You'd have to take that into account when doing your global warming models too.
52 evenly spaced planets in an Earth-like orbit would be about (2pi600)/52 light seconds apart, which comes out to about 72 and a half light seconds. So, the closest neighbor planets would appear a lot smaller than the moon, but a lot bigger than, say, Venus.
I'm not sure how widely the adjacent rings would be spaced, so you might sometimes have neighbors that are closer than 72.5 light seconds as they zip by in the opposite direction.
The article also talks about arranging the planets as binary pairs, in which each planet might be very close to its neighbor, possibly appearing bigger and brighter than the moon from Earth.
Sun −26.74, Moon −12.74 (average full moon), Venus -4.89 to −3.82. So sun is around 400,000 times as bright as the moon, and the moon is ~1500 times as bright as the Venus which is bright largely because it's so close to the sun.
Mars is −2.91 at it's brightest. So 1/2 as much light as Venus because it's further from the sun even if it's closer. These might be closer than Mars, but not closer than the moon.