26
$\begingroup$

In a reference system where the sun is static, the rotation and revolution of the earth are, when viewed from above the north pole, both counterclockwise.

Is it a coincidence that they agree? Or does the earth's angular momentum somehow "interact with gravity" in such a way that agreement between the rotational directions is "favoured"?

I guess in classical mechanics terms, my naive intuition is that there is always the same amount rotating towards the sun as away from it, so gravity shouldn't play a role - or is it actually exactly this which is wrong when taking the motion around the sun into account?

$\endgroup$
6
  • 1
    $\begingroup$ The spin axis inclinations to their orbital planes of the terrestrial planets are 0, 177, 23, 25 degrees. So not really aligned at all. $\endgroup$
    – ProfRob
    Feb 25 at 8:28
  • 2
    $\begingroup$ And the Moon's orbit, too! $\endgroup$ Feb 25 at 15:31
  • $\begingroup$ Similar: astronomy.stackexchange.com/questions/6183/… $\endgroup$
    – BowlOfRed
    Feb 26 at 9:21
  • $\begingroup$ @ProfRob, I don't think we can count Mercury: tidal effects from the Sun mean we're not seeing its original inclination. $\endgroup$
    – Mark
    Feb 27 at 0:32
  • $\begingroup$ @Mark exactly what my answer says. However, the question is not asking about the original inclination of the Earth. $\endgroup$
    – ProfRob
    Feb 27 at 6:25

4 Answers 4

24
$\begingroup$

Not a coincidence, most other planets rotate the same way. It is a consequence of how planets were formed from a disc of gas and dust that was orbiting around the sun as it formed.

The sun formed from a cloud of dust that shrank and collapsed under its own gravity. The cloud would have had some angular momentum, and this was preserved as the cloud got smaller, causing the disc to form rotating around the sun in one direction.

The planets formed by accretion within this disc, they would inherit angular momentum from the disc, and so they would tend to rotate the same way. There a couple of exceptions: Venus rotates very slowly, backwards, apparently a result of complex interaction between Venus, its atmosphere, and other solar system bodies. Uranus rotates sideways. It seems that Uranus might have undergone some cataclysmic event in its early history that tilted it over by more than 90 degrees. The other planets all retain some of their initial angular momentum, and all rotate in the same direction.

$\endgroup$
3
  • 4
    $\begingroup$ This isn't really a good argument. The overall angular momentum is totally dominated by the orbit. The spin is a perturbation. Sure, as I said in my deleted answer, if accretion of a planet is smooth and well-behaved in a fluid, then a Keplerian velocity-radius law for circular orbits results in alignment. $\endgroup$
    – ProfRob
    Feb 25 at 10:04
  • 5
    $\begingroup$ However, terrestrial planet formation happens after the fluid/gas has gone, in the accretion of planetesimals on eccentric orbits with a range of inclinations. This results in a chaotic outcome and random alignment. The state of alignment for the inner 4 planets is is consistent with randomness (Mercury is probably affected by tides) and the Earth is inclined at 23.5 degrees to its orbit (and there is likely an anthropic element to that too). $\endgroup$
    – ProfRob
    Feb 25 at 10:10
  • $\begingroup$ Aren't the inclinations of Venus, Earth, and Mars theorized to each come from a single cataclysmic impact rather than from just slow accumulation? For example, Theia hitting Earth to shift its axis of rotation as well as splashing up enough material to form the Moon. $\endgroup$ Feb 26 at 16:39
16
$\begingroup$

I think it is coincidence, apart from that there may be anthropic arguments for the spin axis inclination (the difference between the spin and orbital axes) to be small but non-zero. i.e. A small, but non-zero inclination is favourable for habitability.

In a previous version of this answer (and I acknowledge that @sno's contribution has made me think a bit harder), I pointed out that the vorticity (see below) of a fluid rotating on circular orbits with a Keplerian velocity profile $v \propto r^{-1/2}$ would favour the accretion of planets with a small orbital inclination. This may well be a factor in the accretion of gas giants.

However, this initial "fluid" phase is only part of the story for the accretion of the terrestrial planets. This will only result in the formation of small planetesimals and indeed, simulations suggest these would predominantly have prograde, aligned rotations (Johansen & Lacerda 2010; Takaoka et al. 2023). The main phase of mass accretion takes place after the gas/fluid has been removed and there is then a very chaotic phase of accumulation (and destruction) of these planetesimals. The orbits become much more eccentric and highly inclined and the final phases of planet construction will consist of a bombardment of a planetary embryo from all directions. The final spin angular momentum of the planet will be dominated by the final few collisions and merger of relatively large bodies, like the collision that probably formed the Earth-Moon system (e.g., Agnor et al. 1999; Agnor 2002).

What all this means is that the orbital inclinations of the terrestrial planets are likely to have been almost random after formation. Examples of simulations that show the spin-axis inclination is essentially random (an isotropic distribution) are provided by Kokubo & Ida (2007); Kokubo & Genda (2010). It is fair to say though that others disagree - arguing that the current terrestrial planets do at least contaim some memory of the initial prograde spin of the smaller planetary embryos (Visser et al. 2020).

Subsequently there are tidal influences that can play a role - either from the Sun or in the Earth's case, from the Moon. However, the timescale on which the spin-orbit alignment can be changed is similar to the timescale upon which the rotation period of a planet is synchronised with its orbital period. Clearly this hasn't happened for the Earth but it probably played a major role in Mercury's zero spin inclination (e.g., Noyelles et al. 2014).

