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We analyze all available solar and related reactor neutrino experiments, aswell as simulated future 7Be, p-p, pep, and ^8B solar neutrino experiments. Wetreat all solar neutrino fluxes as free parameters subject to the conditionthat the total luminosity represented by the neutrinos equals the observedsolar luminosity (the `luminosity constraint'). Existing experiments show thatthe p-p solar neutrino flux is 1.02 +- 0.02 (1 sigma) times the flux predictedby the BP00 standard solar model; the 7Be neutrino flux is 0.93^{+0.25}_{-0.63}the predicted flux; and the ^8B flux is 1.01 +- 0.04 the predicted flux. Theneutrino oscillation parameters are: Delta m^2 = 7.3^{+0.4}_{-0.6}\times10^{-5} eV^2 and tan^2 theta_{12} = 0.41 +- 0.04. We evaluate how accuratefuture experiments must be to determine more precisely neutrino oscillationparameters and solar neutrino fluxes, and to elucidate the transition fromvacuum-dominated to matter-dominated oscillations at low energies. A future 7Benu-e scattering experiment accurate to +- 10 % can reduce the uncertainty inthe experimentally determined 7Be neutrino flux by a factor of four and theuncertainty in the p-p neutrino flux by a factor of 2.5 (to +- 0.8 %). A futurep-p experiment must be accurate to better than +- 3 % to shrink the uncertaintyin tan^2 theta_{12} by more than 15 %. The idea that the Sun shines because ofnuclear fusion reactions can be tested accurately by comparing the observedphoton luminosity of the Sun with the luminosity inferred from measurements ofsolar neutrino fluxes. Based upon quantitative analyses of present andsimulated future experiments, we answer the question: Why perform low-energysolar neutrino experiments?Comment: Updated all calculations to include SNO salt-phase data and improved  GNO and SAGE data, all released September 7, 2003 at TAUP03. Updating  produces only minor numerical changes. Accepted for publication in JHE

A road map to solar neutrino fluxes, neutrino oscillation parameters, and tests for new physics