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In the new movie "Don't Look Up", astronomers discover a comet in the outer Solar System that's going to hit the Earth about 7.5 months later. I think they calculate its trajectory within a day of discovering it, and they're virtually certain that it will impact the Earth, knowing the exact day and time.

While I believe that they can determine when it will pass by with that accuracy, I wonder if they can tell that early how close it will come. In the past astronomers have found asteroids that would come near Earth, and early reporting didn't seem to be so precise about the distance.

The comet was described as an Oort Cloud object, and I think it was its first appearance (they named it after the grad student who found it). I'm not sure how far out it was when they discovered it, but at one point in the movie they showed it passing by a gas giant for effect; it might have been Jupiter, but I'm not sure, and I don't recall how long this was after it was first seen.

How long would they need to observe such an object, and roughly how close would it have to be before they can determine the tractory precisely enough to know that it will hit Earth? How much advance warning would we have of certain cataclysm?

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    $\begingroup$ The movie is allegorical. The asteroid represents climate change, and the fact that they discovered it and reported it to the government, who whisked them off in a plane within a few hours, only to leave them hanging in a waiting room and ignore them is a social comment on the priorities of politicians. It's not supposed to be an actual science-based disaster movie, the comet is a metaphor. $\endgroup$
    – Dave Meteors
    Commented Dec 29, 2021 at 17:14
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    $\begingroup$ Related: astronomy.stackexchange.com/q/39837/16685 $\endgroup$
    – PM 2Ring
    Commented Dec 29, 2021 at 18:46
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    $\begingroup$ I know the movie isn't meant to be taken literally. But it's still fun to discuss the science that they show. $\endgroup$
    – Barmar
    Commented Dec 29, 2021 at 18:50
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    $\begingroup$ @jmoreno I think you're being overly literal in what "science" refers to. Also, the main characters are scientists, they detected the comet while doing research on cosmology. $\endgroup$
    – Barmar
    Commented Dec 30, 2021 at 4:57
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    $\begingroup$ I still think you're using a narrow definition. If you use the principles that were discovered through the scientific method, that's also science. So calculating the orbit of the comet is science. $\endgroup$
    – Barmar
    Commented Jan 4, 2022 at 0:59

2 Answers 2

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Short observational arcs present difficulties in orbit determination. A couple of examples (taken from Wikipedia) :

  • (392741) 2012 SQ31 was observed for one day, and the best-fit orbit was found to be a trans-Neptunian dwarf planet. It is actually a much smaller main-belt asteroid (between Mars and Jupiter)
  • 2004 BX159, with an observational arc of three days (and 8 observations) it was determined to have a perihelion of 1.5 (±3) AU. This made it a potential Near-Earth Object, but note the uncertainty is greater than the estimated value. In fact, it orbits between 2.2 and 2.9 AU and poses no threat.

In principle, three observations are sufficient to determine an orbit. But with only a few observations over a limited time, it would be very challenging to establish the orbit with sufficient accuracy to determine that a collision is certain.

What could happen is that a short observational arc allows for "pre-covery" images to be found. These are photographs of the object at earlier times, which may have been taken for some other purpose and only co-incidentally contain the comet. Finding pre-covery images allow for much greater accuracy in the orbit determination, and may allow for an Earth impact trajectory to be determined.

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    $\begingroup$ anecdotal evidence is not the best scientific evidence unless you want to make a counter example to "there are no..." claims. $\endgroup$
    – planetmaker
    Commented Dec 26, 2021 at 21:24
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    $\begingroup$ I don't understand. I've given a couple of examples of asteroids that were misdetermined after a short observational arc. Not anecdotes. Thsi should be sufficient to establish that "with only a few observations over a limited time, it would be very challenging to establish the orbit with sufficient accuracy to determine that a collision is certain." $\endgroup$
    – James K
    Commented Dec 26, 2021 at 21:31
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    $\begingroup$ In the edits it is mentioned that this body also has a close encounter with Jupiter. This makes orbit determination even harder. I'm willing to call it: you can't determine an orbit to 6400km accuracy with a one day observational arc for a body which is going to experience a significantly non-keplarian orbit due to a close encounter with Jupiter. $\endgroup$
    – James K
    Commented Dec 26, 2021 at 21:35
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    $\begingroup$ I concur with your analysis. Yet I wonder: do you have / does there exist a guestimate on the average accuracy or goodness of prediction after such short observation (more detailed than 'often it's not accurate by a large margin)? Like I know for weather forecast "tomorrow is the same as today" has (where I live) about 60% accuracy to become true. $\endgroup$
    – planetmaker
    Commented Dec 26, 2021 at 22:28
  • $\begingroup$ @JamesK Determining whether it's a hit or not after a major encounter is probably beyond what we can do even with a very good orbital track. $\endgroup$
    – Loren Pechtel
    Commented Dec 28, 2021 at 23:30
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Accurate determination of collision within 1 day of discovery is realistic only if old pre-discovery measurement data is available.

We can approximate the orbit determination accuracy with some assumptions:

  • Comet is at Jupiter distance (780 000 000 km) traveling about 10km/s perpendicular to observation direction
  • Instrument is Hubble (1/20 arc second resolution)
  • Observation time is 24 hours
  • Time to impact is 200 days

At that distance, Hubble can determine the tangential position to ±190 km accuracy, which is 0.02 % of the distance it travels in 24 hours. This is approximately the accuracy the comet's velocity can be determined. Averaging together continuous observations will improve accuracy slightly and various error sources will decrease it. Most important error source is the measurement geometry: velocity in line with the observation direction is much harder to measure than tangential velocity - for this example I picked the easiest situation.

Over 200 days, the 0.02 % error in velocity translates to 35 000 km error in position. Comparing to Earth's 6 400 km radius and the cross-sectional area, we could only predict 1-in-30 probability of collision.

In conclusion: Even by picking unrealistically good observational situation, 24 hours of observation at Jupiter's distance gives 1:30 odds for collision estimate.

For what it is worth, here are screenshots of the two relevant scenes from the movie. The first one reads "2 hours ago", "3 hours ago", and so on, so they do have some pre-discovery data. This scene however does not show a particularly long history, even though it might be available.

The second screenshot appears to show the comet already inside Jupiter's orbit and traveling on a quite direct path towards Earth. This would make it even harder to determine its orbit, but on the other hand the direct collision course does not match the 6+ month timeline.

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    $\begingroup$ +1 on the pre-discovery measurement data--Given the one day of observation, one could possibly look backwards into the record and find other observations to confirm and refine the solution. $\endgroup$
    – Dave X
    Commented Dec 28, 2021 at 4:10
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    $\begingroup$ It is never explained in the movie, but I am pretty sure that is what is happening. After having spotted the comet, the protagonist walks over to a fancy "Hollywood" interface, where by tapping on the screen, she makes an additional four sightings of the comet appear. It was my assumption that what this is supposed to represent is her looking up older observations in some magic Hollywood database via some magic Hollywood visual interactive query system. $\endgroup$
    – Jörg W Mittag
    Commented Dec 28, 2021 at 20:17
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    $\begingroup$ When the protagonist's professor and his students compute the trajectory, they have 14 measurements on the whiteboard. $\endgroup$
    – Jörg W Mittag
    Commented Dec 28, 2021 at 20:21
  • $\begingroup$ @JörgWMittag Heh, inspired by this question I also watched this movie yesterday. A fine comedy, but the science doesn't hold up. I added some screenshots. $\endgroup$
    – jpa
    Commented Dec 29, 2021 at 6:54

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