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If an object as bright as the star Polaris (Apparent Magnitude +1.8) showed up in the night sky, it would be detected almost instantly by stargazers. If an object as bright as Pluto (Apparent Magnitude +13.65) showed up, presumably it would take much longer for someone to notice (perhaps days or weeks?), since it is too dim to be seen by the naked eye. For the faintest objects seen from Pan-STARRS 1.8 meter telescope (Apparent Magnitude +24) are we talking about years or decades to notice a new object?

Specifically, I am looking for a function that gives me something like the MTTD (mean time to detect) a new object in the night sky, given its apparent magnitude. This could also be in the form of a graph. Does such a thing exist?

I am asking this question to improve my answer to How early could we detect an asteroid the size of the one that caused the extinction of the dinosaurs?

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  • $\begingroup$ Each CCD telescope has its own MTTD, as you called it. Simply, the longer you point the telescope the more likely you can see fainter objects (a.k.a. looking deeper/further in the sky). There is a function of limiting brightness that a telescope can see, given a fixed exposure time. For an asteriod, there are parameters such as orientation (e.g., reflecting light from sun to detector), and how the object emits light determining the detectability. So, I don't think there is a general answer for your question. $\endgroup$
    – Kornpob Bhirombhakdi
    Commented Nov 20, 2020 at 18:56
  • $\begingroup$ If an object as bright as Pluto happened to be in one of the many galaxies that are routinely scanned for supernovae, it would be noticed fairly quickly. Otherwise, it might take much longer. $\endgroup$
    – D. Halsey
    Commented Nov 20, 2020 at 22:45
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    $\begingroup$ According to the Wikipedia page on Pan-STARRS en.wikipedia.org/wiki/Pan-STARRS, this survey reaches to magnitude 22 and covers the whole sky in about 10 days. While this doesn’t give us a mathematical function for MTTD, it gives an idea of how quickly most objects could be detected… $\endgroup$
    – Pierre Paquette
    Commented Nov 21, 2020 at 17:58
  • $\begingroup$ @PierrePaquette When a Pan-STARRS survey is performed, do they always know what is new and what is old, or just moved since the last survey? The data may be contained in the survey, but a new object really isn't detected until the data has been 'mined', right? $\endgroup$
    – Connor Garcia ♦
    Commented Nov 24, 2020 at 19:25
  • $\begingroup$ @ConnorGarcia: I don’t know the specifics of Pan-STARRS (not the “Pan-STARRS Survey” as the first “S” in “STARRS” already means “Survey”), but I suppose they have a database of all known objects and their positions to compare their observations with. $\endgroup$
    – Pierre Paquette
    Commented Nov 25, 2020 at 1:41

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