Sunday, 26 January 2014

the sun - How bright would the sun appear from the hypothetical Planet Nine proposed by Caltech?

Between 1/40,000 and 1/8,000,000 of the brightness as seen from Earth, depending on what the actual orbit would turn out to be, and where the planet is in its 15,000 year orbit period.



Brightness drops as dfrac1r2 with distance from the light source. Earth is at 1 textrmAU. The theoretical planet is at 200 textrmAU when it's closest to the sun, and up to 2800 textrmAU at the point furthest from the sun at the upper end of the estimated orbit.




So e.g. 1/2002=1/40,000 of the brightness (luminance) as seen from Earth.



For how a human would experience it, we can convert to exposure value as used in photography: The difference in exposure value (photographic 'stops') is log2 of the luminance ratio, so we would have 15 to 23 stops less light than on Earth.
Sunny noon on Earth is 15 textrmEV.



So the brightness at noon on the planet surface would be:



  • At 200 textrmAU, planet orbit is closest to the sun: About 0 textrmEV, roughly the same as a dimly lit interior


  • 400 textrmAU, lower bound on semi-major axis: 2 textrmEV, similar to a landscape lit by the full moon


  • 1500 textrmAU, upper bound on semi-major axis: 6 textrmEV, similar to landscape lit by a quarter moon


  • 2800 textrmAU, upper bound on aphelion (the point on orbit most distant from the sun): 8 textrmEV. This would be dark, but you would probably still see enough to avoid running into things.


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