GRAVITATION TOPICS: GRAVITATIONAL ACCELERATION

Keywords

How does Newton's Universal Law of Gravitation explain gravitational acceleration?
What are the factors that determine the intensity of a body's gravitational acceleration?
How do the mass and the distance between two bodies influence the gravitational force between them?
How to calculate the weight of an object knowing its mass and the local gravitational acceleration?
What is the effect of variations in the distance between an object and the center of a planet on the gravitational force exerted on the object?

The Universal Law of Gravitation establishes that every body exerts a gravitational attraction force on another body.
Gravitational acceleration is a measure of how an object's speed changes due to gravitational force.
The mass of a planet and the distance to the center of the planet are determinants for the intensity of gravitational acceleration.

Universal Law of Gravitation: ( F = G \frac{m_1 m_2}{r^2} ), where:
- ( F ) is the gravitational force between two bodies,
- ( G ) is the gravitational constant ((6.674 \times 10^{-11} N \cdot (m/kg)^2)),
- ( m_1 ) and ( m_2 ) are the masses of the bodies,
- ( r ) is the distance between the centers of the two bodies.
Gravitational acceleration: ( g = G \frac{M}{r^2} ), where:
- ( g ) is the gravitational acceleration at the considered point,
- ( M ) is the mass of the planet or larger body,
- ( r ) is the distance from the point to the center of mass of the larger body.
Weight (( P )): ( P = m \cdot g ), where:
- ( P ) is the weight of the object,
- ( m ) is the mass of the object,
- ( g ) is the gravitational acceleration at the point where the object is located.

Gravitation: The fundamental force that attracts two objects with mass; described by Newton as the force that keeps planets in orbit.
Gravitational acceleration (g): The rate of increase in speed of a falling object due to gravity, approximately (9.81 m/s^2) on the surface of the Earth.
Universal Law of Gravitation: Proposed by Sir Isaac Newton, mathematically expresses the influence that two bodies with mass exert on each other.
Gravitational field: Vector representation of the gravitational force that a massive body exerts at each point in space around it.
Gravitational force: The attractive force between two bodies due to their masses.
Weight: Gravitational force acting on an object's mass, should not be confused with mass.
Gravitational constant (G): A universal parameter that quantifies the intensity of gravity, determined experimentally.

Gravity is a universal force that acts between any two bodies with mass.
Gravitational acceleration (g) varies at different points in the universe, being affected by the mass of the celestial body and the distance to its center.
The Universal Law of Gravitation enables the calculation of gravitational force and gravity acceleration for different bodies and distances.

Universal Law of Gravitation:
- Exemplifies the interaction between two bodies: the Earth and any object.
- Demonstrates the inverse proportionality with the square of the distance (( r^2 )) and the direct proportionality with the masses involved.
Gravitational Acceleration:
- On Earth, ( g \approx 9.81 m/s^2 ), but varies with altitude and latitude.
- Calculated from the mass of the planet and the distance to its center.
Weight versus Mass:
- Weight is variable and depends on the local gravitational acceleration, while mass is constant.
- Weight is the result of mass under the influence of gravity.

Calculation of Gravitational Force:
- Given two bodies with specific masses and a distance between them, the calculation of gravitational force allows us to understand the magnitude of this interaction.
Gravitational Acceleration on Earth and other planets:
- For a planet with mass ( M ) and radius ( R ), the gravitational acceleration at the surface is ( g = G \frac{M}{R^2} ).
- Changing the distance to twice the radius of the Earth (( 2R )) leads to a decrease in gravitational acceleration to a quarter of the original value, because ( g = G \frac{M}{(2R)^2} ).
Practical example of variation in ( g ):
- When calculating gravity on the surface of the Moon, we notice that it is less than on Earth due to the Moon's smaller mass and radius.

The Universal Law of Gravitation formulates the attraction force between two masses, being inversely proportional to the square of the distance between their centers and directly proportional to the product of their masses.
Gravitational acceleration (g) is a direct consequence of gravitation, indicating the change in speed of an object that is under the influence of the gravity of a celestial body.
Mass and distance to the center of the celestial body are key factors that affect gravity acceleration, meaning that larger or denser planets have more intense gravity at the surface.
The calculation of gravitational acceleration for any planet can be performed using the expression ( g = G \frac{M}{r^2} ), where ( M ) is the mass of the planet and ( r ) the distance from the point to the center of mass of the planet.
The gravitational constant (G) is a universal value that allows the quantification of gravity, acting as a proportionality constant in the Universal Law of Gravitation.

The relationship between gravity and distance is fundamental to understanding phenomena such as the variation of gravity at different points in space.
By doubling the distance between an object and the center of a planet, like Earth, the gravitational acceleration is reduced to a quarter of its initial value, highlighting the inverse square law.
Understanding the distinction between mass and weight is essential, as weight is a force that varies according to the local gravitational acceleration, while mass is an inherent quantity of the object.
The ability to calculate gravity in different locations and conditions is a practical application that reinforces the understanding of the principles of gravitation and gravitational acceleration.