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This article (https://gothamist.com/news/a-green-comet-is-sailing-over-new-york-and-earth-for-the-first-time-in-50000-years) claims that a comet will pass by earth soon for the first time in 50,000 years. How do we know that this exact comet passed earth 50,000 years ago? It obviously was not a recorded event at the time so how can such a claim be made?

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50000 years is the comet's estimated orbital period. That does not necessarily mean that the comet was naked-eye visible from Earth 50000 years ago. That also does not necessarily mean that the comet last came close to the Earth's orbit (as opposed to the Earth) 50000 years ago. The 50000 years is an estimate based on nine months or so of observation time. In addition, the comet's orbit might have been perturbed in the time between its last perihelion passage and the current one. This might even be the comet's first visit to the inner solar system.

From NPR's A bright green comet may be visible with the naked eye starting later this month (admittedly yet another pop-sci article),

"If C/2022 E3 has ever passed through the solar system before, it would have last been seen in the sky more than 10,000 years ago," says Jon Giorgini, a senior analyst at NASA's Jet Propulsion Laboratory.

Note well: This admittedly is yet another pop-sci article. However, NPR has a JPL expert who says it is it least 10000 years ago (if ever) that the comet last visited the inner solar system rather than 50000 years ago. This article is fairly recent. NPR did their research well; they went to an expert from JPL.

Determining the orbit of a long-period comet is highly non-trivial. We have nine months worth of partial observations (mostly azimuth and elevation, which have significant measurement errors, even from the best observatories) of a comet with a suppose 50000 year period. If true, that 9 month interval is 15 millionths of the comet's orbit. That simply is not a long enough of an arc to perform precise orbit determination.

To make matters worse, those long-period comets necessarily travel well beyond Pluto's orbit. At those distances, the entire inner solar system out to Neptune gravitationally act essentially as a single body located at the solar system barycenter. Inside Neptune's orbit, it's better (from an orbital element perspective) to look at objects as orbiting the Sun with the planets as perturbations.

There are now articles saying the comet will never return. That's because using JPL's Horizons to provide osculating orbital elements yields an eccentricity slightly greater than one -- in heliocentric coordinates. Osculating elements can be deceiving, particularly so for long-period comets.

Bottom line: There is no telling if the 50000 year value is anywhere close to correct.

Take popular science articles with a grain of salt.

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    $\begingroup$ But also the probabilities of other objects having interacted with it significantly over that time are very, very small, so the assumption of its orbit not having been disturbed is by far the most likely situation. A grain of salt is fair, but not more than that. :) $\endgroup$
    – Graham
    Commented Jan 13, 2023 at 10:56
  • $\begingroup$ The comet is currently in a parabolic trajectory. I'm not even sure what the period of such a trajectory is supposed to mean. (Has it transitioned from an elliptical orbit in the last 50,000 years?) $\endgroup$
    – chepner
    Commented Jan 13, 2023 at 14:20
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    $\begingroup$ Aphelion isn't really defined for a parabola; the distance grows without limit as the object moves away from the son. $\endgroup$
    – chepner
    Commented Jan 13, 2023 at 15:25
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    $\begingroup$ @MooingDuck it's amusing (to me) that the wikipedia article on this comet uses osculating orbital elements from JPL Horizons as their citation for the 50K year orbit. Clicking on the link shows a period of more than 9e99 years. Determining the orbital period of a long-period comet is highly nontrivial. When the object is well outside the orbit of Pluto, the inner solar system (out to Neptune) gravitational ly acts as a single body. But inside Neptune orbit, it's better to look at an orbit as about the Sun, why the planets as perturbing objects. Aside: space.com articles are oftentimes garbage. $\endgroup$ Commented Jan 14, 2023 at 3:25
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    $\begingroup$ @MooingDuck The error bounds on that 1.00027 eccentricity value are large enough to make the right answer "we don't know". I also suspect space.com (which far too often writes garbage articles; ChatGBT could do better) used JPL Horizons, which provides osculating elements because the calculation is easy. Some sort of mean elements would be better, but that calculation is nontrivial. Some sort of mean elements with respect to the barycenter would be even better, but that calculation is highly nontrivial, and it requires data that spans a lot more than 15 millionths of an orbit. $\endgroup$ Commented Jan 14, 2023 at 3:58
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If I say "Orbital mechanics is easy" some people who know a lot about this will get very angry.

But for the purposes of this question: orbital mechanics are easy.

  • we know where the comet is
  • we know how fast it is going
  • we know which direction it is going.
  • we know about the various objects that might have a large infulence, such as the planets.

so with all this information we can calculate the orbit of the comet. The saying goes "what goes up must come down" but with orbits: what's coming down must have gone up at some point in history.

So with the information about the orbit we can spool back the timeline, and check where the planets were at various points in time. And apparently, 50.000 years ago the orbit of the comet and that of earth got reasonably close together.

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    $\begingroup$ You're right, Orbital mechanics is not easy because the solar system is chaotic i.e the orbit might get Perturbed because of everything $\endgroup$
    – user47732
    Commented Jan 13, 2023 at 11:25
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    $\begingroup$ Well summarized. It's not easy. But the principle is which you describe here - and that's how this number is derived. $\endgroup$ Commented Jan 13, 2023 at 11:49
  • $\begingroup$ We don't know where the comet is. We know measurements of azimuth and elevation, but not range (unless we've pinged it with radar). Unless we've pinged it with radar, we do not know velocity, and even if we did, that would just give range rate (the component of velocity toward the Earth). If you consider a graduate level class on statistical orbit determination easy, then yes, "orbital mechanics is easy". $\endgroup$ Commented Jan 13, 2023 at 13:14
  • $\begingroup$ @uhoh My answer does not say what you read it as saying. Propagating comets, and this is particularly so for long-period comets, is highly nontrivial and not very accurate. There are now articles saying the comet will never come back. We do not know that. We also do not know when the last time the comet visited the inner solar system, if it ever did. What we do know is that it appears to be a long-period comet as opposed to an invader from outside the solar system. $\endgroup$ Commented Jan 14, 2023 at 4:10
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    $\begingroup$ Thanks a lot! @uhoh . Yes, the orbit of an comet can be predicted though it would be tough $\endgroup$
    – user47732
    Commented Jan 14, 2023 at 6:02

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