So I'm building a fantasy world that takes place on a planet with a circumference of about 18,500 miles (it's average temperature is 40℉), and it orbits a Blue-Giant.
How long would a year be, and how far away would it orbit its star? (Preferably this is in AU, though any measurement type is fine).
A Blue Giant will produce about 10,000 times the sun's energy. Energy declines proportional to the square root of distance, so the distance of your planet will be about 100 times the distance to our sun, that is 100AU, to receive the same energy on average. If it would have the same atmosphere as Earth, temperature could be similar.
.. but that's on average: you'll have to take into consideration Blue Giants are very wild, unstable, hot stars. There will be a problem with flares,
A star may be unsuitable for life for other reasons: it may be prone to extreme flares, for example. A blue giant is a star that burns bright and dies young, only lasting a few million years. Planets around such a star would have only just formed (they may still have molten surfaces). Blue giants tend to be unstable, being variable over a range of timescales, and ejecting large amounts of matter into space.
https://astronomy.stackexchange.com/questions/20610/do-blue-giants-have-a-habitable-zone
