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• # Gravitational mass

Posted by on May 2, 2023 at 2:53 PM

If a body, such as a basket ball, is left free in the air, it is attracted downwards by a force, in first approximation constant, called weight force. By means of a plate scale, it can be seen that different bodies, in general, are attracted differently by the weight force, i.e. they weigh differently. The plate balance can be used to give an operational definition of gravitational mass: a unit mass is assigned to a sample object and the other objects have a mass equal to the number of samples needed to balance the plates.

Passive gravitational mass is a physical quantity proportional to the interaction of each body with the gravitational field. Within the same gravitational field, a body with small gravitational mass experiences a smaller force than a body with large gravitational mass: the gravitational mass is proportional to the weight, but while the latter varies with the gravitational field, the mass remains constant. By definition, the weight force $$F_w$$ is expressed as the product of the gravitational mass $$m_g$$ by a vector $$\vec{g}$$, called gravity acceleration, which depends on the place where the measurement is made and whose units depend on that of the gravitational mass.

The active gravitational mass of a body is proportional to the intensity of the gravitational field generated by it. The greater is the active gravitational mass of a body, the more intense is the gravitational field generated by it, and therefore the force exerted by the field on another body; to make an example, the gravitational field generated by the Moon is less (at the same distance from the center of the two celestial bodies) than that generated by the Earth because its mass is less. Measurements of active gravitational masses can be performed, for example, with torsion balances like the one used by Henry Cavendish in the determination of the constant of universal gravitation.

The gravitational mass is to all intents and purposes the charge of the gravitational field, exactly in the same sense in which the electric charge is the charge of the electric field: it simultaneously generates and suffers the effects of the gravitational field. Objects with zero gravitational mass (e.g. photons) would not suffer the effects of the field: in fact a result of general relativity is that any body follows a trajectory due to gravitational field.

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