Eclipse City (APOD 2009 August 20)

[NoelC]

BUT, but, but but,
But the above effect is from reflection, and should cause diverging rays.

The building is convex in one dimension, but straight in the other. Not at all like the convex mirror to which you refer.

-Noel

[Chris Peterson]

This circular building may be considered as a convex mirror, with many parallel light beams striking it.
The mirror would cause the reflected beams to diverge.
The points at which the beams strike a plane in front of the mirror would not be equidistant, but spaced further apart, the further they are from the central beam.
So will the building.
Yet the reflected images are seen as a regular grid.

But they don't form a regular grid. Circumferentially, they are wider apart as they get farther from the building- as you would expect since the windows are at different angles (similar to a convex mirror, but not quite the same since this effect depends on individual flat panes- more like a mirror ball). Radially, the images are equally spaced regardless of distance from the building- again, as expected since any column of windows lies on the same plane.

[Redbone]

1) Why are there two high tides and two low tides per day?

The tidal force of the moon pulls more strongly on what is closer. The moon pulls up water on the near side of the Earth relative to the solid Earth. The moon pulls up the solid Earth relative to the water on the far side of the Earth. This creates two tidal bulges on opposite sides of the Earth. The solid Earth rotates slightly less than once relative to these two bulges each day.

Correct, however I prefer to look at it this way: The moon does not orbit the earth because the earth floats freely in space. The earth moon pair orbit, together, a central point. Thus the moon creates a gravitational bulge on one side and centrifical force a bulge on the other.

2) Why do we skip one tide every ~28 days?

The moon revolves around the Earth once every ~29 days in the same direction that the Earth rotates, so the moon crosses a given meridian on the Earth only ~28 times in ~29 days. Thus the moon rises and sets nearly an hour later every day, and thus the interval from low-to-high or high-to-low tide is somewhat longer than 6 hours, and the interval from high-to-high or low-to-low tide is somewhat longer than 12 hours. We actually never "skip" a tide; there are just slightly less than 2 (by a factor of ~28/~29) tides per day.

Exactly, and if I remember correctly this "missing" tides occurs once a week, not once a month, my mistake.

3) Why does the high tide occur ~two hours after the moon's rise, well before the moon is directly overhead?

It takes a while for the water (many many gallons) to move in response to the tidal pull. The Earth keeps rotating, and the water never catches up. The continents keep the tidal bulges from traveling continuously around the Earth, so instead the ocean tides slosh back and forth between the eastern and western shores. The time lag varies greatly from one ocean, shore, or inlet to another; that's why we need tide charts. Some locations are completely 90° (6+ hours) out of sync with the position of the moon, some even more. In your example, the tide isn't 4 hours early; it's 8 hours late.

In the case of a river, think of a standing wave in a river rocking from the upstream tidal limit to the ocean end and driven by the ocean water level; picture the tidal waters from the ocean not actually making it way up a river themselves, but the water coming from upstream piling up when the level downstream is high and flowing out when the level downstream is low. I once lived over 100 miles north of NYC on the Hudson River and we had tides right up to the first lock on the Erie Canal. Now I live near Washington, DC which is way up the Chesapeake Bay and then way up the Potomac River from the ocean, and we have tides past both Beltway crossings right up to Great Falls. All of these tides are completely out of sync with the visual position of the moon.

Additionally, when the moon is not new or full, the vector component of the tidal force contributed by the sun is either ahead of or behind the component contributed by the moon, which also changes the lag time forward or backward as we go through a lunar month.

Right idea, but it is my understanding that the moon orbits the earth in the same direction as the earth’s rotation. The earth rotates much faster than the moon orbits and thus it is the rotation of the earth that pulls the tidal bulge along way ahead of the moon’s gravitational vector.

[apodman]

the moon creates a gravitational bulge on one side and [centrifugal] force a bulge on the other.

The tidal force is a differential element of the gravitational force that results from gravity acting at different distances, and the tidal bulges are caused by tidal forces that are gravitational in origin. The centrifugal component resulting from the Earth rotating off center as part of the Earth-moon system tends to decrease the size of the bulge on the side of the Earth facing the moon and tends to increase the size of the bulge on the side of the Earth opposite the moon only slightly.

this "missing" tides occurs once a week, not once a month, my mistake.

Yes, if we "miss" one day's worth of tides per lunar month, that's four "missing" tides (two highs and two lows) per lunar month, or about one per week.

it is the rotation of the earth that pulls the tidal bulge along way ahead of the moon’s gravitational vector.

That is a sort of backwards view of the time lag between the passage of the moon and the next high tide. The tidal bulges in Earth's open waters are an idealized view of the result of tidal forces on an Earth with all ocean and no continents. On the real Earth, tides are low-frequency long-wavelength large-displacement waves. These waves are driven by the gravitational pull of the moon and the sun. They stabilize in a standing pattern whose timing is determined by the characteristics of the basins that bound them. Tides flow to the north, south, and east (perpendicular to and opposite the direction of the passage of the moon) as well as to the west (in the same direction as the passage of the moon).

[Redbone]

it is the rotation of the earth that pulls the tidal bulge along way ahead of the moon’s gravitational vector.

