We investigate the possibility of observing very small amplitude low frequency solar oscillations with the proposed laser interferometer space antenna (LISA). For frequencies $ u$ below $3times 10^{-4} {rm Hz}$ the dominant contribution is from the near zone time dependent gravitational quadrupole moments associated with the normal modes of oscillation. For frequencies $ u$ above $ 3times 10^{-4} {rm Hz}$ the dominant contribution is from gravitational radiation generated by the quadrupole oscillations which is larger than the Newtonian signal by a factor of the order $(2 pi r u/ c)^4$, where $r$ is the distance to the Sun, and $c$ is the velocity of light. The low order solar quadrupole pressure and gravity oscillation modes have not yet been detected above the solar background by helioseismic velocity and intensity measurements. We show that for frequencies $ u lesssim 2times 10^{-4} {rm Hz}$, the signal due to solar oscillations will have a higher signal to noise ratio in a LISA type space interferometer than in helioseismology measurements. Our estimates of the amplitudes needed to give a detectable signal on a LISA type space laser interferometer imply surface velocity amplitudes on the sun of the order of 1-10 mm/sec in the frequency range $1times 10^{-4} -5times 10^{-4} {rm Hz}$. If such modes exist with frequencies and amplitudes in this range they could be detected with a LISA type laser interferometer.
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