  In this paper, we solved the Einstein's field equation and obtained a line
element for static, ellipsoidal objects characterized by the linear
eccentricity ($\eta$) instead of quadrupole parameter ($q$). This line element
recovers the Schwarzschild line element when $\eta$ is zero. In addition to
that it also reduces to the Schwarzschild line element, if we neglect terms of
the order of $r^{-2}$ or higher which are present within the expressions for
metric elements for large distances. Furthermore, as the ellipsoidal character
of the derived line element is maintained by the linear eccentricity ($\eta$),
which is an easily measurable parameter, this line element could be more
suitable for various analytical as well as observational studies.
