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How long was an Earth year several billion years ago? (I'm assuming constant days, even though I know days were much shorter back then).

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  • $\begingroup$ Leap seconds are to compensate for irregularities of Earth rotation (about its axis I mean), no? $\endgroup$ – frapadingue Jul 5 '18 at 6:01
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Little can be said about the specifics of earth's orbit far in the past.

  • We have no reliable records

While the seasonal variations may leave effects, they aren't recorded in a way that allows us to directly determine their length. There are instances where we can read the day/year ratio. But the variation in the length of the day over long periods dominates the change.

  • The solar system orbits are chaotic

The planets and other objects of the solar system affect each other. While earth's orbit is stable in the short term, it cannot be predicted over time scales of many millions of years. Simulations of the solar system over time show the orbits of the planets change over time. But the specific changes that have occurred in the past cannot be calculated. The known factors that would push the orbit in a particular direction (tidal drag and sun mass loss) are much smaller than other sources of variation. Without more evidence, the best we can do is assume that the long-term size of the orbit was likely similar to the orbit of today.

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Most of the need for leap seconds is due to variation in the length of the day, not changes in the length of the year.

A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC) in order to keep its time of day close to the mean solar time as realized by UT1. Without such a correction, time reckoned by Earth's rotation drifts away from atomic time because of irregularities in the Earth's rate of rotation. Since this system of correction was implemented in 1972, 27 leap seconds have been inserted, the most recent on December 31, 2016 at 23:59:60 UTC.

(From Wikipedia)

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The need for leap seconds is because the length of the mean solar day - that is, the average time between astronomical midnights (i.e. when the Sun crosses the antimeridian below an observer standing on the Earth's surface at any given point) or likewise, between noons, which defines our usual daily life rhythm, is getting longer. The mean solar day is almost, but not quite, the same as the Earth's rotational period: it is actually a bit longer, by about 236 seconds: this is because while the Earth is rotating, it is also orbiting, and thus in the time it takes to complete one rotation it has moved ahead in its orbit just enough that the Sun's position is now slightly "earlier" than it would be for a hypothetical stationary Earth and it must thus rotate a little more to finish the "job".

(There is also a circum-annual variation in the actual time between midnights due to the fact the Earth's orbit is elliptical, this is why we say "mean" solar day, as it's averaged out over the whole course of the year.)

Thus the length of this period - which is what we think of as 24 hours, or 86.4 kiloseconds - is actually coupled to both the rotation and orbital motion of the Earth, and thus your question about the orbital period changing as a reason for this effect is legitimate.

However, that is not, in fact, the primary reason. What the primary reason is is that the Earth's rotational period is changing, and this is due mostly to the effect of the Moon's gravity raising the tides. As you may know, the Moon's gravity causes the Earth to "bulge" slightly, deforming it into a somewhat prolate (football) shape. Due to the fact the Earth's matter does not immediately respond to an applied force, as the Earth rotates, this bulge gets slightly "behind" the Moon and thus the Moon's gravity tugs forward on it, which produces a torque that opposes the Earth's rotation, causing it to slow down.

As a result of this, the mean solar day is now no longer exactly 86.4 ks, but instead about 86.400 002 ks, or two milliseconds longer, than it was at the time that the first standardized second was created in reference to: namely the mean solar day of the year 1900, which would then later become standardized further to an atomic clock-based definition.

But our calendrical system is based on days of exactly 86.4 ks, as we use atomic time as our standard now, and we like to use simple whole numbers of seconds, minutes, and hours (or just seconds at the base, with time standards like TAI and UNIX time but we love calendars and don't use those outside of computer internals.). As a result, the "days" defined by them slightly fall behind the actual rotation, which means that "clock noon", i.e. 12:00, or 43.2 ks from midnight, gradually comes earlier and earlier - 2 ms each clock day - than the actual solar noon. After about 500 days, this adds up to one full second, and thus to compensate and "push" clock noon back on track, we have to account for that by making one clock day 1 second longer, or 86.401 ks (the last second of which appears on a 24-hour hours-minutes-seconds clock as "23:59:60", not, as one might think, "24:00:00"), effectively elapsing all that undercounted time in one shot.

So the answer is not necessarily - it's that the rotational period is getting longer.

However, that doesn't necessarily mean the orbital period is absolutely constant either, and you also ask about the very beginning of the Earth's history, that is, if it may have been different after initial formation. And the answer to this, I believe, is likely yes: the early Solar System was much more chaotic than today. In particular, some of the planets (I believe Jupiter) migrated to their current positions from ones that were at that time different, and no doubt their passage would have altered orbits as they went due to the shifting gravitational forces. But I do not have a figure for the initial orbital period, and it may not be possible to really know to absolute certainty. That said, the rotational period was definitely much, much shorter: immediately after the Moon formed it was around 4-6 hours (14-22 ks) depending on the sources. This would have at first rapidly slowed down as the same tidal bulging effect occurred but far more severely with both faster rotation and the Moon much closer in, but as it receded - also due to the same effect: in particular, as the rotational energy is robbed from the Earth, it is acquired by the Moon so as to conserve energy, and this means an increase in its gravitational potential and so a higher orbital distance - the rate of decrease decreased (heh) considerably.

Also, while the orbital period now I do not believe can change much in any progressive fashion in a similar manner as there is not a suitably constantly-directed force being applied to the Earth that would be capable of effecting a change in the orbit in a single direction over the long term, if it were to change in such a similar manner, i.e. the orbital period were somehow steadily getting longer, as you suggest, that would actually result in the mean solar day becoming slightly shorter, thus acting to oppose the effect from the slowing Earth rotation instead of supporting it. This is because the orbit would have to be increasing in radius, and that would mean that the total amount of orbital angle that it traverses in a single rotation period would be less, and thus the amount of extra rotation required to get the Sun back into alignment in the sky would be less as well, shrinking the mean solar day instead of increasing it.

To top it all off, though, there is one effect that we know of that is in theory causing a secular change of the Earth's orbit, but there will likely not be enough time for it to do anything significant until the Sun expands in about 5 billion years (160 petaseconds, Ps), causing the Earth to be incinerated. That effect is gravitational radiation - gravity waves, like the ones that were recently detected from merging black holes and neutron stars. Just as they carried away the energy in those systems and led to their collapse, likewise this phenomenon is in theory slowly causing the Earth to spiral inward toward the Sun. Were the Earth to somehow be protected from being vaporized, then over an interval of time of on the order of magnitude of $10^{15}$ years ($10^7$ Ps), the orbit of the Earth would slowly decay, the planet spiralling inward and the orbital period decreasing, to at the end of this period crash into the remnant of the Sun, now a black dwarf (a cooled white dwarf that no longer glows visibly, which is something that does not yet exist in the present Universe as not enough time has elapsed for any white dwarfs to have cooled sufficiently, even those formed very early in the Universe's history). But also, insofar as the length of the day, the mean solar day at this time would now be effectively infinite, because the Earth will have tidally locked itself to the Sun (the Moon would have spiraled back in and crashed into it again) by the same process as discussed before that the Moon is doing right now. That is, it will be rotating at the same speed it is orbiting, and would continue to do so up to the bitter end, a brief X-ray burst as it pierces the crust of the black dwarf at nearly relativistic speeds. (Actually, it probably would have broken up due to the tides before then, and thus would gradually rain down in little bits, sorry...)

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protected by Qmechanic Jul 5 '18 at 7:09

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