Introduction: Gravitation: Gravitational Acceleration

Relevance of the Theme

The study of gravitation plays a crucial role in our understanding of the world. It provides a precise explanation for macroscopic movements in our universe and allows the prediction of celestial phenomena, such as planetary motion. Gravitational acceleration, in particular, is a fundamental quantity that permeates almost all aspects of physics. It not only influences the free fall of bodies, but also is responsible for maintaining the structure of planets and stars.

Contextualization

The study of Gravitational Acceleration falls within the kinematics unit, which is the part of physics that deals with the description of movements, without worrying about their causes. This unit is fundamental in Physics because it is where we begin to develop the language and reasoning that will allow us to understand more complex physical concepts in future units. Understanding gravitational acceleration and how it affects the movement of bodies solidifies us as 'citizens of the cosmos'. This theme serves as an introduction to more advanced concepts such as Kepler's Laws, Universal Law of Gravitation, and beyond.

Theoretical Development

Components

• Universal Gravitation: The theory of universal gravitation, developed by Isaac Newton in the 17th century, postulates that any pair of particles in the universe exert a force on each other, called gravitational force. This force is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

• Universal Law of Gravitation: This law mathematically expresses the force with which two particles with masses m1 and m2, which are at a distance r from each other, attract each other. The force F is given by F = G * (m1 * m2) / r², where G is the universal gravitational constant.

• Gravitational Field: The gravitational field is a region of space in which a body of mass m is subject to a force F. Its intensity is measured by the acceleration it imparts to a body of mass m.

• Gravitational Acceleration: It is the acceleration that an object in free fall acquires due to gravitational force. On the surface of the Earth, this acceleration is approximately constant and equal to 9.8 m/s² (g = 9.8 m/s²).

Key Terms

• Gravitational Force: The attractive force that a mass exerts on another. It is responsible for the acceleration of objects in free fall.

• Free Fall: Motion of a body under the exclusive action of gravitational force.

• Universal Gravitational Constant (G): Constant that appears in Newton's Universal Law of Gravitation. Its approximate value is 6.67 x 10^-11 N·(m/kg)².

Examples and Cases

• The fall of an apple: When an apple is dropped from a tree, it enters free fall, accelerating at a rate of 9.8 m/s² due to gravitational acceleration. The force acting on the apple is the gravitational force of the Earth.

• The orbit of the Moon around the Earth: The Moon is constantly falling towards Earth, but at the same time, it has enough horizontal velocity to 'miss' Earth and continue falling around it in an orbit. Gravitational acceleration is responsible for keeping the Moon in its orbit.

• Space navigation: In space, far from any significant source of gravity, the absence of gravitational acceleration can be simulated by providing astronauts with an equivalent acceleration using rocket engines. This is the underlying principle of space navigation.

Detailed Summary

Key Points

• Universal Gravitation: Newton's theory of universal gravitation postulates that every mass exerts an attractive force on all other masses, regardless of whether they are in contact or not. This force is called gravitational force.

• Universal Law of Gravitation: This is the mathematical expression that describes the gravitational force between two masses. According to it, this force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

• Gravitational Field: It is the region of space where a mass exerts an attractive force. The intensity of this field is measured by the acceleration it produces in a test mass.

• Gravitational Acceleration: It is the acceleration that an object in free fall experiences due to gravitational force. This value is approximately constant (g = 9.8m/s²) on the surface of the Earth.

Conclusions

• Gravitational acceleration is fundamental in physics, as it allows us to understand free fall motion and celestial orbit motion, among other phenomena.

• The gravitational acceleration on the surface of a planet is determined by the mass of that planet and its radius.

• Newton's theory of universal gravitation provides a precise explanation for how all masses in the universe attract each other, from the fall of an apple to the movement of planets.

Exercises

1. Exercise 1: If the mass of the Earth were doubled and its radius halved, what would be the gravitational acceleration on the new Earth's surface?

2. Exercise 2: An object is dropped in free fall from rest. If it takes 4 seconds to reach the ground, what is the height of the fall?

3. Exercise 3: The moon is at an average distance of 384,000 km from Earth. Assuming that Earth's gravity affects the Moon in the same way it affects an object on the surface of the Earth, what is the gravitational acceleration of Earth at the distance of the Moon?