Why is the axial tilt of a planet expressed as a single angle when two angles are necessary to specify a point on a sphere? Imagine if the Earth’s axial tilt were 90 degrees, then the axis of rotation could point anywhere along the circle in the orbital plane. In the extreme cases, either always point directly towards the sun or always point directly towards the direction of orbit. In the former case, half of the planet would have eternal day or night, and in the latter, each half would have equal length day and night. A second angle could distinguish the two.
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$\begingroup$ Axial tilt and tidal lock are two very different things. Earth's rotation is not locked to the sun so one angle is sufficient. $\endgroup$– Rory AlsopCommented Jul 27, 2021 at 8:32
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$\begingroup$ If you want the official data on the Earth's rotation, see the IERS. But be warned, their site is huge. :) iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html $\endgroup$– PM 2RingCommented Jul 27, 2021 at 19:24
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3 Answers
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The Earth's axial tilt is expressed as a single number because it's just an angle. It can be considered to be the angle between the plane of the equator and the plane of Earth's orbit, or the the angle between its axis of rotation and its orbital axis. Its axis of rotation always points to the same two locations in the celestial sphere where all locations are expressed as two angles. The north location is near Polaris.
By "always" I mean right now, over a time scale of a few years. The point actually moves around in a circle over the course of 26000 years. There are other, smaller deviations in a much shorter time scale. Search terms "precession" and "nutation" will find explanations with animations. Neither phenomenon relates to your question, though. The amount of tilt over periods of millions of years stays between 22 and 24.5 degrees, even though Earth's extended axis moves fifty some degrees in thirteen thousand years.
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1$\begingroup$ Axial tilt is the angle between the rotational axis and the orbital axis rather than the angle between its axis of rotation and the plane of its orbit. $\endgroup$ Commented Jul 27, 2021 at 11:22
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1$\begingroup$ OK. the fact that the axis of rotation moves around in a circle (precession) explains why only one angle is used. A single angle identifies the circle. Now it makes sense! $\endgroup$ Commented Jul 27, 2021 at 16:16
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$\begingroup$ Not really anything to do with precession. The angle is the angle between a line and a plane, and a single number identifies that value. Also as the Earth orbits the Sun, the north pole sometimes points towards the sun (northern summer) and sometimes away (northern winter) So even if precession didn't exist, we would only use one number. $\endgroup$– James KCommented Jul 28, 2021 at 16:46
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$\begingroup$ I suppose the second angle determines in which month is the longest day. $\endgroup$ Commented Aug 1, 2021 at 18:32
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$\begingroup$ Axial tilt does determine which month has the longest day and which month has the shortest, but it's still a single angle - not two. $\endgroup$– stretchCommented Aug 6, 2021 at 16:16
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Technically, the Earth’s axial tilt (or that of any other planet, for that matter) is expressed as two angles, namely the right ascension and declination of the point on the celestial sphere towards which the north pole of that planet points. For example, in Earth’s case, it’s 0 h and +90°. For Mars, it’s 317.68143° (21 h 10 min 44 s) and +52.88650°. And so on.
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Axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane.
To distinguish between one or two angles application: There is the angle of inclination which is measured between a reference plane e.g. Invariable plane and the plane of the orbit. Then there is the Longitude of the ascending node which determines the direction that the inclination is pointing. Which is all about orbital rotation and not about the questioners planetary rotation.
https://en.wikipedia.org/wiki/Axial_tilt
https://en.wikipedia.org/wiki/Invariable_plane
https://en.wikipedia.org/wiki/Longitude_of_the_ascending_node
