Liberal Arts Blog — Moon Math — Synchronous Rotation, The Tides, The Phases

John Muresianu
4 min readJun 10, 2024

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Liberal Arts Blog — Monday is the Joy of Math, Statistics, Shapes, and Numbers Day

Today’s Topic: Moon Math — synchronous rotation, the tides, the phases

How precise and how detailed should an 8th grader’s understanding of tides and the moon phases be? How about a 12th grader? How about a 5th grader? a 3rd grader? How about a Harvard graduate?

Have you ever wrestled with this challenge and come up short? Did you ever claw your way out of a dark tunnel of confusion to see the light of understanding? Did a great teacher ever lead you to the light? How?

Could AI help here? Could AI put all this into a sonnet form and set it to a catchy folk tune?

Experts — please chime in. Correct, elaborate, elucidate.

SYNCHRONOUS ROTATION: the moon spins on its axis exactly one time for every rotation of the earth — why? so what? what does a man on the moon see?

1. “It is the natural consequence of tidal friction.”

2. “The Moon has tidal bulges similar to those on Earth. It is thought that the Moon once rotated much faster than it does today.”

3. “The friction created by the stretching and squeezing of the Moon caused the Moon’s rate of rotation to slow down until its rotational period was the same as its orbital period.”

NB: “Most of the far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3.”

“When Earth is observed from the Moon. Earth does not appear to move across the sky. It remains in the same place while showing nearly all its surface as it rotates on its axis.”

WHY ARE THERE TWO HIGH TIDES NOT ONE HIGH TIDE?’

1. The difference in distance between the side of the earth closest to the moon and the side farthest away means that the gravitational force is less on the side furthest from the moon.

2. Remember that in Newton’s gravitational equation the force of gravity is inversely proportional to the square of the distance.

3. The solid mass of the earth is more strongly attached to itself than is the ocean which lags creating the high tide on the far side of the earth.

WHEN IS THE WAXING HALF MOON VISIBLE? THE WANING HALF MOON?

1. The waxing half moon rises at about noon, and sets at midnight.

2. The waning half moon rises at midnight, and sets at noon.

3. If you see a beautiful half moon in the evening, it’s a waxing half moon and it should look like a backward C (ie. a D).

Moon Phases — NASA Science

https://lasp.colorado.edu/outerplanets/math/synchronous_rotation.pdf

Ocean’s Tides Explained

How the tides REALLY work

Libration — Wikipedia

QUOTE OF THE MONTH — Have you made your own Bible yet?

“Make your own Bible. Select and collect all the words and sentences that in all your readings have been to you like the blast of a trumpet.”

- Ralph Waldo Emerson

My spin — then periodically review, re-rank, and exchange your list with those you love. I call this the “Orion Exchange” because seven is about as many as any human can digest at a time. Game?

ATTACHMENTS BELOW:

#1 A graphic guide to justice (9 metaphors on one page).

#2 “39 Songs, Prayers, and Poems: the Keys to the Hearts of Seven Billion People” — Adams House Senior Common Room Presentation, (11/17/20)

#3 Israel-Palestine Handout

NB: Palestine Orion (Decision) — let’s exchange Orions, let’s find Rumi’s field (“Beyond all ideas of right and wrong, there is a field. Meet me there” Rumi, 13 century Persian Sufi mystic)

Last four years of posts organized thematically:

Updated PDFs — Google Drive

YOUR TURN

Please share the coolest thing you learned this week related to math, statistics, or numbers in general.

Or, even better, the coolest or most important thing you learned in your life related to math.

This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.

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John Muresianu

Passionate about education, thinking citizenship, art, and passing bits on of wisdom of a long lifetime.