gravitational influence is, I could be convinced that there isn't any surface water on the back side of your moon. It's all on the planet-side hemisphere.

Disclaimer: The missing sun and radius data could change this answer. But that planetary influence on a tidally locked planet is so great, that I have a hard time believing a sun large enough to cause an oscillation would permit the moon to be habitable.

1What this respondent means is that the concept of a "tidal bulge" due to simple lunar gravitational effects is misunderstood. Read the entire answer to see what he means. I've included his title for dramatic effect — and to point out that the bulge isn't there simply due to gravity, but to a complex affect of gravity.

• What you have missed is that Newton was considering an ideal ocean. I quote from the link that you gave, "The tidal bulge cannot exist because the Earth isn't completely covered by water. There are two huge north-south barriers to Newton's tidal bulge..." However the OP posits a moon that is entirely covered by water. Also it is tidally locked so Laplace isn't relevant - the effects of currents don't exist. So I claim that in the OP's scenario, Newton's analysis was absolutely adequate. – chasly - supports Monica Mar 23 '19 at 21:55
• P.S. The effects of the sun in the OP's scenario are made negligible by the closeness of the moon to the massive planet. Incidentally oceanographers aren't so dumb. They have incredibly accurate and reliable mathematics that perfectly predict the tides. – chasly - supports Monica Mar 23 '19 at 22:02
• @chaslyfromUK, Prove it. – JBH Mar 23 '19 at 23:37
• It'll take some research but for a start take a look at this: "If we assume that the entire surface of the Earth is covered with a uniform layer of water, the differential forces may be resolved into vectors perpendicular and parallel to the surface of the Earth to determine their effect." msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/… – chasly - supports Monica Mar 24 '19 at 11:21
• @chaslyfromUK, what on Earth (pun intended) are you talking about? What edit do I need to suggest to the OP? The question is talking about a habitable moon circling a giant planet and it's the moon we're talking about. Are you confused by the OP's use of "super-earth" and referencing sizes in terms of multiples of the Earth's mass? – JBH Mar 24 '19 at 16:33

tide /tʌɪd/ noun plural noun: tides

1. the alternate rising and falling of the sea, usually twice in each lunar day at a particular place, due to the attraction of the moon and sun.

On a tidally locked planet there would be no tides, according to the definition above. There would be a steady bulge peaked on the line conjugating the moon and the planet.