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Comment by jjk166 | Hacker News Reader

At a distance of 100 km, the gravitational acceleration caused by the greenland ice sheet is .019 m/s^2 or ~0.2% g. Doesn't sound like a lot but it's still 524 times higher than the effect of the moon's gravity which creates the tides. The ice sheet has the same gravitational effect as the moon at a distance of approximately 2300 km.

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> Doesn't sound like a lot but it's still 524 times higher than the effect of the moon's gravity which creates the tides.

Contrary to common belief, tides are not caused by the direct influence of the moon's gravity (it's far too weak to have any effect)[1]. The tidal forces are caused by the gravitational gradient from the moon (and the "centrifugal" forces from our path around the earth-moon barycenter), and I don't believe you'd get the same effects from a gravity source on the surface of the earth.

Even a lot of very respectable scientists and textbooks get this wrong.

[1] See https://www.youtube.com/watch?v=pwChk4S99i4 for a pretty good explanation

Just to add to this answer and perhaps save you the click, what he is referring to is that the force pulling the water upward at high tide is not the direct gravitational pull of the moon. It is that the gravitational force from the moon at the edge of the earth is greater than the force at the center (because it is closer to the moon). Similarly the force on the opposite side of the earth is less (because that side is further from the moon than the earth's center). So the water molecules are drawn away from the center of the earth (near side because they are being pulled slightly harder than the center of the earth, and far side because they are being pulled slightly less hard than the center of the earth). Hence the high tides on both sides of the earth, not just the side closer to moon.

Or, to put it another way, the surfaces of the Earth closest to and farthest away from the Moon are traveling at the same orbital velocity of the Earth. However, they should be in different orbits; the point closest to the Moon is too slow for the orbit it is in and the point farthest is too fast. The former wants to into a lower orbit while the latter wants to go into a higher orbit.

In a further translation from gibberish:

Or, to put it another way, the surfaces of the Earth closest to and farthest away from the Moon are traveling at the same orbital velocity around the center of the Earth/Moon system. However, they should be in different orbits; the point closest to the Moon is too slow for the orbit it is in and the point farthest away is too fast. The former wants to into a lower orbit while the latter wants to go into a higher orbit.

If I correctly understood the video linked above, the primary cause is actually due to the tidal acceleration (e.g. moon's gravity) of objects on sides 1 and 3 (see diagram below), relative towards the earth's surface, being mostly radially inward [1]. The majority of the ocean water along the sides of Earth is being pulled in very slightly, and in aggregate across the massive surface of the ocean, this results in enough pressure to push up the water at sides 2 and 4. Tides are pushed up due to pressure, not pulled up.

The analogy they used is that tides are more like a pimple being squeezed than taffy being stretched.

[1] See timestamp 4:45 in the video: https://www.youtube.com/watch?v=pwChk4S99i4&feature=youtu.be...

---

Diagram:

   1
 4 E 2      M
   3

E = Earth

M = Moon

Numbers = 4 "sides" of the Earth, relative to the Earth-Moon line

It seems this would made the effect from the icebergs bigger rather than smaller, because the gradient decays by r^3 instead of r^2, so the distance is more important?

Like, the gravitational acceleration is a = GM/r^2 while the gradient is da/dr = -2GM/r^3

So for moon vs glacier at 1000km you'd get

- 2 * (Gravitational constant) * (mass of moon) / (391184 km)^3 = - 1.638×10^-13 reciprocal seconds squared

- 2 * (Gravitational constant) * (1e19 kg) / (1000 km)^3= -1.335×10^-9 reciprocal seconds squared

It's the gradient applied over the whole ocean that causes the tides. In other words, the forces are not enough to create any kind of local change in the depth of the ocean. It's not a gravitational "pulling" as we're accustomed to think about, but more of a global squeezing of water from that gradient applied to the entire ocean. I'll have to give some more thought to the idea of a gravity source on the surface of the earth, but I doubt it would work the same way (we're comparing a relatively small mass in a concentrated location on the earth with that same mass distributed mostly evenly over the earth).

Nothing of this disproves the effect of the polar ice. The forces still apply, they're just not shifting daily.

> The forces still apply, they're just not shifting daily.

No, the forces are completely different. If we have an object on the surface of the earth that has enough mass to roughly produce the same nearby gravitational acceleration as that felt by the moon (which is minuscule and undetectable by most instruments), that object would not produce changes in ocean levels as we see with the moon. Again, the oceans are not rising/falling due to the moon's gravity pulling on them. It only happens because the moon is far enough away that its tiny gravitational acceleration on the earth is (1) felt everywhere on earth, and (2) felt everywhere on earth in slightly different amounts.

For a smaller, closer object (even with similar nearby gravitational acceleration), the tidal forces will not be the same because that gravitational acceleration will fall off to near zero in a very short distance.

You are mixing tidal forces with local attraction forces due to ice. Even though the forces due to ice are not felt everywhere in the planet, they do have an effect that can be calculated, and it is stronger in the body of water closer to the poles. The result of this force causes water attraction in the polar regions. So the effect that is felt in other parts of the planet is not due to the gravity force, but due to the displacement of water happening in polar regions - after all the water needs to go somewhere.

I was originally responding to the claim that "it's still 524 times higher than the effect of the moon's gravity which creates the tides" - that's why I mentioned tidal forces. If the ice creates that much direct, local gravitational attraction[1], then my point is we shouldn't be comparing it to the moon at all (because the forces involved are not the same as those involved with the moon and tides).

[1] Even the claim about the ice sheet (and its melting) contributing significantly (via gravity) to global sea level change seems dubious since, as noted elsewhere in this discussion, the Earth Gravitational Model appears to be affected much more by factors other than ice sheet thickness or surface features.

As you said, it's the gradient which matters. The gradient determines how much the sea level changes over a distance. But, the sea level change is distinct from the tides. The difference in water level between two connected locations at the same moment in time is the same for the ocean and the lake.

The video you linked to compares lakes and oceans because the lunar tides vary with time. The lake level difference between Cleveland and Buffalo at 6 will be the same as the sea level difference between New York and Providence at ~5:30. You need to compare your sea level to the sea level a quarter of the way around the world to understand why your local sea level changes from 6:00 to 12:00.

Hmm, but a water molecule 100 km from an Arctic ice sheet is also experiencing the pull of an "equal" weight of water 100km the other direction, albeit ever so slightly offset angularly.

The lunar system is seemingly much less symmetrical but we still get some amphidromic points (points of zero tidal range) and neep tides (lowest "high" tide) can be very small.

That pull would be there regardless though.

The interviewee is talking about ice on land (Greenland and Antarctica), not about ice in the ocean. If the ice on land melts, then those water molecules migrate away from Greenland because they drop to sea level. That loss of mass would happen regardless of the gravitational pull of water 200 km away and would change the gravitational gradient of the water 100 km away.

Another way to think of it: there's not an "equal" weight of water above Greenland because it's raised above sea level by the land. The weight of rock underneath the ice sheet needs to be included as well.

This is the answer which makes the most sense to me.

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