A celestial body in the night sky is twice as bright as Vega. What is its magnitude?

A magnitude is about 2.512 times worse than the brightness

The magnitude is decimal, and the brightness is 2.512. That is, every time the magnitude changes by a specified amount, the brightness changes by a factor of 2.512. If the magnitude is +1, then the brightness is 2.512 times of the original basis. The same magnitude +.1 is also .2512 times higher than the original one. It's a logarithmic relationship. That is, the magnitude difference of 1 star is 2.512 times, and the magnitude difference of .1 is not .2512 times, but about 1.965 times. It's 2.512 to the tenth power.

according to the relationship between magnitude and brightness

the relationship between magnitude and brightness

m1 and m2 are magnitude. E1 and E2 are brightness.

twice as bright as the celestial body and twice as bright as the original contrast celestial body. That is lg(2), so m2-m1=-2.5*lg(2). Look-up table lg(2)=.31, so m2-m1=-2.5 * .31 = -.7525, that is, its magnitude is -.75, etc.