Rotation of the Planets

It may well be that the person who set this question knows more about this subject than I do (which is one reason why I didn't query it during vetting), but I had previously believed that Venus was the only planet that rotated clockwise.

Strictly speaking, before we talk about clockwise and counter–clockwise in this context, we should really specify what we mean. Astronomers tend to talk about "prograde" and "retrograde" motion; basically, all the planets rotate around the Sun in the same direction, and it's the same direction as the one in which the Sun rotates around its own axis. Most of the planets also rotate around their own axes in that same direction. Astronomers call this "prograde" motion, and the opposite direction "retrograde".

If we were looking from above the north poles of the Sun and the planets (which is the way we normally picture the Solar System – particularly if we're thinking in two dimensions), everything would appear to be moving in a counter–clockwise direction. So what's prograde to the astronomers is commonly described as counter–clockwise by laymen, and what's retrograde to the astronomers is clockwise to the layman.

On its Retrograde and Prograde Motion page, Wikipedia says: "the rotations of most planets are prograde, with the exceptions of Venus and Uranus, which have retrograde rotations."

Before I comment on this, I want to look at Uranus in more detail.

Uranus is a special case. Astronomers believe that at some point during the formative years of the Solar System, Uranus collided with what Wikipedia describes as "an Earth–sized protoplanet", and this resulted in its tilting by an angle of about 90 degrees. Its axis now points more or less along the ecliptic (which is the plane in which the planets orbit the Sun). Its rotation, if you're looking from a point perpendicular to the ecliptic, is neither obviously clockwise nor obviously counter–clockwise; it's as if Uranus were a ball rolling along the ecliptic plane.

Except ... it isn't even as simple as that. (!) Uranus's axis of rotation doesn't continually point towards and away from the Sun; it always points in the same direction. Think of it as pointing towards another star, somewhere in an entirely different part of the galaxy. So it does sometimes point almost directly towards and away from the Sun (these are the planet's solstices), and sometimes it points in a direction that's tangential to the planet's orbit (these are the equinoxes). At other times ... well, you get the picture.

The crux of the matter is this: if you imagine Uranus being "righted", in which direction would it be rotating?

Wikipedia doesn't have much to say on this subject on its Uranus page, but it does say that Uranus has "an axial tilt of 97.77° (as defined by prograde rotation)". I think this means that if you assume that Uranus originally rotated in what we call a counter–clockwise direction, it would have had to tilt by almost 98 degrees to behave as it does now.

I turned to Google for elucidation, and the most helpul website I found was that of San José State University (in California), which says: "Uranus is tilted on its side about 90° so its direction of rotation is ambiguous. Its angle of inclination is usually given as 98° which would mean that its direction of rotation is not retrograde. If its direction of rotation is presumed retrograde then its angle of inclination would be 82°."

Imagine, if you will, a model of the Solar System, with all eight planets orbiting the Sun in a counter–clockwise direction (when seen from above). If the model were sophisticated enough, six of them would be rotating counter–clockwise around their own axes, and one (Venus) would be rotating clockwise - albeit very slowly. But Uranus would be spinning in its own unique way, with its axis always pointing in the same direction – but more or less horizontal.

Now imagine you could realign Uranus so that its axis was vertical. Which way would it be spinning?

Because this model is only in your head, it could of course be either way. But think about this. Imagine firstly (for the sake of argument) that Uranus is at the closest point in its orbit to where you're standing. Secondly, imagine its axis as a stick, pointing in your direction but slightly upwards. Thirdly, imagine that Uranus appears (from your viewpoint) to be rotating in a clockwise direction.

Now imagine realigning Uranus so that the end of the stick that was pointing towards you (and slightly upwards) is now pointing directly upwards. This would be a movement through 82 degrees. As you do so, keep looking along that same axis. When the axis is vertical, and you're looking at Uranus from directly above, in which direction is it rotating?

I think it's rotating clockwise (or retrogressively, to the astronomers).

Now go back to the original version, and imagine realigning Uranus so that the end of the stick that was pointing towards you (and slightly upwards) is now pointing directly downwards. This would be a movement through 98 degrees. If you were now to look at Uranus from above, I think (I hope) you'll find that it's rotating counter-clockwise (or progressively).

(To picture this last movement, I find it helps to imagine a spiral being drawn around the surface of Uranus, in the direction of its rotation and towards the pole that was originally pointing away from me.)

SJSU, in the passage quoted above, is basically saying that Uranus is conventionally considered to have a tilt of 98 degrees, and this means that it rotates progressively. Wikipedia, by saying (on its Uranus page) that it has a tilt of 97.77 degrees, seems to be agreeing; but on its Retrograde and Prograde Motion page it says that Uranus, like Venus, rotates retrogressively.

Which is correct?

The answer, I suppose, is that it depends how you look at it, and how you interpret the facts.

What I think Wikipedia is saying, when it says that Uranus has "an axial tilt of 97.77° (as defined by prograde rotation)", is that if Uranus had rotated progressively before the collision, it would have had to tilt by 98 degrees to rotate in the direction it does now. If it had rotated retrogressively, a tilt of 82 degrees would account for what we can observe now. But because six of the other seven planets rotate progressively, the probability is that Uranus did too (before the collision).

It may seem counter–intuitive to assume that the tilt is the greater of the two possibilities, rather than the lesser, simply on the grounds of probability. There's something about a planet starting to turn upside down that just seems a bit illogical. But then again ... I know of nothing in the laws of physics to say that a tilt of more than 90 degrees is intrinsically less likely than one of less than 90; it's just a question of degree (if you'll pardon the pun). The probability, on the other hand (with odds of six to one), is very persuasive.

Anyway ... to return to the quiz question. Because Wikipedia (on one page at least) brackets Uranus with Venus as having retrograde rotation, and because there is clearly some doubt, it's only fair to allow "Uranus" as a correct answer. But if you're ever asked "Which planet rotates in the opposite way to all the others" (or anything similar), the best policy would clearly be to answer "Venus".

Incidentally ... this all begs the question of how the axial tilts of the other planets compare with that of Uranus. Well: Earth tilts by just under 23.5 degrees, and this is why we have seasons in the year. Mars, Saturn and Neptune all tilt slightly more than Earth, and Pluto (now a minor planet of course) comes nearest to Uranus at just under 57.5 degrees. Mercury, Venus and Jupiter are all more or less upright (Jupiter being the most tilted of these three, at just over 3 degrees). The Sun itself tilts at 7.25 degrees compared to the orbits of the planets, and the Moon by 6.68 degrees.

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