# Does more ocean on an Earth analog produce a different rotation period?

Would an exoplanet that has more ocean than Earth rotate at a different speed as a result of this? Would the amount of water impact the weight, gravitational pull, and/or tidal forces and cause a difference in the exoplanet's rotation period? (For simplicity's sake, say, if it was earth-like in every respect other than having more ocean than Earth does at about 70% of the surface area.)

Would an exoplanet that has more ocean than Earth rotate at a different speed as a result of this?

Basically no. Rotation speed, or angular velocity doesn't measurably change with your proposed example.

To explain this in more detail, there's two important concepts. First, is Angular Momentum, (Short explanation or longer) and the 2nd concept is Moment of Inertia.

The basic formula is that Angular velocity (time for 1 full rotation) = Angular Momentum divided by Moment of Inertia. Formulas and explanations are in the link(s) above, and if I was to explain it, it would get wordy, but your question seemed to be more general, less about doing the mathematical calculations, so I'll skip the formulas.

In nutshell, talking about a planet, the state of matter doesn't affect the angular momentum. Angular momentum is conserved and that, divided by moment of inertia determines rotation speed. Now if you get something spinning fast enough the angular rotation can overwhelm the gravity and when this happens, the planet can begin to fly apart, which happens more easily with water than a rocky surface which has some cohesion, but ignoring crazy super fast rotations, a water world, a deep ocean world, a shallow ocean world and a rocky world all obey the the angular velocity law and composition doesn't matter. The angular momentum is conserved. The moment of inertia of a planet can change but for the most part, doesn't change much.

The Earth's moment of Inertia, for example, changes as glaciers grow or shrink, or when there's an earthquake. Even, every time we a tall building is built the Earth's moment of inertia increases a teeny tiny bit, similar to a skater extending their arms to slow down coming out of a spiral.

When there's an earthquake which, for the most part, settles the Earth, there's a small increases in the Earth's rotational speed. The total angular momentum and total mass remaining the same but shifting of material changes the moment of inertia. (Granted space dust and tidal effects change the Earth's moment of Inertia, but quite slowly).

Would the amount of water impact the weight, gravitational pull, and/or tidal forces and cause a difference in the exoplanet's rotation period?

This is harder question to answer precisely because adding water changes the mass of the planet and changing the mass changes the moment of inertia, but sticking to the principal of your question, there's no measurable effect.

Lets take a somewhat simpler example without changing the planet's mass. Ice ages. When the Earth is in an ice age there's less liquid oceans and more ice at the poles but the total mass is unchanged. More mass at the poles and less mass in the oceans decreases the Earth's moment of inertia because the bulk of the Earth's moment of inertia is around the equator, so, as a result, the Earth rotates slightly faster during an ice age and slightly slower after an ice age. Over time, the Earth's crust has a tendency adjust for this effect but that takes tens of thousands of years. Parts of the Earth's crust is still rebounding from the last ice age.

Gravitational pull isn't relevant. Neutron Stars with enormous gravitational pull can rotate very fast and the planet with the fastest rotation in our solar-system is Jupiter and the one with the slowest rotation is Mercury. Angular velocity has no direct correlation to mass or gravity though there is an indirect correlation. As a star, for example condenses it's rotation speeds up, because the angular momentum is conserved but as it settles the moment of inertia decreases. That's why young stars, White Dwarfs and Neutron stars can spin very fast.

Tidal forces can create drag on rotation but the effect is slow, taking millions or hundreds of millions of years. With enough time, tidal forces cause a planet or moon to stop rotating and become tidally locked but there's no short term affect. (I'll say a bit more on this later).

So, a planet with large oceans wouldn't rotate any slower than a planet with no oceans because liquid or solid can have equal angular velocity, but over time, tides will slow a planet with oceans more quickly than a planet without them.

Because the Earth has oceans, the Moon's gravitation on the Earth's tidal bulge does slow down the Earth's rotation, but this has been happening for 4 billion years and the Earth still rotates every 24 hours - one of the faster planets. If the Earth had more water the Moon's tidal tug would slow the earth down a bit faster, but it would still be very gradual.

Jupiter, which is basically a ball of gas, is the fastest rotating planet and Mercury, basically a rock, the slowest, so those are 2 examples of composition not being a factor, though Mercury's slow rotation is in large part due to the strong tidal forces it receives from the Sun.

Now, I Understand the logical approach to your question, as there's something apparent about water resisting rotation - touched on in this question, but the fact that water doesn't spin with a glass when you spin a glass is an example of conservation of angular momentum, not an argument against it. On a planet, the oceans are rotating with the planet and the angular momentum is already there.

Hope that wasn't too long, but that's the gist of it. I can try to clean up or clarify if needed.

If the mass, radius and total angular momentum of the planet is the same as Earth, then I can put forward an answer. (Of course if the angular momentum is allowed to be different you could have any rotation rate...)

First, surface gravity is unchanged since this only depends on the mass and radius of a planet.

Second, if the mass is constant then the average density must be the same as Earth. But water is less dense than the average density of the Earth, so the interior of the planet would need to be denser than that of the Earth in order for the average to be similar.

If the density is higher than Earth on the inside, but lower on the outside, then the moment of inertia, which depends on how far mass is from the axis of rotation squared, will be lower. Then, because angular momentum (assumed constant) is the product of moment of inertia and rotation rate, we deduce that the rotation rate would need to be faster.

NB: Simply covering a larger area with Earthlike ocean would make hardly any difference whatsoever. You need a lot of surface water to make a difference.

I would assume so seeing as how it would change the density

If it is exactly like earth but has a crap ton more of an ocean- it is perceivable that it's (average) density would be lower, Also, minutely, it would compress this water more and heat it and make something of an atmosphere given that it doesn't escape. Trapping more and more energetic particles into a thick foggy atmosphere can change the rotation so slightly it will probably never be noticed.....

Also, if it has a moon, tides/ waves due to gravity can also minutely push the planet in a different state of rotation. Very slightly

I read it wrong, but I'm keeping that in case it helps.

It really depends on how much more water there is. If it was 100% coverage, it would be more "tidy" and the ocean would certainly be more compact (same mass as earth, but add A HUGE amount of water to that to get from 70% to 100% coverage of the area)-- tides may not be as wild. I suppose it would effect the rotation period, but not much.

Note, it might be easier to post this on physics stack exchange, you get better answers, much sooner. This seems like a good question to get up votes off of...

• Does that help? Oct 25 '15 at 1:34