That is a sort of backwards view of the time lag between the passage of the moon and the next high tide. The tidal bulges in Earth's open waters are an idealized view of the result of tidal forces on an Earth with all ocean and no continents. On the real Earth, tides are low-frequency long-wavelength large-displacement waves. These waves are driven by the gravitational pull of the moon and the sun. They stabilize in a standing pattern whose timing is determined by the characteristics of the basins that bound them. Tides flow to the north, south, and east (perpendicular to and opposite the direction of the passage of the moon) as well as to the west (in the same direction as the passage of the moon).

I believe that this is incorrect. It is indeed the rotation of the earth which pulls the tidal bulge ahead an hour or two and speeds the orbit of the moon while slowing the rotation of the earth. But a fascinating and well thought out discussion, thanks.

http://blogs.physicstoday.org/update/20 ... nd-io.html

BTW, I am always surprised at how many people, and scientists, will mangle the answer to the question "What causes the phasing of the moon?" You can't ask it online, of course, but face to face. It was this question, that I asked myself, many years ago at the beach, that started my thinking about all this. I worked out most of the above answers, and many more, on my own over a period of years as a sort of hobby.

[apodman]

I believe ... indeed the rotation of the earth ... pulls the tidal bulge ahead an hour or two

The Earth rotates west-to-east. The tidal bulge moves east-to-west. There is no way this can be described as pulling unless you are talking about pulling opposite the moon's gravity and opposite the bulge's direction of travel. Maybe you could loosely call it dragging in the opposite direction. The Earth's tidal bulge and the moon do pull on each other gravitationally to affect the period of the Earth's rotation and the period of the moon's orbit over the long term, but talking about the Earth pulling on its own tidal bulge creates the wrong impression - it is better to say that the dragging of Earth's tidal bulge against the moon's pull on it comes from inertia (the same rotational inertia it shares with the rest of the rotating Earth).

Ask yourself how high tide occurs on the western shore of a continent. The water does not cross the continent from the ocean on the eastern side of that continent. It flows west-to-east from the open ocean, counter to the motion of the idealized tidal bulge. With the exception of the southern ocean that runs all the way around Antarctica (and in the waters surrounding the north polar ice cap), water tides go back and forth, not around and around. Tides in the Earth's crust go around and around.

---

Referring to the link you provided ...

Because Earth's rotation pushes the tidal bulge slightly ahead of the Moon–Earth line, ...

The word "pushes" is in this case is not much better at creating the proper image than the word "pulls" would be. In any case, it refers (correctly) to the bulge being east of the moon-Earth line, and "ahead" means ahead in the direction of the Earth's rotation - to the east. You are using "ahead" in the opposite sense to mean (incorrectly) that the bulge passes a given meridian earlier than the Moon passes. In actuality a westward-moving bulge located west of the moon-Earth line would pass a given meridian earlier than the moon passes, whereas the westward-moving bulge described in your link (located east of the moon-Earth line) passes a given meridian later than the moon passes. Returning to my earlier phrasing: from the point of view of an observer on Earth, the moon leads and the bulge lags. In your logic also be careful to remember that it is the ~daily apparent motion of the moon (not the ~29 day orbital motion of the moon and revolution of the Earth-moon system) that has the same average period as the tides.

[Redbone]

Well I learned two new things today, that’s pretty good. I know that the overall mechanisms of the tides are too complex for a casual discussion, but still the basics should be attainable. I have found that NOAA has the best info that I could find on the internet.

1) Although the moon produces a tidal bulge, as we discussed, this effect is too small to account for ocean tides. The effect which produces ocean tides is called the Tractive Force, described here:

At any point on the earth's surface, the tidal force produced by the moon's gravitational attraction may be separated or "resolved" into two components of force - one in the vertical, or perpendicular to the earth's surface - the other horizontal or tangent to the earth's surface. This second component, know as the tractive ("drawing") component of force is the actual mechanism for producing the tides. The force is zero at the points on the earth's surface directly beneath and on the opposite side of the earth from the moon (since in these positions, the lunar gravitational force is exerted in the vertical - i.e., opposed to, and in the direction of the earth-gravity, respectively). Any water accumulated in these locations by tractive flow from other points on the earth's surface tends to remain in a stable configuration, or tidal "bulge".

http://tidesandcurrents.noaa.gov/restles3.html

2)The two main reasons for tides being ahead or behind of the moon are:
a)The earth rotating inside the envelope of tidal forces.
b)The Sun’s tidal component either priming or lagging the Moon’s tidal component.

Apparently, because of the tractive force, ocean tides are not “pushed” or “pulled” by the rotation of the earth the way solid deformation tides are.

http://www.co-ops.nos.noaa.gov/restles5.html

[apodman]

I know that the overall mechanisms of the tides are too complex for a casual discussion, but still the basics should be attainable. I have found that NOAA has the best info that I could find on the internet.
http://tidesandcurrents.noaa.gov/restles3.html
http://www.co-ops.nos.noaa.gov/restles5.html

Good links. I have a small bone or two to pick with parts of their presentation, but - as my own slapdash posts show - it's hard for a point to be succinct while being complete and unflawed as well. The alternative, as you point out, is to go beyond the bounds of a casual discussion, which doesn't serve readability very well. So I simply recommend the links, I won't write a book, and I won't ask NOAA to write a book either.