  The problem of mutual gravitational energy $W_{mut}$ for a system of two
homogeneous prolate spheroids, whose symmetry axes are on the same line, is set
and solved. The method of equigravitating elements is applied, where the
external potentials of three-dimensional spheroids are represented by the
potentials of one-dimensional inhomogeneous focal rods. The solution of the
problem is reduced to the integration of the potential of one rod over the
segment of the second rod. As a result, the expression $W_{mut}$ for two
prolate spheroids can be obtained in a finite analytic form through elementary
functions. The force of attraction between the spheroids is found. The function
$W_{mut}$ is also represented by a power series in eccentricity of the
spheroids. Possible applications of the obtained results are discussed.
