Stellar distance is an important basic parameter in stellar astrophysics .
Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust .
They are therefore expected to have common properties .
These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters , such as stellar mass , metal fraction , and distance when tested against an ensemble of cluster stars .
Here we derive a new relation based on solar-like oscillations , photometric observations , and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters \Delta \nu  and \nu _ { \mathrm { max } } and photometric data V .
The values of \Delta \nu  and \nu _ { \mathrm { max } }  are derived from Kepler  observations .
At the same time , it is used to interpret the trends between V and \Delta \nu .
From the analyses of this newly derived relation and observational data of NGCÂ 6791 and NGCÂ 6819 we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus .
This approach fully reflects the characteristic of member stars in a cluster as a natural sample .
From this method we derive true distance moduli of 13.09 \pm 0.10 mag for NGCÂ 6791 and 11.88 \pm 0.14 mag for NGCÂ 6819 .
Additionally , we find that the distance modulus only slightly depends on the metallicity [ Fe/H ] in the new relation .
A change of 0.1 dex in [ Fe/H ] will lead to a change of 0.06 mag in the distance modulus .