# At point A, at the zenith, a meteor with a magnitude of 0m is observed. At point B, the same meteor was seen

At point A, at the zenith, a meteor with a magnitude of 0m is observed. At point B, the same meteor was seen at an altitude of 30 ° above the horizon. What splendor did he have at this point? Neglect the absorption of light in the atmosphere.

Meteor phenomena occur at altitudes of about 100 km. This is much less than the radius of the Earth, and to solve the problem we can forget about the sphericity of our planet and consider it flat. It can be seen from the figure that the distance from the meteor to point B, where it was visible at an altitude of 30 °, is (1 / sin30 °) = 2 times greater than from point A, located directly under the meteor. Consequently, its brightness at point B, excluding atmospheric absorption, was
m = 0 + 5lg 2 = 1.5

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