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Planetary systems as we understand it exist from a disk of mass when the parent star is young. That's why all our planets are in the same plane, or close to it. See also Why is the solar system often shown as a 2D plane?, Inclination of planets, and answers there.

Yet the newly announced Kepler-452b apparently has an inclination of close to 90° (89.806+0.134−0.049°). Do we have any model of solar system formation that explains how this can form?

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As Wikipedia notes,

Since the word 'inclination' is used in exoplanet studies for this line-of-sight inclination then the angle between the planet's orbit and the star's rotation must use a different word and is termed the spin-orbit angle or spin-orbit alignment. In most cases the orientation of the star's rotational axis is unknown.

As of now (7/26/2015), no other planets, smaller objects, or debris disks have been found around Kepler-452. This means that the situation is not as unusual as might be thought. If there were other planets in the system with orbital inclinations near 0°, then things would appear exceedingly odd. Why would this one planet be different than the others?

One possible scenario is that the star's rotation axis has been changed. Think about how Uranus's axial tilt is skewed. Nobody knows for sure what happened, though one popular theory is that it was hit at some point in time by another object. Granted, it would take a rather large object to have any effect whatsoever on the axial tilt of Kepler-452, but it is still possible.

The point of this idea is that perhaps it is the star, not the planet, which is unusual.

Several papers have been written by those much more knowledgeable than I, notably Crida & Batygin (2014) and Xue et al. (2014). Both refer to Hot Jupiter models, but the ideas behind them are still possible for other planets.

The former suggest

Contemporary observational surveys suggest that a considerable fraction of solar-type stars are born as binary or multiple systems (Ghez et al. 1993; Kraus et al. 2011). Moreover, most stars form in embedded cluster environments (Lada & Lada 2003) where dynamical evolution can lead to the acquisition of transient companions (Malmberg et al. 2007). Recently, Batygin (2012) showed that the presence of a companion to a young star can force the proto-planetary disk to precess around the binary’s axis, so that the plane in which planets eventually form and the equatorial plane of the central star can differ.

They also suggest that encounters with other planets could be responsible for some cases of this (although an angle of 90° makes this seem rather improbable); a related idea that has been applied to Kuiper Belt Objects is the Kozai mechanism. The companion to this theory is that the star was perturbed by an encounter, possibly with a companion (as I discussed earlier).

Xue et al. discuss similar scenarios, focusing in part on "dynamic" interactions between planets. Direct tidal interactions between the star and the planet are also a possible scenario.

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