# What is the chance that the Sun will not rise tomorrow?

What is the most likely natural astrophysical mechanism for the "Sun not rising tomorrow", consistent with our scientific knowledge today?

Background

The "sunrise problem - What is the probability that the Sun will rise tomorrow? - is a classic probabilistic conundrum going back (at least) to David Hume. It can be considered as simply a Bayesian or inferential induction question, but as Laplace noted in his 1814 discussion of the rule of succession, the odds of the sun rising are:

… incomparably greater for him who, recognizing in the totality of phenomena the principal regulator of days and seasons, sees that nothing at the present moment can arrest the course of it.

In other words, if there are no plausible physical "phenomena" that could "arrest the course of it", simply extrapolating the fact that it has risen every day in the past grossly overestimates the chance that it will not rise tomorrow. There have been about 1.7 trillion sunrises on 4.54 billion year old Earth, so the extrapolated odds for the Sun not rising tomorrow is $$\sim 10^{-12}$$. Correcting for survivorship bias may increase the odds to $$\sim 10^{-11}$$ (i.e. a lower limit of about a billion years on the Earth's expected lifetime).

Specification

I consider the "Sun not rising tomorrow" to mean one of the following happening with less than a day's warning:

• The Sun turns off or is destroyed
• The Earth stops rotating or is destroyed.
• Something blocks the Sun's light from directly reaching any part of the Earth's surface.

Mechanisms should not invoke bureaucratic aliens, wrathful gods, nuclear winter, Death Stars, comic book supervillains, or magic. To keep things simple (and relevant to Astronomy SE), please consider only astrophysical mechanisms and ignore possibilities such as a government conspiracy to hide an impending catastrophe from the public, or that we are all in a computer simulation whose funding has just been cut.

Mechanisms

When talking with students about uncertainty and the sunrise problem, an example mechanism I have used in recent years is that our universe may be in a metastable false vacuum state that could suddenly decay. One paper estimates that the vacuum decay lifetime of the universe is $$>10^{65}$$ years with 95% confidence, which roughly implies that the chance of the Sun not rising tomorrow is $$\lesssim 10^{-67}$$. I have trouble coming up with more likely possibilities that could sneak up on us without warning:

• I don't think a supervolcano could unexpectedly erupt and block the atmosphere with ash without geophysicists noticing the buildup. (This pretty much leaves only astrophysical catastrophes, which is why I am asking this question on Astronomy SE.)
• Wouldn't modern sky surveys give us more than a day's notice of any incoming planet-busting asteroids, comets, or rogue planets, and wouldn't gravitational perturbations of the solar system reveal approaching rogue neutron stars or stellar-mass black holes? I wonder, however, if a loophole might exist for something like a a 0.0001 solar mass primordial black hole, but they may not even exist.
• A nearby Gamma-Ray Burst could perhaps make the Earth's atmosphere opaque by ionizing the Earth's atmosphere or flash boil the oceans into clouds (and would certainly kill all life capable of seeing the Sun rise). There is an estimate that the average chance of a Gamma Ray Burst sterilizing an earth-like planet is about $$3.2\times10^{-19}$$ per year (i.e. $$\sim10^{-21}$$ per day), but I am not sure what the odds are for the Earth itself.

To repose the question succinctly: Is there some astrophysical mechanism more likely to stop the Sun from rising tomorrow than the $$10^{-67}$$ odds for vacuum decay?

This question is already rather long, but more background may be helpful in light of the many comments.

The sunrise problem appears in myriad books, websites, and videos. Aside from Hume and Laplace, it has been discussed by many others, including Buffon (of Buffon needle fame), Richard Price in his Appendix to Bayes foundational essay, John Maynard Keynes in his "A Treatise on Probability", and Harold Jeffreys in "Theory Of Probability".

Jaynes has emphasized, however, that most presentations and criticism ignore Laplace's essential caveat quoted above.

(Laplace) is pointing out to the reader that the rule of succession gives the probability based only on the information that the event occurred n times in N trials, and that our knowledge of celestial mechanics represents a great deal of additional information. Of course, if you have additional information beyond the numbers n and N , then you ought to take it into account. You are then considering a different problem, the rule of succession no longer applies, and you can reach an entirely different answer.

So Laplace gave the sunrise problem as an example for his Rule of Succession, and then immediately pointed out that the Rule did not apply because there was so much prior knowledge about the celestial mechanics behind sunrises. Laplace was emphasizing that a likelihood estimate must use all available prior information.

The statistical part of Laplace's analysis of the sunrise problem has been discussed endlessly but the astronomical caveat has been almost completely ignored. As far as I am aware, those who do acknowledge the caveat have never quantified the prior, perhaps in part because the typical statistician doesn't have the expertise to assess the astrophysical constraints. This question is exactly about trying to make a better estimate of this prior.

