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Stellar mass $M$, radius $R$, and gravity $g$ are important basic parametersin stellar physics. Accurate values for these parameters can be obtained fromthe gravitational interaction between stars in multiple systems or fromasteroseismology. Stars in a cluster are thought to be formed coevally from thesame interstellar cloud of gas and dust. The cluster members are thereforeexpected to have some properties in common. These common properties strengthenour ability to constrain stellar models and asteroseismically derived $M$, $R$and $g$ when tested against an ensemble of cluster stars. Here we derive newscaling relations based on a relation for stars on the Hayashi track($\sqrt{T_{\rm eff}} \sim g^pR^q$) to determine the masses and metallicities ofred giant branch stars in open clusters NGC 6791 and NGC 6819 from the globaloscillation parameters $\Delta\nu$ (the large frequency separation) and$\nu_{\rm max}$ (frequency of maximum oscillation power). The $\Delta\nu$ and$\nu_{\rm max}$ values are derived from \kepler\ observations. From theanalysis of these new relations we derive: (1) direct observational evidencethat the masses of red giant branch stars in a cluster are the same withintheir uncertainties, (2) new methods to derive $M$ and $z$ of the cluster in aself consistent way from $\Delta\nu$ and $\nu_{\rm max}$, with lower intrinsicuncertainties, (3) the mass dependence in the $\Delta\nu$ - $\nu_{\rm max}$relation for red giant branch stars.

New asteroseismic scaling relations based on Hayashi track relation applied to red-giant branch stars in NGC 6791 and NGC 6819