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This is all about a thought experiment :

Is there an hypothetical (or may it be real?) case of a stellar system, in which both methods of transit and radial velocities, are invalidated by some orbital configuration, providing a constant light dimming (each egress is perfectly compensated by an other planet ingress) and eccentricities and mass repartition of the planets around their star, make the barycenter of the entire system stay still at the center of the star.

I thought about a simple configuration of several similar planets sharing a single circular orbital path (see below). But are there any possibility for this to happen with multiple elliptical orbits, of different sizes & eccentricities? How likely is it to exist since the universe is quite big?

undetactable exoplanets

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  • $\begingroup$ Surely it's more plausible that the orbital plane is such that they don't come between the star and Earth. ​ ​ $\endgroup$
    – user3576
    Apr 5, 2017 at 14:42
  • $\begingroup$ There are also quite real detection limits. We cannot, by far, detect all planets out there, as different techniques have different limits what they can achieve. Maybe you're asking about those? $\endgroup$
    – AtmosphericPrisonEscape
    Apr 6, 2017 at 0:39
  • $\begingroup$ Just curious are you asking about Tabby's Star? - en.wikipedia.org/wiki/KIC_8462852 $\endgroup$
    – Enigma Maitreya
    Apr 12, 2017 at 15:14

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The configuration you have drawn is not gravitationally stable.

However, leaving that aside, the light from such a system would not be anywhere near constant, because of limb darkening. So whilst the geometrically eclipsed area might be constant, the amount of flux blocked is not.

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    $\begingroup$ Thanks for the answer and the link ! Is the stability issue related to the fact that at first perturbation, each planet will change orbit until it finds a stable orbit? Or will it happen even without any perturbation? If we replace the planets by small mass artificial satellites, would it just take more time to find the same stable orbits? $\endgroup$
    – jkztd
    Apr 5, 2017 at 9:26
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    $\begingroup$ I was going to suggest an exoplanet made of transparent aluminum :-) $\endgroup$
    – Carl Witthoft
    Apr 5, 2017 at 12:42
  • $\begingroup$ The problem with having multiple objects of the same mass in the same orbit is that while in the N-Body problem it works (for some arrangements), as soon as ANY other object enters the calculation (ie the rest of the universe) the system collapses catastrophically. $\endgroup$
    – Draco18s no longer trusts SE
    Apr 12, 2017 at 17:09
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    $\begingroup$ Just a quick note that this configuration can actually be stable. It's unexpected (I am an astrophysicist working on orbital dynamics and it surprised me, but I tested it with N-body simulations and it works). For details see here: planetplanet.net/2017/05/03/… $\endgroup$
    – Sean Raymond
    Dec 13, 2017 at 20:50
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It is actually very easy for an exoplanet system to be undetectable through spectroscopy and transit eclipsing. All you need to do is change the angle of inclination. That's the angle at which we see the system from the Earth.

In order to detect exoplanets via spectroscopy, we need to be able to see the planet moving towards or away from us. The strength of the spectroscopic change is dependent on how quickly it is moving. However, if we are looking at it from the top down, we will not be able to see a spectroscopic shift.

Likewise, using the eclipsing method, the system has to be aligned with respect to us so that we see the planet pass in front of its primary. However, if the system is tilted with respect to us, then we may not see the planet pass in front of or behind the star at all. Thus we would see no change in the light curve, and would not be able to tell that there were planets there.

Here's an applet showing the spectroscopic method, and here's one for the eclipsing method. You can mess around with 'i', the angle of inclination, to see at what angles you don't get a noticeable effect. (Note: These applets are for binary stars, but the method is the same for exoplanets. It's just a lot smaller of an effect.)

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    $\begingroup$ So looking down perpendicular to the plane of the orbits then optimizes for the “wobble method” instead. $\endgroup$
    – JDługosz
    Apr 13, 2017 at 6:53
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    $\begingroup$ @JDługosz that is correct. However, while these methods are decent at finding large planets orbiting close to their stars, it's a lot harder to find small planets far from their stars in general. $\endgroup$
    – Phiteros
    Apr 13, 2017 at 13:47
  • $\begingroup$ @JDługosz: On the other hand, the wobble method is a lot harder to use to detect exoplanets. $\endgroup$
    – Vikki
    Jul 22, 2021 at 0:12

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