Tidally Locked, Highly Eccentric Orbits

[Red_Beard_98]

I have a question that I'm hoping someone can answer for me. Is it possible, in reality, to have a body with an orbit that is both highly eccentric and tidally locked?

I don't have a great understanding of orbital mechanics, just what I have taught myself, but my understanding makes me think this isn't really possible. My understanding of tidal locking is that the same side of a given body always faces the parent body meaning the time it takes to complete one orbit is equal to the time it takes to complete one rotation and in my mind that could only be possible with orbits that are petty much circular. A highly eccentric orbit means that it is very elliptical as opposed to a more circular orbit. This would mean that the orbital velocity at the apogee is much lower than at the perigee. In order to have a planet that is tidally locked in an eccentric orbit would mean that the rotational speed would have to vary greatly from one end of the orbit to the other which, as far as I know, is not possible. Is there something wrong with my understanding of that? If so please correct me! I'm always looking to improve my knowledge of these things.

I ask because I found a WW that is both tidally locked and while it's not highly eccentric it is a bit more eccentric that I would think is possible for something to be tidally locked with my limited knowledge of the subject. The WW has an orbit of 250 days with an eccentricity of 0.15xx (again, I know that's not highly eccentric but it made me start to think about it). I did a quick search on the ol' Google but found some conflicting answers, as one would expect. I'm also sure this happens a lot in ED but I just happened to notice this particular body due to how out of place it seemed with the rest of the system it was in which is why I took a closer look at the stats.

 

[Sapyx]

The short answer is "no".

The long answer: it depends on what you mean by "tidal locking". If you mean "1:1 orbital resonance" (day length and year length exactly the same), then no, it is impossible. The opposing forces - the constant rotation rate of a planet and the variable orbital speed of a highly eccentric orbit - would not be stable.

Look at Mercury. Prior to the age of spaceflight, everyone assumed that Mercury would be tidally locked to the Sun at 1:1 orbital resonance. But it's actually in a 3:2 orbital resonance, because Mercury''s orbit is too eccentric for 1:1 resonance to form.

There's a lot about orbital resonance - "tidal locking" - that ED doesn't get quite right. The physical appearance of a tidally locked planet, for starters - they're supposed to be "eyeball planets" or "Easter-egg planets", with a "hot pole" forever facing the Sun, an "cold pole" facing away, and the atmosphere and hydrosphere arranged in rings from hot to cold. But they look no different to non-locked planets. Perhaps more significantly, ED does not take axial tilt correction into account. A truly "tidally locked planet" will have zero axial tilt; the vertical motion of off-axis wobbling would be "locked" just as certainly as the horizontal motion of the planet's rotation. Yet in ED, any axial tilt except for exactly zero degrees is acceptable for a tidally locked planet.

 

[Red_Beard_98]

Thanks for the reply!

I'm sure this sort of thing happens a lot with ED and the Stellar Forge. It was just the first time I really took notice of a tidally locked planet with an eccentric orbit. Just to clarify from my original post, the planet that spurred this question was a 1:1 orbital resonance (250 day orbit and rotation, it was identified as tidally locked in stats of the system map). It was just bugging me since I thought I had a decent understanding of some of these concepts and I couldn't wrap my mind around how it was possible. Glad to know it's just Stellar Forge getting confused and not me!

 

[Ian Doncaster]

Also note: a lot of the bodies marked as "tidally locked" in-game are not perfectly locked - the sun will rise and set as viewed from many points, but it takes several "years" to do so.

There are some with 2:1 orbital resonances as well - I think the World of Death is one?

 

[Orvidius]

I learned this the hard way. During my SRV planetary circumnavigation, I was trying to use the sun's position to gauge my progress, knowing that the planet was "tidally locked". I think the apparent position of the star in the sky had moved by nearly 60 degrees by the time I finished.

 

[Red_Beard_98]

I learned this the hard way. During my SRV planetary circumnavigation, I was trying to use the sun's position to gauge my progress, knowing that the planet was "tidally locked". I think the apparent position of the star in the sky had moved by nearly 60 degrees by the time I finished.

Oh man, that sucks. I guess "Tidally locked" should be taken with a grain of salt when it comes to this game then eh?

