Gravity and mass are intimately related to each other. Mass is a fundamental property of matter that quantifies the amount of matter in an object. It is a measure of an object's resistance to acceleration when subjected to an applied force.
Gravity, on the other hand, is a fundamental force of nature that attracts objects with mass towards each other. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.
Mathematically, the gravitational force (F) between two objects can be expressed as:
F = G * (m1 * m2) / r^2
Where: F is the gravitational force, G is the gravitational constant (a fundamental constant), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
From this equation, it is evident that the gravitational force increases as the masses of the objects increase. The more massive an object is, the stronger its gravitational pull.
Furthermore, the gravitational force is responsible for the phenomenon of weight. An object with mass experiences a force equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2 on Earth). This force is commonly referred to as weight and is the result of the gravitational interaction between the object and the Earth.
In summary, gravity and mass are related in that mass determines the strength of the gravitational force between objects. The more massive an object is, the stronger its gravitational pull, and the greater its weight.