# Would the equatorial region on an alternative Earth spinning on two axes still be +/- 5° above the median "equator?"

Imagine, if you will, the Earth. It's happily spinning around its axis, which is about 23.5° off the perpendicular of its ecliptic. Now, for no scientific reason whatsoever, start a second spin around a line perpendicular to the ecliptic (0°).

To be clear, this alternative Earth is spinning around two axes. One axis is the one we're familiar with: the rotation around our 23.5° tilt. The second rotation is around the perpendicular 0° axis. This means that the northern point of the "normal" axial tilt is, itself, rotating around the perpendicular 0° axis. If I had the skills, I'd make a video. Let me know in comments if I've not been clear enough.

The rotational velocity of both rotations is identical. It takes one "day" for a single point on the Earth's surface to roll back around to the same point it was at 24 hours earlier. Don't worry about the specifics. Thanks.

And I get it that Euler's Rotation Theorem suggests this isn't possible for a sphere. But I'm a fan of model rocketry and I've seen a rocket simultaneously spinning around it's center axis and wobbling around another axis like a drunken llama (make sure the fins are glued on correctly!). No, a model rocket is not a spherical planet, but that's the point of worldbuilding, right? Therefore, for the purpose of this question, I've invited Mr. Euler to sit this one out in a dark closet. I left him with two liters of soda, an empty quart jar, and a treatise on Schrödinger's cat.

Finally, a bit of rapid research online suggests that the "equatorial region" of the Earth is 5° above and below the equatorial line. Let's stick with that — so say we all.

Question: Would I have an equatorial region that's +/- 5° around the average center line as presented to the sun?

I took a shot at explaining this graphically...

Update: @Ash suggests this is a duplicate of How plausible is a 'tilted axis' planet with a "south pole" constantly facing toward its star?. No it isn't — and that's obvious if you actually read both questions. I'm not asking if this is plausible and my southern pole isn't constantly facing the star. That question is asking about a single axis of rotation and I'm asking about two and finally, I'm seeking insight into the resulting equatorial region and that other question is seeking nothing of the sort. Odd that the question was even brought up as a referent for the claim of duplication. Ladies and gentlemen, please take the time to actually read referent questions before using them for the claim of duplicate. Thanks.

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– L.Dutch
Commented Jun 9 at 2:26

### PART ONE!

We at Bespoke Worlds pride ourselves on offering our clients the widest variety of planets --- habitable as well as downright hostile --- on the market today! We offer planets in every shape and size imaginable, as well as in every conceivable dimensional configuration, including half and fractional dimensions that other planetary engineering firms dare not work with!

A planet that rotates on two axes will have a very interesting view of the cosmos during its daily cycles! Essentially if you live on a continent, where today you happen to be in the southeastern quadrisphere at day break, over the course of the next 24 hours, your continent will rotate like the hands of a clock, roughly from SE through SW, then W where you'll eventually cross the equator. Overnight, you'll be heading into the northern hemisphere and on day 2, your sunrise will occur in the northeastern quadrisphere. Day 3 will find you still rotating around and your sunrise will be in the region of the equator and day 4 will find you again in the southwestern quadrisphere. Day 5 your sunrise will be in the northwestern quadrisphere.

Here is a very simple model of what we mean!

You'll notice that this example planet has two sets of complimentary continents, green red and pink and that the two pink continents, the two red continents and the two green continents are directly across from one another with respect to the plane of secondary rotation (the "clock face" rotation).

This planet rotates around its vertical axis (its N-S pole), giving everyone adequate and equal day-night cycles. However, its rotation around its horizontal axis (its E-W pole) is the winning factor in this planet's design! For, it brings the entire surface of the planet within the equatorial zone, thus giving every location its "day in the sun"! You'll notice from the animation that no continent remains trapped at either the far north or the far south, for the poles themselves rotate and face the Sun several times over the course of a month.

To answer your specific query: the only locations on this type of planet that will remain within 5 degrees of the horizontal equator are those areas closest to the East Pole and West Pole. As one moves farther and farther away from either of these poles, the prominent the horizontal rotation will be. Just as on your Earth, anyone standing within a few degrees of the North or South Poles will experience little east - west movement, so it is for those living near the East or West Poles in this planet type.

In aggregate, we at Bespoke Worlds have found that this arrangement of planetary rotation affords a world with a much more stable climate over all and a much more temperate global average climate.

Also! Be sure to check out our comprehensive catalogue of hyperspherical worlds for more interesting rotational concepts for the denizens of your worlds!

• Now, just to be sure... I'm proposing the Earth's 23.5° and a second axis at 0°. Is your model at 0° and 90°?
– JBH
Commented May 20 at 1:36
• Ah! A good point. Our model planet has a vertical tilt of odeg. If you desire a rise and fall of 23 deg for the East and West Poles, then, as on Earth, the Tropics will rise above and fall below the equator, which on Earth give rise to seasons. It is doubtful that any region would remain consistently within 5 deg of the solar equator. Commented May 20 at 1:56
• But do I end up with a median equator? Or does the equatorial region become so complex that the temperatures average out? I.E., the Earth globally warms a bit but there's no equatorial biome zone?
– JBH
Commented May 20 at 2:40
• @JBH, This model has a 2.5:1 ratio between the two axes. You specified that the two rotational axes rotated at the same rate. Can you clarify? Commented May 21 at 16:36

### Take 2, after much calculation

Thank you to Tanner Swett for correcting my initial misconception. I was adding momentum, not rotation. Here's the basic OpenSCAD code I used:

for (change = [0:7:360])
rotate([0,change,change])
{
color("green", .5)
translate([-5,5,5])
cube([1,1,1], center=true);
}


That's for a 0° tilt, but it gives you the idea. Any spot on the planet will follow the figure-8 path that you see for a typical geosynchronous satellite. When you add in seasonal shifts, you still wind up with most of the planet's surface having insane arctic circle issues, but you have a chunk at the east/west poles that have something resembling standard day/night cycle.