Versions of this question could plausibly be asked on Astronomy, Physics, Cross Validated, World Building, or even Philosophy Stack Exchange sites. It is possible that answers to the question are more "useful" (or at least engaging) to teachers and students of scientific uncertainty, probability, and statistics, than to astronomers per se, but Astronomy SE seems more likely to have the relevant expertise to estimate the prior. The most closely relevant research papers are in astrophysics, e.g. "Is a doomsday catastrophe likely?" by Tegmark & Bostrom in Nature and "The Resilience of Life to Astrophysical Events" by Sloan, Batista, & Loeb in Nature Scientific Reports.

Even simply listing poorly quantified possible sunrise-stopping mechanisms could be helpful. It is certainly true that an unknown mechanism might actually be the most likely way that sunrises might stop tomorrow, but bounding the probability from below by listing known processes can still be very useful.

• I think you struggle to get useful anwers here. You are in tiny probability land, and weird things happen there. For example, supervolcano are rare (say one in trillion chance) and you say that the scientists would have noticed -- but perhaps the governments have suppressed this to stop a panic... unlikely, probably not even possible, shall we say a 1-in a million chance. So put those two together and you have 10^-18, still much much more likely than your vacuum decay number. And there are just too many unknowns to make estimations of such tiny probabilities useful. Mar 27 at 20:48
• Among the unknowns are the unknowns about us being completely wrong about the sun. We say it is driven by nuclear fusion in its core.... so it can't "stop working". But perhaps we are completely wrong about that... It's not likely, it is very very unlikely, but I'd bet it is more likely than 10^-67! And if we are completely wrong about the sun, then how can we possibly answer the question. This is the problem of getting into tiny probablities. Mar 27 at 20:55
• The only way to estimate probability is to take a sample size and see how many times it occured. Sample size:Every day of recorded history. Times occured:0. So, 0% probability Mar 27 at 21:59
• @JamesK I think we will struggle, not the OP. If you had some more experience asking questions you'd understand the difference. It's (almost) always the people who don't ask who have the most negative comments on questions.
– uhoh
Mar 27 at 23:15
• @Starshipisgoforlaunch The correct way to show you do not find a question useful is to vote down. Voting to close requires choosing a reason and I'm not of the opinion any of the close reasons quite fit my view. As uhoh points out, it's a well-written question, interesting in a away, but I just regard it as not one that a useful answer can be made for. Mar 27 at 23:28

My guess is that the most likely mechanism would be something like a world-war/pandemic that temporarily prevents astronomers from analyzing sky surveys and/or prevents planetary defense strategies AND a large asteroid/rogue planet that could destroy the Earth. Obviously both of these are extremely low-probability but I suspect that even their intersection would be the most likely mechanism.

And here's some poor quantification for you:

Suppose some of these disastrous wars/pandemics were: COVID-19, Spanish Flu, Black Plague, World War 1, and World War 2. They average around 3 years each, so during human history, about $$(3 \text{ yrs/disaster}) * (5 \text{ disasters}) = 15 \text{ yrs}$$ have been spent in extreme disaster. I know these numbers are very rough estimates but for a question like this, you can't expect much precision. I'll also suppose human history started around 200 000 years ago. Then,

$$P(\text{war/pandemic})\approxeq 15/200000 \approxeq 7.5 \times 10^{-5}$$

Furthermore, let's suppose the only giant-impact in Earth's history was the moon formation event. Also, if the Earth is 4.5 billion years old, it is $$(365)(4.5 \times 10^9) \approxeq 1.6 \times 10^{12}$$ days old. Then,

$$P(\text{earth destruction}) \approxeq 1/1.6 \times 10^{12} \approxeq 6.1 \times 10^{-13}$$

Therefore, $$P(\text{war/pandemic} \cap \text{earth destruction}) \approxeq (7.5 \times 10^{-5})(6.1 \times 10^{-13}) = 4.6 \times 10^{-17}$$

