  A new spectral method is built resorting to $(0,2)$ Jacobi polynomials. We
describe the origin and the properties of these polynomials. This choice of
polynomials is motivated by their orthogonality properties with the respect to
the weight $r^2$ used in spherical geometry. New results about
Jacobi-Gauss-Lobatto quadratures are proven, leading to a discrete Jacobi
transform. Numerical tests for Poisson problems in a sphere are presented using
the C++ library \textsc{lorene}.
