Newton\'s Law of Gravitational Attraction

In Newton's Law of Gravitation, 'G' represents the universal constant of gravitation, which quantifies the strength of the gravitational force between two masses. This constant is essential for calculating the gravitational attraction between any two objects, regardless of their size or distance apart. Its value is approximately 6.674 × 10⁻¹¹ N(m/kg)², indicating how gravitational force varies with mass and distance, and it remains consistent throughout the universe, making it a fundamental aspect of gravitational theory.

The universal constant of gravitation, G, quantifies the strength of gravitational attraction between masses. Its accepted experimental value is approximately 6.674 × 10⁻¹¹ m³/(kg·s²), often rounded to 66.73(10⁻¹²) m³/(kg·s²) for simplicity in certain contexts. This constant is fundamental in Newton's law of universal gravitation, which describes how two masses attract each other, and is crucial for calculations in astrophysics, cosmology, and engineering. The other options provided do not accurately represent the value of G, making the selected answer the correct one.

In Newton's gravitational formula, 'r' represents the distance between the two particles that are exerting gravitational force on each other. This distance is crucial because the gravitational force decreases with the square of the distance between the objects, meaning that as 'r' increases, the gravitational attraction between the two particles diminishes. Understanding this relationship is fundamental to gravitational interactions in physics.

The weight of a particle near Earth's surface is defined as the gravitational force acting on it due to Earth's mass. This force arises from the gravitational attraction between the particle and the Earth, which is proportional to the masses of both objects and inversely related to the square of the distance between their centers. This relationship is described by Newton's law of universal gravitation, making the Earth the primary source of gravitational force that determines the weight of objects in its vicinity.

In the equation W = mg, the weight W of a particle is defined as the product of its mass m and the acceleration due to gravity g. The acceleration due to gravity can be further expressed using Newton's law of universal gravitation, where g is derived from the gravitational force exerted by a mass Me (the mass of the Earth) at a distance r (the radius of the Earth). Thus, g can be represented as G·Me/r², where G is the gravitational constant, illustrating the relationship between gravitational force and mass at a distance.

Weight is the force exerted by gravity on an object, which depends on both the mass of the object and the gravitational acceleration at its location. Since gravitational acceleration varies depending on where you are (e.g., Earth vs. the Moon), the weight of a body changes with location. Therefore, weight is not an absolute quantity; it is relative to the gravitational field strength at a specific point in space.

According to Newton's Law of Gravitation, the gravitational force between two masses is inversely proportional to the square of the distance between them. This relationship is expressed mathematically as \( F = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance. When the distance \( r \) is doubled, the force becomes \( F = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2} \), which shows that the force is reduced to one-quarter of its original value.