  In this study, we continue our previous work (Annu et al., 2023) by
introducing a novel parametrization of the expansion scalar $\Theta $ as a
rational function of cosmic time $t$. The paper provides a comprehensive
analysis of a homogeneous gravitational collapsing system, wherein the exact
solutions of the Einstein field equations (EFEs) are determined using a new
parametrization of $\Theta$ in a model-independent way. The model is especially
significant for the astrophysical applications because we have addressed the
physical and geometrical quantities of the model in terms of Schwarzschild mass
$M$. We have estimated the numerical value of the model parameter involved in
the functional form of $\Theta$-parametrization using the masses \& radii data
of some massive stars namely, Westerhout 49-2, BAT99-98, R136a1, R136a2, WR 24,
Pismis 24-1, $\lambda$ Cephei, $\alpha$ Camelopardalis, $\beta$ Canis Majoris.
We have presented theoretical investigations about such astrophysical stellar
systems. The formation of apparent horizon is also studied for the collapsing
system, and it has been shown that our model produces a continuing collapsing
scenario of star (an eternal collapsing object).