The section at the top and bottom of the figure 8's is experiencing roughly 1/1000 G of sideways centrifugal acceleration that continually shifts in direction. You wouldn't notice that while standing, but nothing would stay balanced. It would add an extra challenge to building tall buildings.

If you hung a pendulum, you could watch it draw an infinity symbol in sand. You could use that shift like a tidal generator to power things.

This would have a huge effect on the weather. No Hadley cells for you. The air would shift around as if it were in a giant paint mixer.

• "If you take a sphere with 0° axial tilt and rotate it along two axes simultaneously, your rotation is identical to the rotation of a sphere with a 45° axial tilt." – I don't think this is accurate. You mention in another comment that you ran a simulation in OpenSCAD and confirmed that it just adds the two rotations. I just ran a simulation in OpenSCAD myself and confirmed that it does not just add the two rotations; the motion is definitely something different and more interesting. Commented May 21 at 22:29

From this alternate Earth you would see the Sun move between the tropics of Cancer and Capricorn then back to its starting point once per day instead of over a year. Just like now, the location of sunrise would shift north and south over the year, but the Sun wouldn't move in a straight line, it would move North and South over the course of the day.

The seasonal changes outside the tropics would depend on whether your continent is tilted toward the Sun during the day or the night. Say in January London the Earth is tilted way from the Sun at Noon. Sunrise would be high in the East, the Sun would move South during the day and be at its most southern location around Noon. It would look similar to a current Winter. 12 hours later the northern hemisphere would be pointed toward the Sun and it would be midnight in London, but Noon in the Aleutian island of Atka. Sunrise would be low in the East and the Sun would move North and be highest overhead at Noon. This would look similar a current Summer there. In July the situation would be reversed with London looking similar to Summer during the day and Atka looking similar to Winter 12 hours later during its Noon.

The same thing would happen for the band 5 degrees from the equator, but the difference between the current conditions in January and those in July are not really that different so it wouldn't change climate very much.

Interestingly, the Earth already moves like this, but the equivalent of the second axis of rotation takes 26000 years to to do one "revolution". This is axial precession.

### PART DEUX!!

Dear Planetary Designer! We have received your clarified specifications and believe that we at Bespoke Worlds can provide a solution for your needs! In fact, our planetary engineering department have on offer two solutions that we believe might satisfy your needs.

The first solution truly is a simple matter of mechanical timing. To take Earth as an example, we can see the daily rotation about the planet's physical axis. We see all points on the surface of the planet moving from celestial left to right in an orderly fashion such that no one place races ahead of another and no one place falls behind. Each time a chosen observation point comes into our centered perspective, all the other points on the planet's surface are arranged in their same places.

Now, there is a second rotational motion of Earth called precession. This motion is unnoticed to earthlings because each rotation, which we would perhaps translate as a Hipparchian Age, stretches out over a period of approximately 26000 terrestrial years. The precessional movement is best described as a sort of 'wobble'. As the Earth rotates around its primary axis, this axis itself rotates around the axis that lies perpendicular to the ecliptic, but in the opposite direction.

We can certainly provide you with a quote for a standard Earth type planet with both a 24 hour axial rotation and a 24 hour precessional rotation! We must alert you that there will be certain, perhaps undesirable, consequences. As you can see from this model, a rapid precessional motion will negate steady sky navigation that early humans relied upon. By this we mean navigating by locating the northern Pole Star: your new planet will rotate through several pole stars each day.

As for your specific question, yes, there will be two relatively smallish regions that will directly face the Sun consistently each day, resulting in two equatorial regions that are +/- 5° around the average center line as presented to the Sun. In the model video, observe as the red diameter line rotates around along the ecliptic while the green disc rotates around the planetary axis. All points as one approaches 90 degrees from the red line will continually travel above or below the ecliptic. All points along the planetary equator closest to the red line will constantly be within 5 degrees of the ecliptic.

It should be noted that, as with our previous offering, all points on the planet's surface will receive daily sunlight. This will naturally affect the polar climates most, as there will never be the phenomenon of "polar night" or "polar day" wherein the Sun either never rises or never sets through the course of the year.

• Why did you abandon nutation? Commented May 21 at 1:12
• @user58697 --- An engineering choice based on the customer's wishes! We compressed the 26000 year precession cycle to 24 hours. There are about 1444 nutations per Hiparchian Age and our engineers determined that a nutational wobble per minute might be noticeable to the inhabitants of the planet and so this feature was deleted. Commented May 21 at 17:40

Given you have expressed a willingness to rewrite the physics of the universe to have this work, which frankly you have to, the answer is... weird: the celestial equator isn't going to be a straight line at all on any given day but rather a sine wave. Because the rotational periods of the two axes are identical the sine wave is going to be in exactly the same phase throughout the year so there won't be an "average centre line" on a human timescale. As such the equatorial zone will be the same width as on Earth but will cover a particular sine wave shaped area.

If the Sidereal year is an exact number of days there isn't going to be any precession and there won't be an average centre line on the geological timescale either just a locked equatorial zone shaped, if seen in it's whole, as a sine wave wrapping the globe. If the year and day lengths are out of phase then the equatorial sine wave is going to migrate around the globe at a rate dictated by the difference between orbit and rotation, i.e. on Earth you'd move the phase of the sine wave by 25.6363004% of the equatorial circumference annually.

The more I think about this the more certain I am that there will be no seasonal variation on this world whatsoever. with the tilted rotational axis going through a full turn of its solar orientation in a day means that the annual cycle, and the seasons it would usually create, no longer exists.