Time for an accurate 3-D simulation, accounting for Newtonian gravity, a hydrosphere, and an orbiting point source. There must be a few out there already, of course; but I'm thinking of something simple and user-friendly. Adjustable distance, density, a solid core, and (maybe) viscosity would be nice; implementation in JavaView, say ... Any volunteers? WFL On 2/12/14, Bill Gosper <billgosper@gmail.com> wrote:
Thank you Scott! I couldn't have managed it without profanity. Anyone living on an East Coast barrier island knows that the surfside tide floods just as the Full Moon pops over the horizon, *exactly* the opposite of those stupid bulging blob illustrations!
What is it that makes water so susceptible to exogenous gravity? Lower density? Lower viscosity? Then why aren't there huge tides in the atmosphere?
Gravity *gradient* and "solid" tides rule. Not all of the great sloshing ocean of truth eluded Sir Isaac. But it sure eluded most of his successors. --rwg
ScottH>On 2014-02-11 15:25, Huddleston, Scott wrote:
I think this link is a typical incomplete and rather misleading explanation of tides. It doesn't even suggest the solid tides that earth experiences, much less hint at an explanation for them. Nor does it suggest or begin to explain the asymmetrical ocean tides.
It's all gravitational gradient, experienced equally by solid earth and liquid ocean. Tidal forces stress solids and liquids equally. The reason ocean tides are much bigger than solid earth tides: the tidal gradient has a component normal to earth's surface (which lifts or lowers), and a component tangent to earth's surface (which causes water, but not the semi-rigid earth, to flow). If it were not for the tidal-induced water flows (away from the tidal "equator" and toward the tidal "poles"), ocean and earth tides would be almost indistinguishable and we wouldn't notice them.
Re symmetry of near/far tides: IIRC, the ratio of solar : lunar tidal effects is about 4 : 9. Also, tidal effects are proportional to d^3, where d is the earth-moon (or earth-sun) distance. Given the much farther earth-sun distance, the 4/13 solar tidal near/far component is pretty close to symmetrical. The much close earth-moon distance makes a stronger tidal gradient, and (I think) is the biggest factor in asymmetrical daily tide. I get a back-of-envelope estimate of about 1.066 near vs. far for the 9/13 lunar tidal effect, using .25M miles as rough earth/moon distance and 4K miles as rough earth radius.
I make no claim having a good explanation for K-12 level. And I welcome any clarification or correction to any of the above.
Thanks, - Scott
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Tuesday, February 11, 2014 2:35 PM To: math-fun Subject: Re: [math-fun] atomic clocks & gravitational time dilation
This explanation from the text Mike sugggests is the same explanation I've long heard from reliable sources:
----- * Water on the side of Earth facing the moon is pulled hardest by the moon's gravity. This causes a bulge of water on that side of Earth. That bulge is a high tide.
* Earth itself is pulled harder by the moon's gravity than is the ocean on the side of Earth opposite the moon. As a result, there is bulge of water on the opposite side of Earth. This creates another high tide.
* With water bulging on two sides of Earth, there's less water left in between. This creates low tides on the other two sides of the planet. -----
But I'm curious:
* Are the tides on the sides of the earth nearest and farthest from the moon symmetrical?
* If so, why (since the reasons given for those tides are different) ?
--Dan
On 2014-02-11, at 2:17 PM, Mike Stay wrote:
On Tue, Feb 11, 2014 at 2:41 PM, Bill Gosper <billgosper@gmail.com> wrote:
PS, has anyone ever found a correct explanation of tides in a middle or high school text?
http://www.ck12.org/earth-science/Tides/lesson/Tides-Basic/
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun