# What factors go into whether a moon or planet is tidally locked?

I was thinking about a different possibilities for habitable planets. And I was wondering what actually causes a planet to be tidally locked? I am assuming it more than chance that the bodies rotation and period are the same.

I started thinking what it would be like to be on a planet that circles a huge star, one that would take earth decades or even centuries for one year. Seasons would be the same for most of ones life etc. I can think of a lot of cool questions for that, but I then thought that maybe the planet would be tidally locked if the star was very large. So what are the things that go into a body being tidally locked? What causes it?

• It seems logical that the relevant afctors are the original angular momentum of the planet, the actual size of the star and the age of the planet, sadly a young planet is less likely to have complex lifeforms on it. – overactor Oct 7 '14 at 13:57
• Eventually, the planet rotation will slow down but without the help from the exterior, it could take billions on year. And even if they have a satellite like the Moon we have, it's still going to take a very long time. I don't have the specific formula, but it would be nice if someone could come up with one about this. – Vincent Oct 7 '14 at 15:08
• The other things is : if your planet is close enough from the star, it will become naturally tidal locked after only a short amount of time. It is generally so close to the star that life become impossible. Unless you have a very small star like a red dwarf. Then, I think it could be tidal locked and inside the habitable zone. – Vincent Oct 7 '14 at 15:14

There is quite simple formula that will give you the tidal-locking half-time

$$T = 6 × 10^{12}\, \frac{a^6 R \mu}{ (M_s M_p^2)}\; \mathrm{years}$$

• $a$ - semi-major axis, or simply the radius of circular orbital trajectory in meters
• $R$ - satellite radius in meters
• $M_s$ - satellite mass in kg
• $M_p$ - parent planet/star mass in kg
• $\mu$ - rigidity, approximately $3×10^{10}$ for rocky objects and $4×10^9$ for icy ones.

Please note that the prefactor $6 × 10^{10}$ currently used on Wikipedia is very probably wrong, so I provided a more realistic one. (See the discussion.)

The tidal locking is approximately exponential process, so it is very quick at the beginning and gradually slows down. Typical situation is, that planets in the habitable zone are tidally locked for red dwarf stars. Moons are very often tidally locked, unless they are very far from their planet.

Tidal forces primarily. When two bodies are orbiting each other, they're both pulling on each other. However, this pull is not uniform across the entire mass of each planet. On each body, the surface nearest to the other body has more pull than the surface farthest from the other body. This changes the shape of both bodies. Making them a little more oblong. Other factors would be when the internal mass of a body is not evenly distributed. Making one side heavier.

You're correct that it's not chance that the rotation and period are the same. The 1:1 ratio of rotation:period is what results after long iterations of orbits and tidal forces. It's actually a stabilization of a orbital system. For example, the Moon and Earth are still stabilizing. Ever so slowly the rotation of the Earth is slowing due to tidal forces. Eventually making a day on Earth as long a Lunar month (don't worry though, that process is so slow, the Earth and moon will be consumed by the Sun's expansion by then).

There are many questions and nice answers about this over on physics.SE. One example is this one. Which also points towards Wikipedia here. See them for the long answer. The short answer is this. You have a planet, you have a moon. They each have their own gravitational fields that "pull" at the other. This pull is not evenly spread through the planet or the moon so there is some flexing in the planet and the moon as they rotate under the other one. This produces enough friction to slowly decrease the rate at which the other body appears to rotate until the system is tidally locked. This drag means that the net forces in a pair of orbiting bodies is towards a tidally locked pair so it is a stable configuration that can endure other millions of years if not longer.

There are a huge amount of details I am glossing over here but that is what the other references are for.

Since the Earth/Moon system is tidally locked you can see what this flexing looks like by going to the beach and watching the tides. I know scientists sometimes have very unimaginative names for things.