Due to Pandora's lower gravity, most creatures on Pandora are hexapods (six-legged), although the Na'vi resemble Humans and have only two legs. Creatures roam the air and forest canopy below, similar to Earth's animals, but on a scale several times larger. We are interested in the velocity component that is tangential with the celestial plane (perpendicular to the observer’s line of sight), that is to say, the sky-projected velocity. We describe this direction by a unit vector e t and we introduced a unit vector e r for the (negative) radial velocity component: The orbits of the planet and the moon around their local center of mass are modeled as Keplerian orbits. By default, the planet–moon orbital eccentricity is zero, but users can parameterize nonzero eccentricities ( epm). In the default mode, the planet–moon orbit is modeled with an additional five parameters: orbital inclination i pm, longitude of the ascending node (Ω pm), semimajor axis ( a pm), orbital period ( P pm), and time of periap-sis passage ( τ pm). In Pandora, τ pm is normalized with respect to P pm, that is τ pm€ (0,1). This choice is motivated by a significant boost in the convergence speed of our Monte Carlo sampling method ( Sect. 3). For the calculation of the position of the planet and the moon on their elliptical orbit, however, we used τP pm. For eccentric orbits, the number of orbital elements increases to six, including e pm and the argument of periapsis ( ω pm). Finally, the moon mass M m is required to model the motion of the planet and moon around their joint barycenter. and using as the transit path across the star, we constructed the transit duration of a point-like M b as

The posterior distribution of our simulated exomoon search with Pandora in Fig. 5 is multimodal and it shows an interesting aliasing effect for the orbital period of the planet-moon system. This effect was first theoretically described by Kipping (2009). It has also been observed before in analyses of the four transits of the giant planet Kepler-1625 b and its Neptune-sized exomoon candidate, namely in Fig. S16 of Teachey & Kipping (2018) and in Fig. 4 of Heller et al. (2019). We expect this to be a general effect of Monte Carlo approaches for exoplanet-exomoon data analysis that includes a small number of transits. In other words, if only a few transits are available, there are multiple combinations of planetary masses, moon periods, and moon orbital positions that result in equally likely solutions. This degeneracy can be increasingly resolved with additional transit epochs. Some of our tests also suggest that eclipses can have an important effect on the resolution of this degeneracy. In extremely close exoplanet-exomoon systems, in which P pm/2 < d, multiple eclipses can occur and possibly constrain the planet-moon orbital period substantially. First, we can substitute Q = arctan(tan( k)) = k. Then, profiling shows that almost all time is spent on the expressions sin(2 k) and cos(2 k) (where , which is trivially fast to calculate). As trigonometric functions are very expensive, we can substitute the sine and cosine calculations for one tan calculation through the following identity: Staff (January 4, 2010). "Avatar fans promised alien sex scene on DVD". The Daily Telegraph . Retrieved January 7, 2010. Like on Earth, the forests of Pandora contain a wide diversity of flora and fauna. These are all part of the giant neural network that covers Pandora. The forests are full of bioluminescent life that glows in shades of blue, green, indigo and violet during the night. Richard, Michael G (February 16, 2010). "Y'Know the Flying Dragons in Avatar? Tiny Real-Life Version Discovered in Indonesia". Treehugger.com . Retrieved February 17, 2010.

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The assumption that the in-transit velocity component of the planet-moon barycenter that is tangential to the celestial plane is constant in Eq. (11) provides a substantial computational acceleration of Pandora compared to a dedicated solving algorithm that approximates Kepler’s equation for the eccentric anomaly. Here we estimate the error that is introduced by our approximation. Planet 2 – Endless repetition – a planet where all the inhabitants live the daily grind perpetually. According to Entertainment Weekly, "The Na'vi can commune with animals on their planet by literally plugging their braid into the creatures' nerve systems. To become a warrior, a Na'vi must tame and ride a flying creature known as Ikran." [2] The Na'vi also use this neural bonding system, called "tsaheylu", to mate with a "life partner", a bond that, when made, cannot be broken in the Na'vi's lifetime. This is akin to human marriage. [5] A portion of Pandora (only the equator) extracted from the Wii game with approximate locations of notable locations

Athena is the principal member or primary of the binary system, being slightly larger and more luminous than Sol. It is a solar-like main sequence star with a similar yellowish-white color, whose stellar classification is spectral type G2 V. From mutual orbital parameters, Athena is about 10% more massive than Sol, with a radius about 23% larger. Pandora's wildlife also has bioluminescent qualities. Pandora looks like a lush paradise by Earth standards during the day, but at night, virtually all life on the moon exhibits bioluminescent qualities in various shades of blue, purple and green. This possibly explains the Na'vi's blue skin color, which most likely provides them better camouflage at night on Pandora.

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Various alternative algorithms exist which could further improve Pandora’s performance. We have deferred the implementation of these for future releases, given sufficient interest by the community.