The origins of extrasolar gas giant planets have been discussed, based on our understanding of the gas giant planets in the solar system, Jupiter and Saturn. However, how Jupiter and Saturn formed is still uncertain because of the uncertainty in their interiors, especially the core mass (Mc). The uncertainty in Mc is partly due to those in observational data such as gravitational moments (J2n), equatorial radius (Req) and 1-bar temperatures (T1bar). New frontiers mission to Jupiter by NASA (JUNO) launched in 2011 is expected to reduce the observational errors. However, it is not necessarily clear yet which observational uncertainty dominates and how accurate observation is needed to constrain Mc enough to know the origin of Jupiter. Thus, modeling the interior of Jupiter, we evaluate each effect on Mc and required precision. We have found that the observational error of 5% in T1bar yields an error of several M in Mc. We have also found that the values of J6 of our successful models are confined in a narrow range compared to its observational error. This implies that comparison between the values of J6 of our successful models and the J6 value obtained from JUNO mission helps us to know whether the present theoretical model is valid.