 

[Sapyx]

I learned this the hard way. During my SRV planetary circumnavigation, I was trying to use the sun's position to gauge my progress, knowing that the planet was "tidally locked". I think the apparent position of the star in the sky had moved by nearly 60 degrees by the time I finished.

This planet? It "should" be tidally locked, horizontally, and the eccentricity is zero, but that moderate axial tilt (erroneously reported in EDSM; it's actually not 0.1297 degrees, but 0.1297 radians, which converts to 14.86 degrees) means that, from "summer solstice" to "winter solstice", which would take half the day/orbit (about 18 hours), the sun will move 30 degrees vertically, then back again 30 degrees for the next 18 hours, before the cycle repeats.

 

[Orvidius]

This planet? It "should" be tidally locked, horizontally, and the eccentricity is zero, but that moderate axial tilt (erroneously reported in EDSM; it's actually not 0.1297 degrees, but 0.1297 radians, which converts to 14.86 degrees) means that, from "summer solstice" to "winter solstice", which would take half the day/orbit (about 18 hours), the sun will move 30 degrees vertically, then back again 30 degrees for the next 18 hours, before the cycle repeats.

Yep, that's the one. But it migrated considerably further than 30, it was close to 60 degrees difference between start and finish, along the equator (not a north/south libration). EDSM doesn't show the numbers to enough decimal places to look at things accurately, but the orbital and rotational periods are actually different, and I didn't double-check that before starting.

mysql> select rotationalPeriodTidallyLocked locked,rotationalPeriod,orbitalPeriod from planets where name='Smojeia LI-E c14-1 1'\G
*************************** 1. row ***************************
          locked: 1
rotationalPeriod: 1.46198
   orbitalPeriod: 1.50997
1 row in set (0.00 sec)

Or full detail:

Spoiler

mysql> select * from planets where name='Smojeia LI-E c14-1 1'\G
*************************** 1. row ***************************
                           id: 18556185
                   systemId64: 347591185786
                     systemId: 25146850
                         name: Smojeia LI-E c14-1 1
                      subType: Metal-rich body
                   isLandable: 1
                   updateTime: 2018-12-12 18:29:07
                      updated: 2019-11-22 00:03:27
                       offset: NULL
            distanceToArrival: 11
                    orbitType: 3
rotationalPeriodTidallyLocked: 1
             rotationalPeriod: 1.46198
                    axialTilt: -0.12966
                      gravity: 0.0570915
           surfaceTemperature: 1092
                  earthMasses: 0.000066
                       radius: 216.856
           orbitalInclination: 0.000163
               argOfPeriapsis: 162.663
                semiMajorAxis: 0.0218819
          orbitalEccentricity: 0.000005
                orbitalPeriod: 1.50997
            terraformingState: Not terraformable
                volcanismType: Minor Metallic Magma
               atmosphereType: No atmosphere
              surfacePressure: 0
                       bodyId: 5
                      parents: Star:0
                   parentStar: 18556248
                 parentPlanet: 0
                commanderName: NULL
                discoveryDate: NULL
                deletionState: 0
1 row in set (0.01 sec)

 

[Red_Beard_98]

I find it interesting that the data is obviously present in the game for it to know that the orbital and rotational periods are in fact different than the display value, which is rounded to the nearest tenth, however the game still considers the body tidally locked. One would think that the game should notice the numbers are different and not list it as such. I know I have seen bodies in the game that have the same displayed rotational and orbital periods but are not listed as tidally locked.

This is all good info to know when/if I decide to do my own circumnavigation of a planet.

 

[Sapyx]

We don't know how the Stellar Forge algorithms work out whether a planet is "tidlaly locked" or not, but as can be seen from the planet stats posted by Orvidius above, it's a simple binary switch: either a planet is locked, or it isn't; the actual orbital periods and rotation rates seem to be calculated independently of this. Assuming that FD actually meant "tidal locking" to mean "1:1 syncronization", then logically there should be a line in the Forge algorithms that says something like: IF tidal_lock=true THEN rotation_period=orbital_period AND THEN axial_tilt=0. And back to the discussion point of the OP, there should be a line something like IF orbital_eccentricity>0.1 THEN tidal_lock=false.

