The way I would briefly explain it myself would be to say that we know how fast time is proceeding at great distances from Earth by observing the rate of the passage of time through observing the natural processes taking place there, such as the frequencies at which various gases emit or absorb light.
Another method is by observation of the revolution of binary stars around their common centre of gravity. By measuring the distance between the components (the ratio of their angular separation and their parallax) and their orbital period, one can obtain the total mass of the binary from Newton's theory of gravitation. It turns out that not only are the measured masses of binary systems of the same order of magnitude as the mass of the Sun, but the masses increase with the luminosities of the stars, as one would expect.
None of this would be true if space and time in the stellar realm were different from space and time as we experience them on Earth.
quote:Seeing a star does not tell us its size or distance or true nature. Yes we have info in incoming light that tells us that it seems to have certain elements in it. What else stars may have that we cannot detect/see we do not know.
The intensity ratios of lines of different ionisation stages in a stellar spectrum of can tell us its temperature, and the line widths can tell us its surface gravity (and therefore indirectly its radius and its luminosity). The shifts of the spectral lines can also tell us whether the star is a binary; the line widths (again) can tell us its rotation speed, and the polarisation of the light from the spectral lines can tell us something about the star's magnetic field. Changes in the line profiles can tell us about the star's profile. The presence of emission lines can tell us about the star's chromosphere and about the presence of a stellar wind or circumstellar shell. The different intensities of the spectral lines can also provide information about the abundances of the different elements in the star's atmosphere, and, therefore, indirectly about the nuclear reactions that are taking place in, for example, carbon stars, S-type stars and supernovae.