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Four elements of variation in the motions of the Earth were recognized by Milutin Milanković in the 1920s as having effects on Earth’s long-term climate . Milanković didn’t study the Earth’s orbital inclination, but it has since been recognized as also having an effect, and is now considered one of the "Milankovitch Cycles".
These five periodic variations are:
It is reasonable to assume that if Earth experiences these variations, a Worldbuilt planet would also, with differences unique to each world’s particular circumstances, of course.
While all of the Milankovitch Cycles are important to be aware of, axial tilt by far has the most direct impact on the question of a planet’s habitability; so, I pay the most attention to it in the sections below. The other cycles are discussed in brief for the sake of completeness, but the reader is encouraged to consult the wide variety of sources available elsewhere for more in-depth coverage of these topics.
Knowing the durations of these cycles can lend a fullness to the understanding of a planet, but unless one has a specific reason to be concerned with very long-term changes in the planet’s climate, it is simpler and more straightforward to simply declare the magnitude of these variations arbitrarily as it suits one’s needs.
Obliquity (Axial Tilt)
Venus is technically "upside-down" with respect to the Earth's orientation. This is because the International Astronomical Union (IAU) uses the “right-hand rule” , which—in short—defines all planetary rotation as counter-clockwise as viewed from the planet’s positive pole (the one which lies in the same direction as the north-seeking pole of a compass would point). Thus, for planets like Uranus and Venus, the axial tilts exceeding 90° indicate that their north poles are pointed “below” their orbital plane. However, it is just as valid to say that Venus rotates clockwise—or retrograde—with an axial tilt of 2.63°—it is simply a matter of convention.
Obliquity (axial tilt) is the primary determiner of seasons on a planet (even the ice- and gas-giants). The larger the amount of tilt, the greater the variation in temperature over the planet’s orbital period. Our concern, here, is with the effect of axial tilt on habitable or inhabitable worlds.
The obliquity of Mars, which has no large moon, varies from 15° to 35° over a period of 124,000 years , resulting in it having endured about 40 glaciations in just the past 5 million years . (The relatively large eccentricity of Mars’ orbit, at 0.0934, also causes its distance from the Sun to vary by 19%  over the course of its year. Thus, there is a greater variation in the amount of solar heating (insolation) the surface gets than that which Earth experiences. (See the section below, "Variations In Orbital Eccentricity", for more information.)
Using Earth as the example, the axial tilt results in a differential in irradiance, or the amount of power-per-unit-area received from sunlight due to the angle at which it strikes the Earth’s surface.
Two special latitudes (imaginary lines circling the Earth at specific angles as measured north or south from the equator), indicate the farthest north and south at which sunlight is ever able to strike the surface at a 90° angle.
The Tropic of Capricorn lies at 23.439° N latitude and the Tropic of Cancer lies at 23.439° S latitude. (If those numbers look familiar, they should; they are the same as the Earth's obliquity. Tropic latitudes will always be located at the latitude equating to the obliquity of the planet's axis. Whenever I refer to the “tropic latitudes”, these are the ones to which I am referring.)
These latitudes are named according to the constellations in which the Sun is found at noon on the solstices.
The Arctic and Antarctic Circles are located at 66.561° north and south latitude, respectively. (Note, here, that 90.000° - 23.439° = 66.561°: the "polar latitudes" will always be the obliquity angle subtracted from 90.000°.)
As can be seen in the illustration above, on the day of the solstice in the northern hemisphere the Sun’s illumination reaches beyond the north geographic pole. At this time, the entire area of the Earth’s surface within the area bounded by the Arctic Circle experiences daylight. On that day in the Antarctic Circle, the Sun never rises above the horizon. Six months later, the situation is reversed.
The angle at which the rays of the star’s light strike the ground is called the sun angle. Directly overhead is a sun angle of 90°.
The area of a circle with radius 0.5 (diameter 1.0) is found by:
At a sun angle of 30°, the sunlight striking the ground forms an ellipse with a semi-minor axis of 0.5 and a semi-major axis of 2.0.
The area of this ellipse is:
Obliquity and the seasons
Again, using Earth as our example, we see in Figure 2 that the tilt of the Earth’s axis points in the same direction, regardless of where the Earth is in its orbit . The change in the distance between Earth and the Sun from one extreme of its orbit to the other (see the section "Variations In Orbital Eccentricity" below), is measurable, but has far less impact on solar irradiance than does axial tilt.
The magnitude of the axial tilt, does, however have a significant impact on how large an area of the total surface of the planet is able to experience maximum stellar irradiance.
At 0° tilt, there are no polar or tropical zones and the planet has no seasons. The star would always be directly overhead at the equator, and always be on-or-near-to the horizon at the poles; indeed, at the exact location of the poles, the star would never set, but simply roll around the horizon once per day. (The latitude at which the star would touch the horizon would be a factor of the radius of the planet and the apparent size of the star in the planet's sky, which is determined by its distance from the star.)
Such a planet would still have seasons; in fact they would be more extreme than Earth’s, with high temperatures ~50% warmer than we see on Earth, and low temperatures ~50% colder. Locations at 45° north or south latitude would see the star directly overhead at midday on the summer solstice. In the winter, the star would not actually rise above the horizon on the day before, the day of, and the day after the solstice. The equinoxes would still be exactly half daylight and half night, with the equator alone seeing the star directly overhead at midday on those days.
