Question about Moon's gravitational effect on tidal bulge

[jeffinbath]

TL;DR Summary

I am thinking only about that tidal bulge on the side of the Earth OPPOSITE to the moon and the nature of gravitational fields.

Am I correct in thinking that the gravitational field of the moon passes straight through the Earth as if in a vacuum, to produce a tidal bulge on the opposite side to where the moon is, while the Earth’s much stronger field cannot actually bend or modify it as it passes through but can only add to it or counteract it in effect?

 

[Baluncore]

That is correct. In classical physics, gravity adds linearly, and radiates straight through matter at the speed of light, as if the matter was not there.

 

[jeffinbath]

Thank you for that clarification.

 

[Ibix]

That is correct. In classical physics, gravity adds linearly, and radiates straight through matter at the speed of light, as if the matter was not there.

That's not quite right. In Newtonian physics gravitational fields do add linearly and are not affected by anything else, yes, but they do not have a propagation speed. In relativity gravitational fields do not add linearly, although the error from pretending that they do is utterly negligible for weak fields like Earth's. That they propagate at the speed of light is one of those things that you hear a lot, but pinning down exactly what it means turns out to be quite tricky. Certainly gravitational waves propagate at the speed of light.

So the gist of your answer I agree with, but the details are based on a slightly uncomfortable mix of models.

 

[Arjan82]

Be sure to check this video about how tides really work though:

 

[A.T.]

Be sure to check this video about how tides really work though:

The video (at 4:10) dismisses the differential gravity along the Eath-Moon line (stretching) as irrelevant to the tides, and attributes them mainly to the radial nature of the Moons field (squeezing).

How would you test this argument quantitatively? The following comparison comes to mind:

a) Pure stretching by a field with parallel field lines and magnitude falling off, so the different between Moon nearest and furthest point are the same as in reality

b) Pure squeezing by a field with radial field lines from the Moon's center and constant magnitude that matches the Moon's gravity at the center of the Earth in reality.

Would effect b) really be so much bigger than a) ?

 

[Vanadium 50]

The moon pulls the near side bulge towards it. It also pulls the (nearer) body of the earth towards it, leaving the far side bulge behind.

 

[A.T.]

The moon pulls the near side bulge towards it. It also pulls the (nearer) body of the earth towards it, leaving the far side bulge behind.

It also pulls the far bulge, but less than the Earth. And it pulls the Earth less than the near bulge. That is the "stretching" effect, dismissed by the video is irrelevant compared to the radial field's "squeezing" effect.

 

[Arjan82]

The video (at 4:10) dismisses the differential gravity along the Eath-Moon line (stretching) as irrelevant to the tides, and attributes them mainly to the radial nature of the Moons field (squeezing).

How would you test this argument quantitatively? The following comparison comes to mind:

a) Pure stretching by a field with parallel field lines and magnitude falling off, so the different between Moon nearest and furthest point are the same as in reality

b) Pure squeezing by a field with radial field lines from the Moon's center and constant magnitude that matches the Moon's gravity at the center of the Earth in reality.

Would effect b) really be so much bigger than a) ?

The way I understand it is that it is not just the size of the force, but also the direction. The squeezing force is in horizontal direction, and because of the vast horizontal stretch of the oceans the pressure can really build. This is what in the end causes the bulging of the ocean (and not of lakes, since they are just way smaller).

 

[Baluncore]

That's not quite right.

I totally agree.
I tried to provide a simple framework for analysing tides, in less than two lines. By referring to the 'speed of light', I was conveying that the presence of Earth does not delay the gravitational potential fields that propagate through the Earth, while avoiding instant communication.

The term 'tidal bulge' has two meanings to an Earth scientist. There is the pretty much instant 'solid Earth' tidal bulge, then also the 'ocean tides' that are significantly delayed by the horizontal flows and resonances in the fluid that moves around in the relatively shallow, connected puddles on the surface. The OP did not specify which bulge was being discussed.

The solid Earth tide should be studied first, followed later by the complexity of the ocean flows. It really confuses things when the two are mixed in the first analysis.

 

[A.T.]

The squeezing force is in horizontal direction,

I assume that by "horizontal direction" you mean tangential to the Earth's surface. I agree that this the most relevant direction to move water around, and thus cause the ocean tides.

But I think that calling the surface-tangential component "squeezing" is a complete misnomer. Especially if you differentiate it from "stretching", because the stretching due to differential pull also has a surface-tangential component, at places that aren't on the the central Earth-Moon line.

To me the only definition that makes sense here is:
squeezing : tidal force component perpendicular to the central Earth-Moon line.
stretching : tidal force component parallel to the central Earth-Moon line.

The surface-tangential tidal force (relevant for moving water around) has obviously components of both, and their relative contribution depends on location.

 

[vanhees71]

That is correct. In classical physics, gravity adds linearly, and radiates straight through matter at the speed of light, as if the matter was not there.

If by "classical physics" you mean "Newtonian/non-relativistic physics" then gravity is described as an action at a distance, i.e., by a static central two-body potential,
$$V(\vec{x}_1,\vec{x}_2)=-\frac{\gamma m_1 m_2}{|\vec{x}_1-\vec{x}_2|},$$
i.e., "gravity" doesn't "radiate" in any sense.

