Recently, a comet with a brightness of 10 ^ m was discovered. Calculations of the orbit showed that in two months it will approach the Sun and the Earth twice. Can it be observed with the naked eye at this time? Consider that the brightness of a comet is inversely proportional to the fourth power of the distance to the Sun.
Solution: When the comet approaches the Sun twice, it will send 16 times more light into space. At the same time, it will approach the Earth twice more, and its apparent brightness on our planet will increase 64 times. It is easy to calculate that, in this case, its stellar magnitude will decrease by a little more than 4.5 ^ m (remember that a difference of 5 ^ m corresponds to the brightness ratio by 100 times, and 1 ^ m – by 2.512 times). Thus, it will shine slightly brighter than the 5.5 ^ m star, i.e. may well be found with the naked eye in a dark, clear moonless sky, of course, if it is not too close to the Sun.
Answer: Yes, you can.
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