A factor that is worth mentioning is that the small but non-zero (23.5 degrees) obliquity of the Earth's spin to its orbital axis may be a coincidence, but it could be that we observe it to be that way because it is important for our existence (an anthropic argument). The spin inclination of Earth is stabilised by the Moon and ensures a relatively small variation in temperature across the globe and drives the seasons. A very high inclination or a very low inclination may well not be favourable to life (see the introduction in Heller et al. 2010).

Vorticity

If a collection of particles or a fluid coagulates, then the direction of rotation will be given by the vorticity, which is the curl of the velocity vector field.

The planets formed in a flattened protoplanetary disc around the Sun, which accounts for their common direction of orbit and roughly planar geometry. For circular Keplerian orbits around the Sun, the velocity field is $${\bf v} = \left( \frac{GM_\odot}{r} \right)^{1/2} \hat{\phi} $$ and the vorticity is $${\rm curl}\ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r}\left(r v_{\phi}\right)\ \hat{z} = \frac{1}{2}\left(\frac{GM_\odot}{r^3}\right)^{1/2} \hat{z}\ . $$ The direction of this vorticity (i.e. the sense of the spin) is in the same direction as the angular momentum vector of the orbit, given by $$ {\bf L} = m{\bf r} \times {\bf v} = mrv_\phi\ \hat{z}\ . $$

If the tangential velocity component of the fluid depends on $r^{\alpha}$ then the vorticity will be in the same direction as the angular momentum as long as $\alpha > -1$. It is zero if $\alpha = -1$ and in the opposite direction to the orbital angular momentum of $\alpha < -1$. In this case we have $\alpha = -0.5$.

In reality, protoplanetary discs do not rotate in such a uniform fashion. They can be unstable to the formation of large scale patterns and vortices that complicate the planetary formation process. There is also the possibility of fairly random catastrophic collisions between larger bodies near to the end of the accretion process.

$\endgroup$
3
  • $\begingroup$ Out of curiosity, what’s the argument for very small or zero inclination being bad for habitability? $\endgroup$ Feb 26 at 16:07
  • 1
    $\begingroup$ @PeterErwin "For ψp ≲ 5° the habitability of a terrestrial planet might crucially be hindered. Decreasing obliquities induce less seasonal variation of solar insolation between higher and lower latitudes. Thus, winters get milder and summers become cooler. Given that cool summer temperatures turn out to be more important than cold winters for the emergence of continental ice sheets, smaller tilt angles lead to more glaciation. " $\endgroup$
    – ProfRob
    Feb 26 at 16:45
  • 1
    $\begingroup$ @PeterErwin "As a consequence, the temperature contrast between polar and equatorial regions gets very strong (Spiegel et al. 2009), possibly leading to a collapse of the potential atmosphere (priv. comm. with Frank Selsis), which freezes out at the poles or evaporates at the equator." $\endgroup$
    – ProfRob
    Feb 26 at 16:45
5
$\begingroup$

During the giant impact stage, the thickness of a protoplanetary disk is far larger than the size of planetary embryos so collisions are equally likely to come from any direction in three-dimensions. This results in the axial tilt of accreted planets ranging from 0 to 180 degrees with any direction as likely as any other with both prograde and retrograde spins equally probable. Therefore, prograde spin with a small axial tilt, common for the Solar System's terrestrial planets except Venus, is not common in general for terrestrial planets built by giant impacts. The initial axial tilt of a planet determined by giant impacts can be substantially changed by stellar tides if the planet is close to its star and by satellite tides if the planet has a large satellite.

See: Terrestrial Planet Formation at Home and Abroad Sean N. Raymond, Eiichiro Kokubo, Alessandro Morbidelli, Ryuji Morishima, Kevin J. Walsh

https://arxiv.org/abs/1312.1689

$\endgroup$
1
  • 3
    $\begingroup$ I agree. There is probably some anthropic argument for the Earth's inclination to be small but non-zero. $\endgroup$
    – ProfRob
    Feb 25 at 10:12
0
$\begingroup$

As mentioned already in the other answers, the rotation of the initial gas cloud from which the solar system formed is reflected both at a large scale (orbital angular momentum) and a small scale (spin angular momentum) because of angular momentum conservation.

Moreover, even if the planetary rotation would initially be unrelated to the orbital motion, it will eventually become locked (rotation period = orbital period) due to tidal effects. So again in this case the rotation will be in the same sense as the orbital motion (which indeed would be a result of the spin interacting with gravity).

$\endgroup$
2
  • 1
    $\begingroup$ I think the timescale for synchronization of the spin and orbital period is similar to the spin-orbit alignment timescale. Clearly, only Mercury has been affected in that way, the effects are much weaker for the Earth. $\endgroup$
    – ProfRob
    Feb 25 at 10:18
  • $\begingroup$ @ProfRob Yes, the time scale will obviously increase the greater the distance of the planet, but given enough time, all rotations should eventually become locked. Apart from the usual tidal effects there should also be a 'pseudo-tidal' locking effect due to the finite speed of gravity, although that is probably very small as well for small to moderate rotational velocities (compared to the speed of light). See this answer for more astronomy.stackexchange.com/a/55576/35115 $\endgroup$
    – Thomas
    Feb 25 at 15:55

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .