  The gravitomagnetic field generated by a rotating sphere is usually
calculated from the ideal dipole model. However, for a sphere with a
homogeneous mass density, this model is not generally valid. Trying to obtain a
more accurate value of the gravitomagnetic field inside and outside the sphere,
series expansions for this field are presented in this paper. The calculated
polar gravitomagnetic field of the sphere and that from the ideal dipole model
appear to coincide, but the field in the vicinity of the sphere may deviate.
The deduced field within the sphere strongly deviates from the ideal dipole
result. As an illustration, the gravitomagnetic precession rate (or
frame-dragging effect) of a gyroscope moving in the gravitomagnetic field from
a large rotating sphere is calculated. For the Gravity Probe B experiment the
result may coincide with the prediction from the ideal dipole model and in fair
agreement with observations. In addition, the obtained Lense-Thirring
precession rate for the LAGEOS satellites probably coincides with the standard
prediction. For both experiments alternative predictions are calculated, when
the gravitomagnetic field and the magnetic field from moving charge are
equivalent. Theoretical and observational indications for such an equivalence
are summarized. The obtained series expansions for the gravitomagnetic field of
a sphere can also be applied to the calculation of the magnetic field,
generated by a rotating sphere with a homogeneous charge density. Results for
this case are also discussed.
