What is the relationship between mass weight and gravity

Let's start by defining what is mass, gravity and weight:

The mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

Gravity is an attraction force, which depends on the mass of the bodies and their distance.

Weight is the force that gravity exerts on matter and changes depending on where the body is located. Therefore, the weight of an object on Earth will not be the same as the weight of the same object on the Moon or on Mars.

Now, according to Newton's law of Gravitation, the force exerted between two bodies of masses and  and separated by a distance  is equal to the product of their masses and inversely proportional to the square of the distance:

   (1)

Where is the gravitational constant

In the case of our Earth, its mass   and radius (distance from its center to its surface where an object is) are constant. So, we can write all these constant in one, in the following way:

  (2)

Where  is the gravity force on Earth and its value is

.

Rewriting equation (1) with this consideration:

  (3)

Where is known as the weight:

   (4)

Here we can see the relationship among  mass  , weight  and gravity

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