At what time of day does the illuminance coincide with that on my planet at noon?
My planet (I'll call it
For
With the following formula you can find the illuminance (in lx) on the Earth if you know the apparent visual magnitude of the Sun:
For the Earth:
Then, by multiplying the illuminance on Earth by 0.25, the illuminance on
My question is, what angle must the Sun form with the Earth's surface for this illuminance to occur, and at what time of day does this happen?
I found this formula to find the illuminance (in lx) knowing the distance to the light source (in m), its intensity (in cd) and the angle of incidence:
Solving for
For the Sun from Earth at noon:
The intensity of the light source (the Sun) is this, in cd.
Then, solving for
And finally replacing the corresponding values:
Here, the value of
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