![]() ![]() Oh dude.Why-oh-why did you start bloging about astrophysics? At least, lok up some fact, like how may years did it take for the Moon to get tidally locked. Like we often say in banking about our financial models, "garbage in, garbage out" - our projections are only as reliable as our inputs! Other than for the moon, $Q$ and $k_2$ are extremely poorly known for other satellites in the Solar System, which explains our difficulty predicting tidal locking in satellites we can't directly observe. A satellite's Love number is a function that relates a satellite's density, surface gravity, and rigidity to its susceptibility to tidal forces Love, whose work covered the mathematical theory of elasticity. $k_2$ has nothing do with romance, it's named after the mathematician Augustus E.H. But the transfer isn't perfect, some of angular moment ends up being dissipated as heat due to friction from the movement of the Earth's oceans. Basically, angular momentum is being transferred from Earth's rotation to the moon's revolution, and as with everything in physics, angular momentum must be conserved. I found $Q$ to be super complicated, but here's my best crack at explaining it: it's a known fact that the moon is gradually accelerating and drifting away from the Earth, due to the same forces that cause high tide and low tide in our oceans. That explains why the moon locked so quickly but the Earth will take an eternityįinally, while all the other terms are relatively commonplace units from math and physics, $Q$ and $k_2$ are unique and very interesting: ![]() Earth is larger than the moon, which should make it lock faster, but it's so much further from the Sun than the moon is from the Earth that the distance factor significantly outweighs all others. All else equal, smaller and more distant satellites take longer to lock. I know the formula's crazy, I have no idea how it's derived, but don't let that scare you away because there are just a few simple takeaways I'm trying to highlight - notice how the terms $a$ and $R$ are raised to the 6th and 5th powers! Two enormous factors that determine tidal locking timescale are 1) distance between the satellite and the central body and 2) the size of the satellite. But here's the formula that describes the timescale of tidal locking: It's actually an exceptionally difficult phenomenon to predict (almost as hard as projecting future cash flows at my job in investment banking, haha!). But it's a question of time - while the moon probably took only about a thousand years to become tidally locked (a blink of an eye in astronomical time scales), the Sun will probably expand and die (destroying the Earth with it) long before our planet becomes tidally locked. So then the next logical question to ask is, why are some satellites tidally locked but not others? After all, the Earth isn't tidally locked to the Sun, otherwise one hemisphere would see perpetual day while the other experiences endless night (what a strange world that would be!) Here's how it works - any imperfectly spherical satellite will eventually become tidally locked by the gravitational lasso described above. One level deeper - what about the Earth and the Sun? In fact, the pull of the moon is so strong that the ground itself rises up 30 cm, about a foot, as it passes by.Confused? Don't be - it's a concept that's hard to explain in words but easy to visualize in motion. Astronomers call this tidal locking, and happens because of the gravitational interaction between worlds.Īs you're aware, the moon is pulling at the Earth, causing the tides. Pluto and Charon are even stranger, the two worlds are locked, facing one another for all eternity. All major moons of Jupiter and Saturn show the same face to their parent. The moon isn't the only place in the solar system where this happens. It's always turning, showing us exactly the same face. If you could look at the moon orbiting the Earth from above, you'd see that it orbits once on its axis exactly as long as it takes to orbit once around our planet. As you know, our modest moon only shows us one face. Look again tomorrow, and you'll be able to see… the exact same things. ![]() ![]() Isn't it beautiful? Take out a nice pair of binoculars, or a small telescope tonight and you'll be able to see huge craters and ancient lava plains. ![]()
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