Mass is a fundamental concept in physics, describing the amount of matter in an object and its resistance to changes in motion. Gravitational mass is the specific property that governs how an object interacts with the force of gravity. It determines both the strength of the gravitational field an object creates and how strongly it responds to fields created by other objects. This interaction shapes everything from an apple falling from a tree to the orbits of planets.
Defining Gravitational Mass
Gravitational mass has two distinct roles: active and passive. Active gravitational mass is the source of a gravitational field, determining the strength of the force an object exerts on other masses. This property causes large objects, like Earth, to curve the space around them, creating the effect we perceive as gravity.
Passive gravitational mass measures how strongly an object is affected by an external gravitational field. This is the mass that responds to the gravitational force created by the active mass of another object. Measuring weight on a standard scale is an indirect measurement of passive gravitational mass as Earth’s gravity pulls on the object.
This interaction is mathematically described by Newton’s Law of Universal Gravitation. The law states that the gravitational force between two objects is proportional to the product of their gravitational masses and inversely proportional to the square of the distance between them. In this formula, the variables representing the masses are specifically their gravitational masses. The principle of action and reaction requires that the active mass generating the force must equal the passive mass responding to the force.
The Distinction: Gravitational Mass Versus Inertial Mass
While gravitational mass relates to attraction, inertial mass is a separate concept relating to an object’s resistance to acceleration. Inertial mass is the quantity used in Newton’s Second Law of Motion, where force equals mass times acceleration. It describes how difficult it is to change an object’s state of motion, meaning a larger inertial mass requires a greater force for the same acceleration.
Conceptually, these two types of mass describe different physical phenomena. Gravitational mass measures an object’s coupling strength to the gravitational field. Inertial mass, by contrast, measures an object’s reluctance to accelerate under the influence of any non-gravitational force.
Despite these distinct definitions, the two masses are observed to be numerically equal for every object ever measured. This equality is not immediately obvious from their definitions, as one governs gravitational interaction and the other governs resistance to motion. The fact that an object’s ability to create gravity is precisely equal to its resistance to being pushed by a force remains one of the most profound observations in physics.
Measurement of Gravitational Mass
Gravitational mass is typically measured through two primary methods: static comparison and dynamic interaction. The most common method is static comparison using a balance scale, which directly measures passive gravitational mass. A simple two-pan balance scale compares the gravitational force exerted on an unknown mass to the force exerted on a known standard mass.
When the scale is balanced, the gravitational forces acting on both sides are equal, meaning the passive gravitational masses are also equal. This method relies on the uniformity of the local gravitational field. It is distinct from a spring scale, which measures weight (a force) and must be calibrated for local gravitational acceleration.
Dynamic measurement of active gravitational mass uses experiments like the one performed by Henry Cavendish in 1798. The Cavendish experiment uses a sensitive torsion balance to measure the faint gravitational force of attraction between two pairs of laboratory-sized masses. By measuring this force, along with the masses and distance, scientists calculate the universal gravitational constant, G. Since the force calculation depends on the product of the active gravitational masses, this experiment directly determines the gravitational mass interaction.
The Equivalence Principle
The observed numerical equality between gravitational mass and inertial mass is formally stated by the Weak Equivalence Principle (WEP). This principle asserts that the acceleration of a freely falling body is independent of its composition or mass. This means that a bowling ball and a feather, if dropped in a vacuum, will fall and accelerate at the same rate.
The WEP was a foundational concept for Albert Einstein’s theory of General Relativity, which describes gravity as a curvature of spacetime rather than a force. The principle suggests that one cannot locally distinguish between being at rest in a gravitational field and being uniformly accelerated in gravity-free space. This insight helped Einstein conclude that the motion of an object in a gravitational field is its natural, straightest path through the curved geometry of spacetime.
Modern experiments, such as the MICROSCOPE satellite mission, have tested the WEP with extraordinary precision. These tests compared the accelerations of different test masses in orbit, finding no violation of the principle down to a precision of about one part in \(10^{15}\). The continued verification confirms that the property of matter that resists a push is identical to the property that generates and responds to gravity.