Final answer:
The gravitational field of a uniform toroid cannot easily be calculated using Gauss's theorem due to the complex symmetry, which complicates the integration needed for the Gaussian flux. Gauss's Law is applicable, but other methods might be more practical for such calculations.
Step-by-step explanation:
The calculation of the gravitational field of a uniform toroid using Gauss's theorem is indeed more complex than that of a simple ring or spherical objects due to the lack of a strong symmetry that would simplify the integral needed to find the total gravitational flux. Gauss's Law for gravity states that the gravitational flux through a closed surface is proportional to the enclosed mass. However, due to the shape of the toroid and its distribution of mass, finding a Gaussian surface over which the gravitational field is constant and where the field is always perpendicular or parallel to the surface is not straightforward.
To tackle this problem, one must set up the integral for the Gaussian flux based on the symmetrical properties of the toroid and its cross-sectional area. The field inside the torus is not uniform, hence the need for integration over the toroid's volume to determine the field at various points. While in principle Gauss's Law could be applied to calculate the field, due to the lack of symmetry it is usually more practical to use other methods to compute the field of a toroidal mass distribution, such as numerical integration or analytical approximation methods for specific locations in and around the toroid.