Within relativistic physics the gravitational interaction is describe by GR and the gravitational field is reinterpreted as a dynamical spacetime geometry. Here indeed the gravitational field propagates at the speed of light, but it's not a linear field theory anymore. GR is also a classical field theory. There's no satisfactory quantum theory of the gravitational interaction found yet.

 

[sophiecentaur]

Within relativistic physics the gravitational interaction is describe by GR and the gravitational field is reinterpreted as a dynamical spacetime geometry. Here indeed the gravitational field propagates at the speed of light, but it's not a linear field theory anymore. GR is also a classical field theory.

Aren't we giving too much attention to Non-Newtonian relativity, here. Nearly every process in the Solar System is described quite adequately using Newtonian Physics so we could be misleading newcomers by even touching GR.

The guy on that YouTube video is too manic / breathless for me to listen to him sensibly. It's almost as if he's had DSP applied to make the video cost less. Saying things faster doesn't make them more correct or understandable.

My problem here is that no one seems to be including (or linking to) the orbital situation. It's obvious (I think) that, if you took non orbiting situation and held the Moon near the Earth and then let go, the sea nearest the Moon would accelerate towards the Moon faster than the Earth's CM and faster still than the sea on the far side. The sea on the far side would be 'left behind', producing two bulges. That experiment isn't going to last long (not 4Ga, at least).

To account for the continuing bulges you have to move the Moon at an appropriate tangential velocity to keep all the components in circular orbits. The forces on each bit will cause almost the right speeds and periods for this to happen and it does. I think it would be a good thing to introduce the notion of superposition of the fields in the arguments so far. All the fields and accelerations produce the effect of the same bulges but they are orbiting around the barycentre of Earth and Moon.

The Movie makes a good point that tidal bulges can only occur in bodies of water where there's enough water available to flow around to form them. Moreover, the Earth's rotation will 'average out' the bulges (to some extent) over the day. The tides in the Med are pretty mild because there's not much water available to allow East West flow but there's a fast flow through the strait of Gibraltar. But nothing is simple because the Med has other currents than tidal at work. Salinity and temperature cause currents of the same magnitude as the tide. This link diverted me for a while and it makes good reading. Nothing is simple and the only workable model would have to be of an Earth which is covered in deep seas.

 

[Arjan82]

Aren't we giving too much attention to Non-Newtonian relativity, here. Nearly every process in the Solar System is described quite adequately using Newtonian Physics so we could be misleading newcomers by even touching GR.

I totally agree.

The guy on that YouTube video is too manic / breathless for me to listen to him sensibly. It's almost as if he's had DSP applied to make the video cost less. Saying things faster doesn't make them more correct or understandable.

It also doesn't make him less correct... It is a style form which you see often in these kind of science videos. You may like it or not, but that's totally besides the point... It is aimed at a younger public for who'm life's still short ;).

My problem here is that no one seems to be including (or linking to) the orbital situation. It's obvious (I think) that, if you took non orbiting situation and held the Moon near the Earth and then let go, the sea nearest the Moon would accelerate towards the Moon faster than the Earth's CM and faster still than the sea on the far side. The sea on the far side would be 'left behind', producing two bulges. That experiment isn't going to last long (not 4Ga, at least).

I don't see your point here. Why is dynamics important here? If you keep both the earth and moon at the same distance but otherwise stationary (which you could only do in theory of course) I would expect the same tidal effects. If anything the heights become lower due to dynamics because the bulge is always lagging due to friction. Or what am I missing?

The tides in the Med are pretty mild because there's not much water available to allow East West flow but there's a fast flow through the strait of Gibraltar. But nothing is simple because the Med has other currents than tidal at work. Salinity and temperature cause currents of the same magnitude as the tide. This link diverted me for a while and it makes good reading. Nothing is simple and the only workable model would have to be of an Earth which is covered in deep seas.

If you look at local tides, sure, you need to include all kinds of local effects, and these can become quite significant. However, for a global understanding of the tides, what drives them in the first place, I don't think that's necessary.

 

[sophiecentaur]

Why is dynamics important here?

I'd say it's important for visualisation because, in the static start situation there would be / have been no distortion until some time has passed. The bulges would grow and, as you say, friction would affect their sizes.
If you just hold Moon and Earth in position then how would there be any bulge away from the Moon? The nearside bulge would stay there with equilibrium for the water in the bulge but forces on the far side water would only be in the direction of Earth / Moon. You have to 'let go' for the far side bulge to form.

 

[pikpobedy]

In tides two things are important. The earth is made of materials that do not distort instantly to the forces applied. The earth rotates faster than the moons orbital velocity; as such the near tidal bulges are dragged away from the moon and transfer energy to it, the far tidal bulges vice versa but weaker.
The earth is not a point object. As such the surface closer to the moon would orbit faster than its center of mass, the surface farther would orbit slower. In other words the orbit tries to shear the earth apart. This type of force is a type of explanation for tidal forces. It's all linked inverse square laws, material science and diffrences in velocities. Other examples, the moon is tidally locked to the earth, its rotation and orbit are the same albeit the effects of perigee and apogee cause velocity variations which are perceived as librations.