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About the apparent magnitude of moon

Hi I'm Howoo, univ student majoring astronomy.

 

 They say that the full moon is almost 10 times brighter than the half moon since the reflected light travels different way.

So I tried to check on Starry NIght if it is true.

However, I found something confusing.

 

I collected data from late April through early May. (This year)

The magnitude of the first quarter moon(25/Apr) was about -11.80 , and the full moon(3/May) was about -12.56.

Since the relative brightness is 2.5^(difference) . The difference of brightness was just a twice not 10 times.

 

I want to know if I made mistake here, or the Starry Night needs to correct this.

(I'm probably sure that Starry Night didn't make any mistake here)

 

Thanks for considering.

Howoo

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