# Twin worlds system orbiting a red dwarf?

## Twin worlds system orbiting a red dwarf?

This is something I wanted to feature in my fictional universe. A set of twin planets, orbiting a red dwarf star. I have a slight problem with the worldbuilding though. It has to do with the tidal locking.

99% of the planets in habitable zones around red dwarfs achieve tidal lock status at some point in their existence. What confuses me is, would a pair of twin worlds like Earth and Venus tidally lock? Would they retain residual rotation around their own axis? I've heard something like moons that orbit a red dwarf planet tend to slow down its process of tidal locking by some percentage, but not from actual scientific papers, just hypotheticals and speculation. I need something a bit more firm than that, and I think this could be the right place to ask?

If true, that moons of planets that orbit red dwarfs tend to slow down their parent planet's process of becoming tidally locked - wouldn't that apply even more for, say, worlds the size of Earth and Venus perhaps?

Or would it only apply if the star in question is young/younger?

Mind that I mean worlds that are supposed to be each other's "moons", not co-orbiting planets sharing the same orbital path (last time I asked this question people got confused between the two).

I appreciate any help you could give me, or shedding the light on the issue.

Baltazar
Meteor

Number of posts : 29
Registration date : 2011-01-08

## Re: Twin worlds system orbiting a red dwarf?

Only if the HZ is far enough from the star that the twin planets would be able to orbit well within their combined Hill sphere, and without tidal forces heating them up to the point of being lava worlds. Since red dwarfs can burn for several trillion years, this is a possibility, because of the fact that they orbit really close to each other.

Example: 2 Earth-like planets orbit each other at a distance of 0.2 AU from their parent star. They are separated by 76880 km (1/5 the distance to the Moon). Since the Moon is tidally locked at 5 times this distance, it's highly likely that 2 close orbiting Terran worlds would be tidally locked to each other after the same amount of time, but their orbits must be nearly circular or they won't lock to one another.

stargate38
Micrometeorite

Number of posts : 12
Registration date : 2013-05-28

## Re: Twin worlds system orbiting a red dwarf?

stargate38 wrote:Only if the HZ is far enough from the star that the twin planets would be able to orbit well within their combined Hill sphere, and without tidal forces heating them up to the point of being lava worlds. Since red dwarfs can burn for several trillion years, this is a possibility, because of the fact that they orbit really close to each other.

Example: 2 Earth-like planets orbit each other at a distance of 0.2 AU from their parent star. They are separated by 76880 km (1/5 the distance to the Moon). Since the Moon is tidally locked at 5 times this distance, it's highly likely that 2 close orbiting Terran worlds would be tidally locked to each other after the same amount of time, but their orbits must be nearly circular or they won't lock to one another.
Hi stargate38!

Thanks for the input.

The star is an M0V red dwarf with the following characteristics:

Mass: 0.50 s.m.
Temperature: 3720 K
Luminosity: 0.05 of Sol
Surface Gravity: 4.65 cgs
Rotation: 41.2 days
Ice Line: 0.6 AU
Current Age: 2.1 Gyr

The planets are with the following characteristics:

A

Mass: 1.9 e.m.
Density: 7.869 g/cm3
Gravity: 1.5 gE

B

Mass: 1.18 e.m.
Density: 7.836 g/cm3
Gravity: 1.3 gE

A and B orbit each other at 220 212 km distance. They orbit their star at 0.16 AU, in ~38 Earth days interval. Is this close enough for tidal locking, but not as close for them to start to become Earth-sized Io analogues of each other? :/

Baltazar
Meteor

Number of posts : 29
Registration date : 2011-01-08

## Re: Twin worlds system orbiting a red dwarf?

At that distance, if they orbit prograde, the binary planets would be unstable; not because of tidal forces, however. The planets aren't deep enough into the Hill Sphere, so after a while, they get pulled apart from one another by the star's gravity. However, if they orbit each other in a retrograde direction, they'll be stable for a very LONG time. They wouldn't become giant Io's either.

Last edited by stargate38 on 24th November 2013, 6:30 pm; edited 1 time in total (Reason for editing : Add some info.)

stargate38
Micrometeorite

Number of posts : 12
Registration date : 2013-05-28

## Re: Twin worlds system orbiting a red dwarf?

stargate38 wrote:At that distance, if they orbit prograde, the binary planets would be unstable; not because of tidal forces, however. The planets aren't deep enough into the Hill Sphere, so after a while, they get pulled apart from one another by the star's gravity. However, if they orbit each other in a retrograde direction, they'll be stable for a very LONG time. :)They wouldn't become giant Io's either.
Thank you for your feedback. I was worried that they would be too close that they would eventually collide with each other or make each other too geologically active for any life to exist there. Its why I put that large distance between them. If you say that's too much, I'll definitely lower it. Is half the moon's distance from Earth close enough for stable tidally locked orbit?

I also originally wanted retrograde orbits just to make the planets interesting, but it seems from what I read on the net, that this also provides stability. Very interesting.

My main worry was if the planets night tidally lock to the star. That would've ruined everything. I wonder how a double tidal locking would look like (tidally locked to each other, and at the same time, to the star too)

Baltazar
Meteor

Number of posts : 29
Registration date : 2011-01-08

## Re: Twin worlds system orbiting a red dwarf?

I checked and 160000 km seems to be the largest stable prograde orbit for the planet pair.

It's absolutely impossible for the planets to become tidally locked to each other and the star at the same time, because that would result in a violation of angular momentum conservation. Also, if they did become locked, the angular momentum of the planets would be too high. The normal force (the combination of inertia and angular momentum, always points directly opposite the reference object), caused by the planets' motion around their star, would be stronger than the centripetal force represented by the gravity of the planets themselves. In other words, they would fly apart from each other.

stargate38
Micrometeorite

Number of posts : 12
Registration date : 2013-05-28

## Re: Twin worlds system orbiting a red dwarf?

stargate38 wrote:I checked and 160000 km seems to be the largest stable prograde orbit for the planet pair.

It's absolutely impossible for the planets to become tidally locked to each other and the star at the same time, because that would result in a violation of angular momentum conservation. Also, if they did become locked, the angular momentum of the planets would be too high. The normal force (the combination of inertia and angular momentum, always points directly opposite the reference object), caused by the planets' motion around their star, would be stronger than the centripetal force represented by the gravity of the planets themselves. In other words, they would fly apart from each other.
You have saved me my storyline . Thank you very much! If you were anywhere near where I live I'd buy you a beer for this, seriously!

I'm a bit of a layman when it comes to science or math so I appreciate when somebody helps out like this.

I think I will go with 148 767 km distance, retrograde orbit.

Baltazar
Meteor

Number of posts : 29
Registration date : 2011-01-08