Boreal B[l]og

“There is a tide in the affairs of men.” (Shakespeare; Julius Caesar)

Eclipse Day on Green Island, off the coast of Cairns, Australia, and by morning twilight I was on the beach, ready. We had arisen at 1 am, were aboard the boat from Cairns at 2 and were on the island by 3. I had plenty of room on the beach, which should have been a warning.

The eclipse began shortly after sunrise, and so did morning high tide, a true spring tide, a king tide.  With a total eclipse, by definition the Sun, Moon, and Earth were lined up and the Moon was near perigee, its closest point to us. I had to rather unceremoniously move inland, apologizing to the locals that I lived in a desert and didn’t appreciate how quickly water levels change with tides. The beach where I had stood was soon several feet under water. The eclipse was stunning; so were the tides.

King tides, a non-scientific term, are high tides when the Earth is closest to the Sun in its orbit (perihelion), which happens to be early January, the Moon is new or full and is close (perigee) to the Earth. The lineup doesn’t have to be perfect. There is one new and one full Moon a month, and for each of about three days for three consecutive months there will be such tides.

Spring tides are when the Sun, Moon and Earth are in alignment (sygyzy), when the Moon is new or full. For a day or two on either side of that alignment, there isn’t much difference.  Both the Sun and Moon pull on the Earth; the Sun has half the tidal effect of the Moon on the Earth. I experienced king tides in Australia for the November 2012 eclipse. A month later, at new Moon, the tides were still higher. The Moon wasn’t in exact alignment with the Earth, but it was closer than it was in November, the Earth closer to the Sun, and proximity overcame the loss of perfect alignment.

Why do tides occur later each day here? Suppose the Moon is culminating (due south) at 9 p.m. and there is a high tide. A day later, at 9 p.m., the Moon, which is constantly moving eastward among the stars, another way of saying it rises later each day, is not quite due south at 9 p.m. It will be some time later, and that average time is about 50 minutes. This is split up into two high tides a day, so each one is about 25 minutes later. Two important disclaimers; first, 50 minutes is not exact; it varies with the season and the Moon’s orbit; second, the configuration of the ocean bottom near the shore affects the time as well.

Every object exerts a gravitational attraction with any other object—your phone with you; two people with each other; Saturn with a car, proportional to the product of the two masses (think of mass* as “stuff”) divided by the square of their distance. We know gravity is universal, but we didn’t always know that until the observed changes in the double star Porrima (in Virgo) over several years showed that gravity worked in deep space as well as on Earth. Richard Feynman once said about a globular cluster of stars, “if you can’t see gravity operating here, you’ve got no soul.”

If the Sun is so large, why is its tidal interaction with the Earth only half that of the Moon, when its gravitational effect is so much more, which is why we orbit around it?  The answer is because tidal forces are inversely dependent not on the square of the distance but the cube, the third power.

Centripetal force directed into a circle is inversely proportional to the distance from the center, or radius; gravitational force is inversely proportional to the distance between two bodies squared; tidal forces are inversely proportional to the distance between two bodies cubed. For those with a calculus background, the rate of change of gravity is the tidal force the same way the rate of change of velocity is acceleration. The derivative of an inverse square, (1/x^2) is (-2/x^3). I find the derivation as beautiful as seeing a king tide right up to the rock wall in Newport.

The Sun, 330,000 times more massive than the Earth, is also nearly 400 times further away than the Moon, so the tidal force exerted by the Moon on the Earth is almost double that of the Sun. We are held in place by the Sun’s gravity; our tides are more a function of the Moon. When it all lines up in early January, all bodies closest to each other, we have a king tide!

If you go to Anchorage, look up the time of the tidal bore in Turnagain Arm. If you are lucky, you may be able to see it and hear it moving southward as a long wave across the arm.

*“If you want to lose weight, go into space. If you want to lose mass, diet.”

This entry was posted on November 7, 2023 at 13:42 and is filed under UNPUBLISHED OUTDOOR WRITING. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.