At obliquities above 45°, day/night cycles become increasingly odd, and the tropic and arctic latitudes “reverse”.
After the solstice, its path becomes increasingly more inclined, until it reaches its highest point once again, midway between the solstice and the autumnal equinox. A few days after the autumnal equinox, it drops below the horizon and does not reappear for months.
At the poles, the star would appear above the horizon shortly after the equinox and spend the next quarter of the orbit spiraling toward the zenith, circling the sky once per day. At the solstice it would pause briefly directly overhead, appearing to rotate north-to-south once during a day’s span, and then it would begin spiraling toward the horizon again, finally disappearing at the antipodal equinox. For the other half of the year, there would be no sunlight whatsoever.
Temperature variations at this obliquity are at their maximum and the likelihood of advanced life evolving naturally in such an environment is a matter of debate. However, given the ability of Earth‑borne extremophiles to exist in quite hostile environments, it is not beyond possibility that at least microbial lifeforms might evolve on such a world. Humans would very probably need to build artificial environments if they were planning an extended stay.
The axial tilt of the Earth is kept from varying widely by the gravitational effect of the Moon. Without the Moon, the 1.0 degree variation in the Earth’s tilt would be more like 10 degrees , but this would not necessarily render Earth uninhabitable .
A wonderful interactive tool for envisioning these scenarios can be found at McGraw-Hill's Interactive Seasons Astronomy site.
At this current time in Earth’s history, the North Pole points more-or-less directly at the star Polaris (α Ursae Minoris), which is thus referred to as “the North Star.” Five thousand years ago, the axis pointed to the faint star Thuban (α Draconis) in the constellation of Draco; a thousand years from now, the Pole Star will be Alrai, (γ Cephei); around 5000 CE, Iota Cephei (ɩ Cephei) will serve as Pole Star; and, Deneb (ɑ Cygni) will take over the role in 10,000 CE. Around 27,800 CE, the axis will have circled around to Polaris once again .
Variations in Orbital eccentricity
The current eccentricity of Earth's orbit is 0.0167086, and decreasing, meaning the Earth's orbit is becoming progressively more nearly circular. As with most of the other variations in the Milankovitch Cycles, gravitational interactions with other Solar System bodies (primarily Jupiter and Saturn) cause the Earth’s orbit to vary in its eccentricity over a period of ~100,000 years. The eccentriciy varies between e = 0.000055 and e = 0.0679, with an arithmetic mean (and median) of e = 0.033978, and a geometric mean of 0.00193249. The difference between the minimum and maximum eccentricities amounts to a difference of 0.00229 AU in Earth’s semi-major axis over the 100,000 year period. This may not seem like much, but it equates to a change in the distance to the Sun of 342,878 km, or 26.909 times the diameter of the Earth.
While this change has some measurable effect on the climate of Earth, it is not nearly as marked as the changes resulting from changes in obliquity (see above).
The apoapsis of an orbit is the point at which the orbiting body is farthest from its primary (more precisely, the farthest point from the gravitational barycenter). This point rotates about the center of mass as a result of the gravitational action of the bodies in the stellar system, the shape of the star(s) being orbited, and a number of other factors , and thus traces out a Spirograph™ flower pattern around the center of mass over a long period of time.
For Earth, the precession of the apsides occurs over a period of ~112,000 years. This cycle will affect interactions of the planet with other bodies in its star system, and could contribute to moon captures.
The inclination of a planet’s orbit also changes over time. Think of a juggler spinning plates atop sticks; the plates tend not to spin in one orientation, but to wobble around the center point of their rotation.
Most major planets will have very small orbital inclinations. The protoplanetary disk from which they formed won’t have been exceptionally thick, and the gravitational interactions among the disk and other massive bodies in the system will have the cumulative effect of pulling them all into more-or-less the same orbital plane (the same thing happens in the accretion disk of a black hole, and indeed, in spiral galaxies).
In the Solar System, inclinations of the orbits of the planets are measured relative to the invariable plane. The major planet with the highest orbital inclination is Mercury, at 7.005°; Uranus has the smallest orbital inclination, measuring only 0.77°.
The inclination of planetary orbits in the Solar System is measured either against the Sun's equator, or the invariable plane. Earth's orbit is at ~7.155° to the Sun's equator, and ~1.578690° to the invariable plane, and it varies by ~2.86°  on a cycle of ~70,000 years.
Elsewhere in the star System
For instance, let us imagine the following scenario between two planets:
- They are both midway through the cycle of their orbital inclinations; in other words, they are orbiting in the same plane;
- They are both at the maximum extent of their orbital eccentricity cycles; which is to say, each of their orbits is the most elliptical it ever becomes; and,
- The periapsides of their orbits (when each planet is at the farthest point in its orbit) are oriented on opposite sides of their central star.
For the Worldbuilder, awareness of these kinds of cycles in the relationship of a planet to its star and the other bodies in its local neighborhood can provide fertile ground for hypothesizing interesting effects to be observed and/or experienced by inhabitants of the various worlds in the system.
6. For simplicity, the Earth’s axial tilt in this diagram has been rounded to 23.5°
9. en.wikipedia.org/wiki/Pole_star - Historical