Fixed Rotation?

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Fixed Rotation?

Post by NuclearVacuum on 30th April 2009, 12:58 pm

How close would a planet need to be from its parent star to loose its rotation and be tidally locked to the star? Would close orbiting stars (like DEL Tri and IOT Peg) be tidally locked onto each other?

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Re: Fixed Rotation?

Post by Sirius_Alpha on 30th April 2009, 4:47 pm

Tidal locking has no cut-off distance, it just takes longer and longer to happen over larger semi-major axes.

An (oversimplified) approximation can be given by:
0.0483 (T M^2 / p)^(1/6)

Where T is the age of the system,
M is the mass of the star in solar masses
p is the density of the planet.

This equation gives you the distance from the star in AU within which a planet with the parameters you provide would be tidally locked. Note that this distance increases over time, as it takes a while for planets to tidally lock when they're farther out from the star. If you allow the star to survive long enough, every planet would become tidally locked.

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Re: Fixed Rotation?

Post by NuclearVacuum on 1st May 2009, 5:58 pm

This helps me out, thank you very much. But you didn't answer my other question.

Would close orbiting stars (like DEL Tri and IOT Peg) be tidally locked onto each other?

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Re: Fixed Rotation?

Post by Sirius_Alpha on 1st May 2009, 9:14 pm

Embarassed Sad I'm afraid I don't know much about those stars.

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Re: Fixed Rotation?

Post by NuclearVacuum on 2nd May 2009, 9:16 am

Sirius_Alpha wrote:Embarassed Sad I'm afraid I don't know much about those stars.

I only used them as an example (sorry for that). I was asking would circumbinary stars be locked onto each other? Two stars in close orbits.

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Re: Fixed Rotation?

Post by Sirius_Alpha on 2nd May 2009, 11:13 am

Ah, it's quite alright. And I think the answer is "most certainly". I can't think of a reason why stars would behave differently. I would furthermore assume tidal locking to be more efficient for tight binary stars due to their higher mass and increased tidal effects.

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Re: Fixed Rotation?

Post by NuclearVacuum on 2nd May 2009, 3:06 pm

Thank you so much for your answer. That question has been bugging me for a long time. Also, sorry for my stupid questions.

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Re: Fixed Rotation?

Post by Sirius_Alpha on 2nd May 2009, 9:26 pm

I'm glad I could help. And your questions weren't stupid Smile.

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Re: Fixed Rotation?

Post by Edasich on 3rd May 2009, 6:06 am

If this can help, cataclysmic variables have the low-mass secondary quite tidally locked. There was also a peculiar one (I don't remember at the moment, maybe LY Aqr) where the (probably substellar) seconday would show strong temperature differences between "dayside" and "nightside", just alike Upsilon Andromedae b.

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Re: Fixed Rotation?

Post by Sirius_Alpha on 3rd May 2009, 10:45 am

Edasich wrote:There was also a peculiar one (I don't remember at the moment, maybe LY Aqr) where the (probably substellar) seconday would show strong temperature differences between "dayside" and "nightside", just alike Upsilon Andromedae b.
Probably not the one you're thinking of, but HW Vir is like that.

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Re: Fixed Rotation?

Post by Edasich on 3rd May 2009, 4:23 pm

Yeah, also.
But I have to find that paper again, because there I've read this interesting coincidence Laughing

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Re: Fixed Rotation?

Post by marasama on 25th May 2009, 12:14 am

Can be any distance if you factor in collisions.
Some impact that slow (instead of speed) the rotation could cause the planet to lock at even further distances.

But on the gravity itself, I don't know.

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Re: Fixed Rotation?

Post by NuclearVacuum on 26th May 2009, 7:56 pm

Sirius_Alpha wrote:Tidal locking has no cut-off distance, it just takes longer and longer to happen over larger semi-major axes.

An (oversimplified) approximation can be given by:
0.0483 (T M^2 / p)^(1/6)

Where T is the age of the system,
M is the mass of the star in solar masses
p is the density of the planet.

This equation gives you the distance from the star in AU within which a planet with the parameters you provide would be tidally locked. Note that this distance increases over time, as it takes a while for planets to tidally lock when they're farther out from the star. If you allow the star to survive long enough, every planet would become tidally locked.

I SUCK AT MATH!!!!!! But let me see if I got it right.

I wanted to calculate whether Gliese 581 d rotated or was locked to its star. But since there is no confirmed density of the planets, I made another calculation. But in order to calculate the density, you need the volume. So I had to calculate the volume. No

Just to see if I got the idea, I tested out Gliese 581 c (which is widely thought to be locked). Here is what I got

Code:

T = 9000000000 (9*10^9) (9 billion years old)
M = 0.31 (solar masses)
p = 1.4 (g/cm^2)
x = 1.7 (AU)

This means that Gliese 581 c would have to be orbiting its star within 1.7 AU (which it does) to be tidally locked. This calculation seems to be accurate, not to try Gliese 581 d.

Code:

p = 0.84 (g/cm^2)
x = 1.53 (AU)

According to this, Gliese 581 d would be locked to its star. Does this sound right?

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Re: Fixed Rotation?

Post by Sirius_Alpha on 27th May 2009, 7:06 am

I confirm your result for Gliese 581 d, using your value for the density.

However, the density seems a bit low for a 7 M_e planet.


Last edited by Sirius_Alpha on 27th May 2009, 10:22 am; edited 3 times in total

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Re: Fixed Rotation?

Post by NuclearVacuum on 27th May 2009, 10:05 am

Thank you so much for the help.

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