It's legitimate to treat an object as a point particle when the size and shape of the object are insignificant relative to the scale of the problem being considered. In other words, the object's dimensions are much smaller than the distances involved in the problem or the object's internal structure is irrelevant to the analysis. Here's a breakdown:

When it's legitimate:

* Large distances: When considering the gravitational interaction between planets, treating them as point masses is perfectly valid. The distance between planets is vastly larger than their diameters.

* Center of mass calculations: For rigid bodies in rotational motion, it's often useful to consider the entire mass concentrated at the center of mass. This simplifies the calculations without losing crucial information about the body's motion.

* Simplified models: In physics, we often create simplified models to understand complex systems. Treating objects as point particles is a common simplification that allows us to focus on the essential aspects of a problem.

* Internal structure irrelevant: If the object's internal structure doesn't affect the problem, it can be treated as a point particle. For example, when calculating the gravitational force between a star and a planet, the internal structure of the planet is generally unimportant.

When it's NOT legitimate:

* Small distances: If the object's size is comparable to the distances involved in the problem, treating it as a point particle will lead to inaccurate results. For example, when analyzing the collisions of billiard balls, the point particle approximation would be insufficient.

* Internal structure crucial: If the object's internal structure plays a significant role in the problem, it cannot be treated as a point particle. For example, the stress distribution within a beam under load depends on its shape and material properties, making a point particle approximation unsuitable.

* High-precision calculations: For extremely precise calculations, even small objects may need to be considered in their entirety.

In summary:

The decision to treat an object as a point particle is a matter of judgement and simplification. It's a powerful tool for simplifying problems, but it's crucial to understand its limitations and when it's appropriate to apply. Always consider the scale of the problem and the role of the object's size and internal structure before making this simplification.