Abstract
From general considerations, we have obtained a series of actions (?)~((n))=(Gm_n~2/e~2)~(n-6/2)(?) which can be regarded as characters of various typical scales n in the universe. Here, (?), G, e and m_a are the Planck quantum of action, gravitational constant, fundamental charge and the effective mass of elementary particles, n is the scale parameter. Based on these actions, we may further get the characteristic angular momentum J~((n))=(?)~((n)) and the characteristic mass M~((n))=((?)~((x))Ca/G)~(1/2) of various astronomical objects which are compatible with observations. We have also found that their relation is J~(n)/(M~((n)))~2=G/Ca, where C is the speed of light in vacuum and a is the fine structure constant.
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