

Tonight will be the longest night in the history of Earth - mocy
http://www.vox.com/2014/12/21/7424371/winter-solstice

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MichaelCrawford
Those diagrams of the tides always show that there is a bulge opposite to the
moon and sun, yet say that both bulges are due to the increased gravity being
nearer to the moon and sun than is the center of the earth.

That never made a whole lot of sense to me.

Actually the bulge on the opposite side of the earth is due to the centripetal
accelleration of the earth as it orbits the moon. Yes, the earth orbits the
moon. Similarly, the sun orbits the earth. While quite small, I expect we
could measure the earth's tidal influence on the sun.

I had to major in astronomy at Caltech before I was able to get anyone to tell
me why the tides bulge on both sides. Even at Tech, no one seemed to grasp
that the earth orbits the moon &c.

~~~
StephanTLavavej
That's incorrect. I majored in CS at Caltech, but I think I can explain this
properly. It doesn't have anything to do with orbiting or angular momentum.

Imagine that only the Earth and the International Space Station exist. The ISS
is doomed because it has stopped orbiting, and is falling straight down.
Inside the ISS, an astronaut has placed 5 marbles in the shape of a plus sign
(center, left/right/up/down). For convenience, the "center" marble is also at
the center of mass of the whole ISS. There's no air or anything to mess up the
results. What happens to the marbles?

Look at the problem from the frame of the Earth. The Earth is exerting a
certain force on the center marble, call it F. The "down" marble is slightly
closer to the Earth, so it experiences a greater force, F + Something. The
"up" marble is slightly further from the Earth, so it experiences a lesser
force, F - Blah. The "left" and "right" marbles experience forces very very
close to F (slightly less, if they're in a straight line, but much closer to F
than F - Blah). However, those forces are directed towards the center of the
Earth, so those vectors have small components directed towards the "center"
marble.

Now that we've figured out the forces, look at the problem from the frame of
the marbles. We're in free fall, so the "center" marble floats motionless. The
"down" marble is going to float further away from the center marble (F +
Something pulls "down" harder), and the "up" marble will also float further
away from the center marble (F - Blah pulls "up" less than everything else).
The "left" and "right" marbles float towards the center.

Using only Newton's laws, this reveals that gravity's behavior over a volume
has a stretching effect in the up-down direction, and a squeezing effect in
the left-right direction. GR confirms this. This effect is the tidal force.

When applied to the Earth and the Moon, this explains the two bulges. The
bulge closer to the Moon is due to F + Something, because that water is being
pulled stronger. The bulge away from the Moon is due to F - Blah, because that
water is being pulled less than everything else.

~~~
dalke
I didn't go to Caltech ;)

It can also be described via a conservation law. If the Earth were frozen
solid, and the Moon+Earth system started up to something like we have now,
then they would be in a stable orbit.

Next, thaw the water. If only one lobe forms then there's a violation of
conservation of angular momentum.

To really see the problem, use the planet "H2O", made entirely of ice, instead
of Earth. Once the ice thaws, which water decides to form the single lobe? If
all of it flows towards the Moon then it wouldn't be a stable orbit.

There can't be zero lobes because the system is asymmetric around the
barycenter. If everything is in equilibrium then the result needs to be
axially symmetric, giving two asymmetric lobes; one towards and one away from
the Moon. (The asymmetry is due to the size of the Earth vs. the distance to
the Moon. It's about 60 radii away, so not that asymmetric, but the near-side
tides will be higher. As another example, a micro black hole orbiting very
close to the water surface will only have noticeable local effects.)

Of course, in real life the system isn't in equilibrium. The Earth isn't
tidally locked to the Moon, the orbits aren't perfectly circular, the bodies
wobble and aren't spherical, etc. and the sea isn't deep enough for this lobe
wave to travel, so it isn't true that there are two bulges.
[http://physics.stackexchange.com/a/121858](http://physics.stackexchange.com/a/121858)
gives a lovely explanation and
[http://www.lhup.edu/~DSimanek/scenario/tides.htm](http://www.lhup.edu/~DSimanek/scenario/tides.htm)
works through many "Tidal Misconceptions".

As a result, some places have more than two tides, like
[http://www.southamptonvts.co.uk/live_information/tides_and_w...](http://www.southamptonvts.co.uk/live_information/tides_and_weather/high_and_low_tide_times/)
, with High Water, Second Tide, and Low Water.

P.S. I hope I got that correct! The last time I did this sort of analysis was
20 years ago. And personally, my intuition is based on the stretching force
interpretation. One of the mechanics problems I worked out then was to explain
why tidal forces radially align the long axis of a spacecraft.

------
danieltillett
It was actually the longest day in history where I am :)

