Classical mechanics can be used to approximate and provide reasonably accurate predictions for the motion of comets in certain situations. However, for a complete and precise understanding of the behavior of comets in their orbits, the effects of gravity from other celestial bodies and relativistic corrections need to be taken into account.
Classical mechanics, as formulated by Newton, describes the motion of objects under the influence of gravitational forces. Using Newton's laws of motion and the law of universal gravitation, it is possible to calculate the trajectory and motion of a comet under the influence of the Sun's gravity alone. This simplified approach is often sufficient for many practical purposes and can provide a good approximation for comets with large orbital distances compared to the sizes and masses of nearby objects.
However, when studying the motion of comets with greater precision or considering interactions with other celestial bodies like planets, classical mechanics alone may not be accurate enough. The gravitational effects of other bodies can perturb the comet's orbit, leading to complex and unpredictable behavior. In such cases, more sophisticated mathematical models that incorporate the gravitational interactions of multiple objects, such as numerical methods or perturbation theory, are required.
Additionally, if the speeds of the comet approach a significant fraction of the speed of light or if extreme gravitational conditions are present, classical mechanics is insufficient, and special relativity and general relativity must be taken into account to accurately describe the motion.
In summary, while classical mechanics can provide useful approximations for the motion of comets under certain conditions, a more comprehensive understanding often requires more advanced models that consider the gravitational interactions of multiple bodies or relativistic effects.