# When will the Sun shine on Sunshine?

February 14, 2017 12:18 PM Subscribe

My four story apartment building is about 15 feet from a nearly identical four story apartment building to the south. I live on the third floor, and my apartment windows face south into the space between the buildings. Today at midday I can see the sun shining fully on the windows of the fourth floor apartment above mine, with the shadow from the other building starting just below their windows. How many days until it starts shining into my apartment and onto my cat?

I thought I'd have to solve this mathematically (I am definitely interested in re-learning the math/science) but it turns out I can answer it socially. According to my faceboobs post last year on this exact topic, I first

posted by carsonb at 1:02 PM on February 14, 2017 [5 favorites]

*noticed*the sun light on February 23, so the answer is sometime just before then, in about one week.posted by carsonb at 1:02 PM on February 14, 2017 [5 favorites]

I think I'm doing something wrong, as I get around May 21 — so that means that Sunshine will only get about two months of full sunshine/recharging.

I made a sun path chart for your location (here) that shows that the current maximum solar elevation is about 44°. If your floor is 10' lower the the upper floor, and there's 15' between the buildings, the sun has to get higher by tan¯¹(10/15) degrees, or 33.7°, for Sunshine to be happy. That puts the illumination elevation at 77.7°, which when you go back to the chart, happens around May 21. The kitteh illumination will go through solstice and for about another month after.

posted by scruss at 1:03 PM on February 14, 2017 [1 favorite]

I made a sun path chart for your location (here) that shows that the current maximum solar elevation is about 44°. If your floor is 10' lower the the upper floor, and there's 15' between the buildings, the sun has to get higher by tan¯¹(10/15) degrees, or 33.7°, for Sunshine to be happy. That puts the illumination elevation at 77.7°, which when you go back to the chart, happens around May 21. The kitteh illumination will go through solstice and for about another month after.

posted by scruss at 1:03 PM on February 14, 2017 [1 favorite]

The math looks good but the initial numbers are probably off. There must be more space between the buildings.

posted by carsonb at 1:06 PM on February 14, 2017 [1 favorite]

posted by carsonb at 1:06 PM on February 14, 2017 [1 favorite]

*If your floor is 10' lower the the upper floor*

Wrong number to use, because the fourth-floor window is entirely in sunlight today, and carsonb is asking when sunlight will first graze the top of his window, so you'd have to use the distance between the bottom of the fourth floor window and the top of the third floor window. Secondly:

*the sun has to get higher by tan¯¹(10/15) degrees*

That would give you the difference between a sunlight elevation of 0 ft (defining that to be the top of the roof) and -10 feet, but not between, for example, -10 feet and -20 feet, because tan¯¹ is not a linear function.

If the top of carsonb's window is X feet below the bottom of the window above, and the estimate of distance between buildings of 15 feet is accurate, the solar elevation you'd need would be tan¯¹(tan(44°) + X/15). And even for X=10 that's 58.5°, not 77.7°.

posted by DevilsAdvocate at 1:40 PM on February 14, 2017 [1 favorite]

fair enough, DevilsAdvocate; I thought there was something with my reckoning.

posted by scruss at 1:50 PM on February 14, 2017

posted by scruss at 1:50 PM on February 14, 2017

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posted by showbiz_liz at 12:43 PM on February 14, 2017 [1 favorite]