The increasing precision of astronomical observations of stars and stellar systems is gradually getting to a level where the use of slightly different values of the solar mass, radius and luminosity, as well as different values of fundamental physical constants, can lead to measurable systematic differences in the determination of basic physical properties. An equivalent issue with an inconsistent value of the speed of light was resolved by adopting a nominal value that is constant and has no error associated with it. Analogously, we suggest that the systematic error in stellar parameters may be eliminated by: (1) replacing the solar radius Rsun and luminosity Lsun by the nominal values that are by definition exact and expressed in SI units: 1 RnomSun = 6.95508 x 10^8 m and 1 LnomSun = 3.846 x 10^{26} W; (2) computing stellar masses in terms of Msun by noting that the measurement error of the product G.Msun is 5 orders of magnitude smaller than the error in G; (3) computing stellar masses and temperatures in SI units by using the derived values Msun(2010) = 1.988547 x 10^{30} kg and Tsun(2010) = 5779.57 K; and (4) clearly stating the reference for the values of the fundamental physical constants used. We discuss the need and demonstrate the advantages of such a paradigm shift.
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