 

[Eahlstan]

Well, on the other hand if you look at Earth and the Moon...
Moon is said to be in an synchronous rotation (although it has a latitudinal libration) and has an axial tilt different to Earth's axial tilt and also an orbital eccentricity greater than zero..
There's more to look at than just these two to see if a body is tidally locked.

en.wikipedia.org/wiki/Orbit_of_the_Moon

 

[Eahlstan]

My understanding of tidal locking is that the same side of a given body always faces the parent body meaning the time it takes to complete one orbit is equal to the time it takes to complete one rotation and in my mind that could only be possible with orbits that are petty much circular.

And that's wrong.
What you're referring to is called 'synchronous rotation'.
'Tidal locking' means, that there is no net transfer of angular momentum between the planetary rotation and orbit ( books.google.at/books?id=-7KimFtJnIAC&pg=PA248&redir_esc=y#v=onepage&q&f=false ).
This simply means, that the length of a 'day' on that body and the length of a 'year' on that body will never change. Over the course of millions of years this will happen to most (if not all) bodies in a system.
A good example is Mercury: For every two revolutions around the sun it rotates three times, and this 2:3 ratio will no longer change over time.

 

[Orvidius]

I think more often than not, "tidal locking" implies a 1:1 resonant synchronous rotation. To avoid confusion, if the ratio is different, astronomers usually call it a resonance, rather than say it's tidally locked. At least from what I've seen so far. I don't work in that field though.

EDIT: My point is, I think sometimes in an effort to maintain clarity, the misconceptions can be inadvertently perpetuated.

 

[Eahlstan]

A widely spread misapprehension is that a tidally locked body permanently turns one side to its host.

...

As long as ‘tidal locking’ denotes only the state of dωp/dt = 0, the actual equilibrium rotation period, as predicted by the CTL model of Lec10, may differ from the orbital period, namely when e ≠ 0 and/or ψp ≠ 0 ... As given by Eq. (23), one side of the planet is permanently orientated towards the star if both e = 0 and ψ = 0.

https://arxiv.org/pdf/1101.2156.pdf

There are many bodies in E: D that are tidally locked and have a ratio that's far off from 1:1 e.g. this one and this one.
Therefore I don't think that in E: D 'tidally locked' is synonymous to 'synchronous rotation'.

 

[varonica]

https://arxiv.org/pdf/1101.2156.pdf

There are many bodies in E: D that are tidally locked and have a ratio that's far off from 1:1 e.g. this one and this one.
Therefore I don't think that in E: D 'tidally locked' is synonymous to 'synchronous rotation'.

Tidal locking actually has nothing to do with 1:1 synchronous rotation, that's just a thing we earthies imagine due to having a moon in 1:1 synchronous rotation as our closest example. There are bodies in the solar system that are tidally locked but not synchronous, Mercury for instance is in a spin orbital resonance of 3:2, and that is tidal locking also, so even in the real world tidal locking isn't synchronous 1:1 rotation, ED actually has it correct.

 

[Red_Beard_98]

And that's wrong.
What you're referring to is called 'synchronous rotation'.
'Tidal locking' means, that there is no net transfer of angular momentum between the planetary rotation and orbit ( books.google.at/books?id=-7KimFtJnIAC&pg=PA248&redir_esc=y#v=onepage&q&f=false ).
This simply means, that the length of a 'day' on that body and the length of a 'year' on that body will never change. Over the course of millions of years this will happen to most (if not all) bodies in a system.
A good example is Mercury: For every two revolutions around the sun it rotates three times, and this 2:3 ratio will no longer change over time.

Thanks for your reply, and everyone else who has replied here as well. I had already figured out that I was mistaken but I always appreciate extra resources to read. One thing I quite enjoy about these forums, especially the exploration section, is the willingness of members to educate others which is why I like asking questions here.

I think more often than not, "tidal locking" implies a 1:1 resonant synchronous rotation. To avoid confusion, if the ratio is different, astronomers usually call it a resonance, rather than say it's tidally locked. At least from what I've seen so far. I don't work in that field though.

That pretty much sums up where my head was at. I did know about resonance but obviously my understanding is very limited. Now that I have been paying closer attention to it I have been finding more bodies like this it just wasn't something I had specifically noted prior to this.

Thanks again to everyone for sharing your knowledge, it's much appreciated.