Tidal Forces

I’ve been thinking a lot about tidal forces lately.  Specifically, I’ve been thinking about the gravitational forces in the earth-moon system and how they affect each other.  There’s more going on than the moon just circling the earth.

The gravitational pull of each body affects the shape of the other.  This is due to a gradient in the gravitational field, a difference in the field’s strength from point to point.  The strength of the moon’s gravitational field is felt the strongest on the side of earth closest to the moon, and weakest at the point furthest from the moon, so you get bulges on both sides.  Despite the fact that the planet is fairly rigid, we get a tidal bulge in the rock that deforms it roughly thirty centimeters each way.  It’s not the kind of thing you’d notice just standing around, but the ground does stretch.

The oceans, however, are not fixed to the planet and have a lot more freedom to move.  The bulges in the water caused by the moon’s pull are a phenomenon we’re more familiar with and are the causes of oceanic tides.  If the earth and moon were fixed in place and we drew a line through the centers of mass of the two bodies, the tidal bulges would fall right along that line.   Of course that’s not actually the case.

The tidal bulges in the water try to stay aligned with the moon’s position.  However, the earth rotates beneath the water at a much faster rate than the moon revolves around the earth.  The surface of the earth rubs against the bottom of the ocean pushing it along.  This has the effect of pushing the water’s tidal bulges slightly forward of where they would otherwise be.  Because all of that oceanic mass has been pushed ahead by the earth’s rotation, it puts a slight torque on the moon, forcing it ahead in its orbit.  Due to this torque, the moon is actually receding from us at the rate of about 2.3 centimeters a year.  If we want to go back to the moon we’d better hurry.  It’s inching away!

You can’t just forget about Newton’s third law: if you push on something, it’s pushing back.

While the earth is rubbing on the bottom of the oceans, forcing it forward and ultimately driving the moon further away, the oceans are actually causing drag on the planet.  Our rotation is slowing.  Our days are gradually getting longer.  Eventually, the earth will be tidally locked to the moon, meaning the same face of the earth will face the moon at all times.  The length of a day would be a month, just like it is on the moon now.  Enjoy these shorter days now.  We’ve only got a few more billion years of them left.

(As a side note, I wonder if a slowly rotating earth would have a smaller magnetic field.  Without the one we have, solar winds would blow our atmosphere off and evaporate all of our water, leaving the earth as dry and dead as Mars.)

As I’ve gotten older it has seemed that the work days have gotten longer.  I think others have felt this as well.  Some people say it’s because I’ve got more responsibilities at work.  I can’t just shut down at five and go home when things need to get done.  Others consider this merely a myth of perception: the work days aren’t longer, they just seem longer.  Now I can show that the workdays are actually getting longer and there is a real, physical reason for it.  It’s because of the damned moon.