Feasibility of a retrograde planet

well , of course , the individual retrograde planet would have the secondary and primary dips reversed , but it wouldn't be discernable from the others. silly me.
Appart from doppler effects that i don't think would be easy to perform for a terrestrial planet arround Alfa Cent , in the near future , how could you tell if it is indeed retrograde?

And still , i wonder , shouldn't there be some funny thing about the stellar rotation in a system that gets one massive enougth object going backwards? I mean , conservation of angular momentum should do very bad things to that kind of systems. Or , if not bad things , things at least interesting to note at the stelar level, if we are talking about jovian-mass bodies in near orbit around red dwarfs, in the mid M range like Proxima

well , thank you for reading my rants. -my math is not good enougth to figure the answers by myself , so i will continue to imagine systems weird enougth to resemble what is awaiting out there for us to peek at them.

ciceron wrote:Appart from doppler effects that i don't think would be easy to perform for a terrestrial planet around Alfa Cent , in the near future , how could you tell if it is indeed retrograde?

As far as I know, the only way to do this is to measure the Rossiter-McLaughlin effect. If (as will likely be the case), the hypothetical Alf Cen Ab or Bb is in a non-transiting orbit, this is of course impossible. With only knowing the radial velocity, you don't have a clue what direction the planet is actually moving (other than toward or away). Remember that as long as HAT-P-7 b has been known from radial velocity measurements, no one suggested it was in a retrograde orbit until it's Rossiter-McLaughlin effect was measured. However, even though we know WASP-17 b and HAT-P-7 b are in retrograde orbits, we don't know just how the orbit looks in the plane of the sky (whether the planet(s) transit from north-to-south in the sky, or from east-to-west in the sky). Essentially, we don't know the full orbit in 3D.

Furthermore, as far as I know there's no way to determine exactly how the stellar rotation axis is inclined relative to Earth. We can in some cases measure the rotation axis's inclination, but we don't know if we're seeing the north stellar pole, south stellar pole, or which direction the star is rotating. Remember that all we get to see is a dot of light that might as well be infinitesimally small (except for nearby stars (Altair) or epic huge stars (Alpha Ori) that have been spatially resolved).

So in summary, we don't even know which way the orbit of the planet is orientated, or which way the stellar rotation axis is orientated.

I guess given sufficient technological development, after the orbit of a planet is astrometrically fully known in 3D, you could use an amazing telescope and watch star spots move across the surface to determine for sure the stellar rotation axis.

Ciceron wrote:And still , i wonder , shouldn't there be some funny thing about the stellar rotation in a system that gets one massive enougth object going backwards? I mean , conservation of angular momentum should do very bad things to that kind of systems. Or , if not bad things , things at least interesting to note at the stelar level, if we are talking about jovian-mass bodies in near orbit around red dwarfs, in the mid M range like Proxima

Anything that orbits a body faster than the body rotates will have its orbit raised. An example is the moon/Earth system. Lunar gravity pulls up the oceans, Earth's rotation puts the oceans slightly ahead of the sub-Lunar point on Earth, and the raised mass of the oceans has a gravitational exertion on the moon. Since the mass is ahead of the moon (albeit slightly, but it is ahead of the sub-lunar point on Earth's surface), the moon gets a little gravitational "push" in the direction it's already orbiting. Increasing orbital velocity increases semi-major axis... thus the moon drifts away.

Anything that orbits a body slower than the body rotates will have its orbit lowered. An example is Phobos. It raises a little bit of tides on Mars, but since the moon is below synchronous orbit of Mars (and thus orbits Mars faster than Mars rotates), the tidally raised area "drags" behind Phobos, exerting a gravitational pull against the moon's direction of travel. This lowers it's orbital velocity. Slower orbital velocity decreases semi-major axis... Phobos falls into Mars.

(and for completion, any bodies that are tidally locked will not experience a chance in semi-major axis)

The Neptune/Triton system could be thought of as being similar to WASP-17 b (or any retrograde orbit.... ). Triton raises a tide on Neptune, but since Neptune is rotating in the opposite direction as the moon is orbiting, the tide gets pushed behind the sub-Triton point on Neptune. This has the same effect as Phobos does on Mars, in that Triton is slowed by the gravitational pull of the tidally raised part of Neptune. This is why Triton's orbit is decaying.

Stellar rotation rates are usually on the order of weeks. 35 or so days for our sun. Hot Jupiters of course orbit their stars much faster. So I am sure that most hot Jupiters are destined for tidal obliteration, with the retrograde ones to die faster.

Expect a retrograde planet to have a very low eccentricity. Triton's is (as far as I know) indistinguishable from zero. I think Wikipedia says it's measured out to 16 decimal places or something (not that Wikipedia or my memory are 100% reliable...). Tidal circularisaton seems to be quite efficient for retrograde orbits.

Edit:
I would assume a more massive planet would exert a more massive tide, which would exert a more massive gravitational force on the planet, causing its orbit to drop faster than a planet with lower mass. Maybe that's why they're talking about WASP-18 b's orbital period changes being detectable in only a decade, being 10 Jupiter-masses and all.

thank you for your extensive explanation. I'm thinking of some of the implications of your explanation about what happens with the tides and semi-major axis variation.

I was refreshing my math from a pair of decades past , about conservation of angular momentum with the help of wikipedia
http://en.wikipedia.org/wiki/Angular_momentum
And that pointed me to the question of what the effects would be on a complex system like Alfa Cent.

My next world question will be more exotic, i hope

Sirius_Alpha wrote:Expect a retrograde planet to have a very low eccentricity. Triton's is (as far as I know) indistinguishable from zero. I think Wikipedia says it's measured out to 16 decimal places or something (not that Wikipedia or my memory are 100% reliable...). Tidal circularisaton seems to be quite efficient for retrograde orbits.

WASP-17b, retrograde planet, orbital eccentricity = 0.129

Lazarus wrote:WASP-17b, retrograde planet, orbital eccentricity = 0.129

Hmm. Do you think this may just be an exception? Or was I wrong about retrograde orbits being more efficient at tidal circularisation?

maybe the event that made it retrograde is recent and the orbit hasn't had time to shed the eccentrity.

Triton's low orbital eccentricity is a bit of a problem, as apparently tides would take longer than the age of the solar system for reasonable post-capture orbits to get to such a low value. Probably something in the environment around Neptune helped the process, perhaps a circumplanetary disc helped things along...

Triton's interaction with a circumplanetary disk at Neptune would be interesting, since Triton is not co-planar with the rest of Neptune's moon system.