• Thanks Thomas. I was initially thinking in answers for "tomorrow", where "today" is March/April 2023, but I certainly agree that averaging "today" over the near future (e.g. the next 100 years) where disasters may happen, as you have effectively done, is also a reasonable approach and very interesting. Given the huge uncertainties, I am very happy with very rough order-of-magnitude estimates. Apr 3 at 14:29
• I tend to agree with overall concept of this answer, but the probabilities need more work. It could be argued that two world wars, & very destructive ones at that, & pandemics are features of only the 20th Century. The Black Death Plagues, affected large areas over significant time periods, but they weren't global pandemics during a particular era. Also, pandemics rely on large numbers of people moving global with ease & speed over short time spans. Applying any statistics specific to the 20th Century for the period that homo sapiens have been extant is incorrect. ...
– Fred
Apr 7 at 5:09
• Moon forming, nearly Earth destroying events, OK, but what about Chicxulub meteor type events (the so called dinosaur killer), or even smaller ones wiping out a locality?
– Fred
Apr 7 at 5:12
• @Fred the meteor would have to "destroy the Earth" as per the specifications provided in the question so it excludes events where localities are wiped out. I agree that it's inaccurate to apply recent world-wide catastrophes to the entire duration of human history but then again, planetary defense systems have only existed for about 10 years, so there's really not a large enough sample size to estimate a probability with much accuracy anyways. I was erring on the safe side and trying to underestimate the probabilities. Apr 7 at 14:17

I have thought a bit more about possible mechanisms that might "stop the sunrise", so I am posting my own incomplete answer in case anyone might find it pedagogically useful.

Supervolcano

I confirmed onthat an unexpected supervolcano eruption could not block the sun by tomorrow. Although there is no single model for supervolcanoes, the time taken for magma to gather is far longer than a day. Also, even if a single supervolcano could unexpectedly erupt, it would take more than a day for its ash to cloud the entire Earth. For example, after the Chernobyl disaster, it took almost two weeks for the radioactive cloud to reach eastern Canada.

Asteroid Impact

Unlike a supervolcano, a single asteroid impact could cloud the entire Earth's atmosphere within a day because hot ejecta rains down over the entire planet, setting fires and vaporizing water. It is estimated that the gases and ejecta from the 10 km Chicxulub impactor covered the globe within hours. It might take a few days for a 1 km impactor. Taking human crises into account, @Thomas's very rough order-of-magnitude estimate of $$\sim 10^{-17}$$/day risk averaged over the the near future seems reasonable. Since a Chicxulub impact is sufficient, however, I think the appropriate impactor time scale is closer to 100 million years than Thomas's 4.5 billion years, giving $$\sim 10^{-15}$$/day risk. Pretty much all answers for this question must be Fermi estimates, so a factor of two uncertainty difference in the exponent is not really significant. The answers to "How early could we detect an asteroid the size of the one that caused the extinction of the dinosaurs?" illustrate some of the challenges in estimating how much warning we might have.

Failures due to human crises aside, there might be some impactors that would be tough to detect, but I haven't been able yet to make a quantitative odds estimate:

• Interstellar objects might be missed even if current detection networks are working well. ʻOumuamua was only detected a week after its closest approach to Earth, but it was likely too small to be a sunrise stopping impactor.
• A group of smaller co-travelling objects (perhaps produced in an earlier asteroid-asteroid collision?) might be harder to detect and require less total mass to cloud the Earth if the impacts were spread over the globe. This would be similar to Comet Shoemaker-Levy that was a 21 piece "freight train" that hit Jupiter over several days.

Primordial Black Holes

If primordial black holes exist, the probability of one colliding with the Earth is estimated by Rahvar to be $$\frac{dN}{dt} \approx 10^{-8}f\left(\frac{M}{10^{23}\mathrm{gr}}\right)^{-1}\mathrm{Gyr}^{-1} \sim10^{-30}f\left(\frac{M_\odot}{M}\right)\mathrm{day}^{-1}$$

where $$f$$ is the fraction of dark matter made of mass $$M$$ primordial black holes, and $$M_\odot$$ is the Sun's mass. For the $$0.0001 M_\odot$$ mass primordial black hole mentioned in the question, Carr et al estimate and upper bound of $$f\lesssim 10^{-2}$$, giving $$\frac{dN}{dt} \lesssim 10^{-28}\mathrm{day}^{-1}$$, considerably less than the asteroid impact probability above.

Sun going dark

Although this question is primarily about mechanisms that could unexpectedly destroy the Sun or the Earth or block the sunlight, it is interesting that there is a current ongoing research project that simply looks for stars that disappear. The VASCO project has recently searched for vanishing stars and other astrophysical objects that may have disappeared. Based on 5399 sources that disappeared over $$\sim$$70 years out of 600 million objects from the United States Naval Observatory (USNO) B1 catalog, the naive disappearance rate is $$4\times 10^{-10}$$/day. This is much higher than the undetected asteroid impact rate above, but it isn't a very helpful number since most (and perhaps all) of these disappearances are for sources unlike the Sun, and we expect that most (and likely all) are due to known processes e.g. failed supernova or observation artifacts. Some of the disappearances and the sheer number seem hard to explain, but the data are not yet well enough understood to set limits on specific classes of stars.