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Consider an Earth like planet is orbiting around a Sun like star, it is almost identical to our Solar system, except the orbital inclination of the planet is 90 degree to the equator of the star (note: it means the planet have chance to face to the pole of the star, not the case that the planet has 90 degree rotational axis.

Is the environment of the planet similar to current Earth? If not, what is the difference? For example, is the pole brighter? Or emits more radiation? What other effects need to consider?

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    $\begingroup$ You might ask on Astronomy if the pole of a star is any different from the equator. Trying to tell what we’re looking at is a subject of astronomy, so how to tell and what looks different might inform you. $\endgroup$
    – JDługosz
    Commented Jul 25, 2016 at 7:23
  • $\begingroup$ Does the angle between the solar system ecleptic and the planet's rotational axis change in line with the change of orbital plane from the ecleptic, or remain the same? (Wow, that's a lot of technical terms in one sentence.) Basically, does the planet's rotational pole face the star's pole (to within some small error), or does the planet's equator face the star's pole? You can't just change the angle to the ecleptic and ask if things will be the same, without saying something about the rotational axis. $\endgroup$
    – user
    Commented Jul 25, 2016 at 7:41
  • $\begingroup$ You will also have to come up with a decent explanation for how the planet ended up in such a massively weird orbit. Remember that the accretion disk orbits around the star's equator, it's not just a random jumble of "stuff" everywhere around the star; it's called a disk for a reason. But that's clearly outside the scope of this question. $\endgroup$
    – user
    Commented Jul 25, 2016 at 7:43

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Simple mechanics dictates that what you suggested is extremely improbable.

Planets form as ejection matter from a new sun. Logically, the place with the highest speed is where the matter is most likely to be expelled. In a spherical body, this would be near the equator. It's why all bodies in the solar system lie, more or less, on the same plane.

That said, it's not impossible for an ejecta (ejectum?) to form near a pole. Conservation of momentum + the sun's gravity would then cause it to enter orbit at that solar latitide parallel to the sun's spin.

Again, it's not impossible for some sufficiently large mass to impact it such that it negates it's horizontal momentum and gives it sufficient vertical momentum to send it on an orbit perpendicular the sun's axis of rotation. Thirdly, bear in mind that the sun itself orbits the galaxy. Objects on the same plane are pulled along by their own centrifugal force as part of the original angular momentum of the sun. Objects in a vertical plane might just get left behind or simply run into the sun. Think of a hammer throw. The athlete swinging the hammer can move around in the plane of rotation because the string will ensure the hammer doesn't get too far away. If he tries to swing it vertically, let's say standing on a tightrope with a counterweight on his other side, then, when walking forward, the hammer vertically above or below him or in front of him will not receive sufficient tension in the string. Only when it goes behind him will the string be pulled taut. This means that the orbit will be extremely unstable, with scorching summers and freezing winters planetwide.

Lastly, being the one object on a vertical axis where everything else is horizontal means a far greater change of collision with something. This doesn't include the presence of gas giants like Jupiter pulling the little upstart back in line.

In short, extremely unlikely and probably wouldn't even be liveable, Mercury in front of the sun and Neptune behind it.

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Does the axis of rotation change with it? Because if the axis of rotation stays fixed wrt. to the sun, then you'd have one half of the planet bathed in sunlight for half a year, and the other half in complete darkness for half a year. Pretty hostile.

If the axis of rotation also changes, not much would be different. The sun is almost completely a perfect sphere (one of the most perfect spheres we have yet found in nature), so I suspect that radiation emitted is quite uniform. many features of the sun are equally found at the poles and at the equator (e.g. coronal holes).

But our ability to reach other planets would be drastically dimished, because plane changes are very, very expensive. You have to spend $\Delta v = v_0 \cdot sin \left( \frac \theta 2 \right)$ m/s just to change the plane. In case of the earth, the mean orbital speed is ~30km/s, so you would need another 21km/s delta-v for the plane change. This is pretty prohibitive (say goodbye to space travel to anything else then the moon).

And you'd have to explain how that came to be, since conservation of angular momentum dictates that all bodies should (roughly) orbit in the same plane. So such a solar system could only evolve if the planet got pulled there by another big source of gravity, e.g. a big rogue planet passing through.

I sadly don't have good information on the suns radiation from the poles. But the suns magnetosphere does not seem to be much of a concern for your planet.

A much greater concern would be the stability of the orbit. Jupiter and the other bodies perturb the earths orbit, but since we are in the same plane, the system is quite stable for the forseeable (million of years) future. but with Earth being heavily inclined, I could imagine the system to be a lot less stable. Maybe you plug it into Universe Sandbox or similar see the results.

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