  The recently approved Juno mission will orbit Jupiter for one year in a
highly eccentric (r_min=1.06R_Jup, r_max=39R_Jup) polar orbit (i=90 deg) to
accurately map, among other things, the jovian magnetic and gravitational
fields. Such an orbital configuration yields an ideal situation, in principle,
to attempt a measurement of the general relativistic Lense-Thirring effect
through the Juno's node Omega which would be displaced by about 570 m over the
mission's duration. Conversely, by assuming the validity of general relativity,
the proposed test can be viewed as a direct, dynamical measurement of the
Jupiter's angular momentum S which would give important information concerning
the internal structure and formation of the giant planet. The long-period
orbital perturbations due to the zonal harmonic coefficients J_L, L=2,3,4,6 of
the multipolar expansion of the jovian gravitational potential accounting for
its departures from spherical symmetry are a major source of systematic bias.
While the Lense-Thirring node rate is independent of the inclination i, the
node zonal perturbations vanish for i=90. In reality, the orbit injection
errors will induce departures \delta i from the ideal polar geometry, so that
the zonal perturbations will come into play at an unacceptably high level, in
spite of the expected improvements in the low-degree zonals by Juno. A linear
combination of Omega, the periJove omega and the mean anomaly M cancels out the
impact of J_2 and J_6. A two orders of magnitude improvement in the uncanceled
J_3 and J_4 would be needed to reduce their bias on the relativistic signal to
the percent level; it does not seem unrealistic because the expected level of
improvement in such zonals is three orders of magnitude.
