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Well, the question says it all; is there a definition of body in physics? What is to be considered a physical object and what it cannot?

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There is no general definition of a body for physics, as in everyday speech where one has to qualify further either by context or content.

A body of water, means a bulk ensemble of water molecules and further analysis depends on the context.

Two colliding bodies could be billiard balls or asteroids. It is a blanket term that needs further attributes if it is to be used in a problem that needs a mathematical solution in physics.

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If you are talking about rigid bodies like billiard balls or asteroids one has a definition of a body:

In physics, a rigid body is an idealization of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it.(Wikipedia)

However this seem a little bit fishy since it also uses the word “body” in its definition. However one can also define a body in Classical Mechanics as a collection of atoms (or just one atom for that matter) having a well-defined energy, velocity, mass and momentum. Things get a little complicated when you are dealing with QM.

To answer your second question: You can think of anything as physical object so long as you obey the above-mentioned rules. E.g. a body with infinite mass is not a physical object, it is just an idealisation of a very heavy physical object.

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