Star A has an apparent magnitude of 1.0 and an absolute magnitude of 1.0. How would the apparent and absolute magnitudes of this star change if the distance between earth and the star were decreased?

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You may use the inverse square law that states the brightness decreases by the square of distance and since the brightness is expressed in magnitudes, hence, if you need to evaluate the change in magnitudes if the distance between earth and star decreases, you should use the following formula, such that:

`d = 10^((m-M+5)/5)`

`M` represents absolute magnitude

`m` represents the apparent magnitude

`d` represents the distance

Since the problem does not provide the information how much the distance between the earth and star decreases, hence, supposing that the distance decreases by x parsecs yields:

`d/x = (10^((m-M+5)/5))/x => d/x = 10^((1-1+5)/5)/x => d/x = 10/x`

Hence, evaluating the change in magnitudes, under the given conditions, yields `d/x = 10/x.`

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