Tuesday, August 31, 2010

Dark Side of the Moon

That title sounds cool, but should be amended to read "Far Side of the Moon". The moon rotates around the earth and is "locked" so that we only see one face of it. My sister and bro-in-law were wondering what the explanation was for this. I took a crack at it, and had a tough time convincing them. So, I've studied up and am writing it here for them.

Why is the moon locked facing the earth? I looked this up years ago and learned that it is basically due to what's called "tidal locking". From the wikipedia article on tidal locking, "A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner." Tides basically cause an spherical body (like the moon and earth) to be stretched in the direction of it's orbital partner.

How is it that something related to tides could cause a celestial dance between giant objects like the earth and moon? Don't tides just make the oceans go up and down? The image below gives some idea of what's happening on earth.


Tidal bulges. Earth's oceans are stretched toward the moon on the side facing the moon and away from the moon on the opposite side. The diagram above also shows earth's rotation dragging the stretched shape slightly counterclockwise such that the bulge "leads" the moon.

The moon is also stretched like the earth, and the stretched direction always points to the earth. This is because when the stretched direction is not pointed at the earth, there is a correcting force that rotates the stretched direction to point at earth.

When the moon was liquid, it was bulged, and rotated "under the bulge" just like the earth does. As it cooled and froze, it's rotational energy must've tried to move the bulge from its orientation toward earth, but the corrective force mentioned won and we have our tidally locked moon.

Cool, huh? My dad asked the tough question of why the stretched shape is formed. For example, why doesn't earth just have a single bulge on the side facing the moon? Why another bulge on the opposite side? How the devil does this really work? Ike Newton was one of the first (if not the first) to understand this scientifically. The wikipedia page on tidal force is excellent. A summary follows.

Tidal forces diagram. Moon's gravitational forces (red arrows) are acting on the earth (the black sphere).

The red arrows in the top pane shows the moon's gravity which is weaker farther from the moon. The earth (the black sphere) is in free fall. Thus, it makes sense to subtract off the average gravitational force acting on the earth. This is done in the lower pane. Now you can see the forces that cause the tidal stretching.

Keep in mind that the tides are only ~10 feet. This is a tiny bulge for an object with a radius of 20 million feet.

Another cool thing I learned in the article is that the debris that makes up Saturn's rings would have condensed into moons if not for tidal forces exerted by Saturn.


Cassini image of Saturn.

Tidal forces are stronger closer to the source of gravity. Moons formed around Saturn when the debris was far enough away that tidal forces didn't disturb the formation.

4 comments:

Janie said...

This is a good explanation, and I even think I sort of understand it! Interesting that proximity of the rings kept moons from forming around Saturn.

Anonymous said...

eric,
c my e mail but i think i cracked the code.
those little vector arrows on the far side of earth from sun are due to ocean inertia and to solar gravity.
in fact the effect from the moon actually tends to cancel these vectors and reduces far side tides which would in fact be higher if moon gravity on the far side were zero.
what do i miss?
steve

Unknown said...

I've always wondered that too. Here in Florida a 4 foot change from high to low is our biggest difference. On the gulf we get high high and low high tides which really complicates the math.

Eric said...

Robert -- The sun puts a bulge in the earth too. So when the sun and moon are stretching the oceans in different directions, you get two high tides (at different heights) and two low tides (different low marks). These are semi-diurnal, right? I see you're a hydrologist, so probably know this stuff like the back of your hand.