Gravitational force and Newton's law of gravity

Gravitational Force

Definition: Gravitational force is the attractive force that exists between any two masses. It is one of the four fundamental forces of nature.

Newton's Law of Universal Gravitation: Isaac Newton formulated the law of universal gravitation in 1687, which quantifies the gravitational force between two masses.

Formula: $𝐹=𝐺\frac{{𝑚}_1{𝑚}_2}{{𝑟}^2}$ where:

• $𝐹$ is the gravitational force between the two masses.
• $𝐺$ is the gravitational constant, approximately $6.67430\times 10^{-11}\text{N}\cdot {\text{m}}^2\mathrm{/}{\text{kg}}^2$.
• ${𝑚}_1$ and ${𝑚}_2$ are the masses of the two objects.
• $𝑟$ is the distance between the centers of the two masses.

Key Concepts

1. Gravitational Constant (G):

   • A fundamental constant that quantifies the strength of the gravitational force.
   • Its value is $6.67430\times 10^{-11}\text{N}\cdot {\text{m}}^2\mathrm{/}{\text{kg}}^2$.

2. Inverse Square Law:

   • The force decreases with the square of the distance between the masses.
   • If the distance between the masses is doubled, the gravitational force is reduced to a quarter.

3. Mass and Distance Dependence:

   • The gravitational force is directly proportional to the product of the two masses.
   • The gravitational force is inversely proportional to the square of the distance between the centers of the masses.

Applications

1. Planetary Motion:
   • Newton's law explains the elliptical orbits of planets around the sun, as described by Kepler's laws of planetary motion.
2. Satellites:
   • The principles of gravitational force govern the orbits of artificial satellites around Earth.
3. Tides:
   • The gravitational pull of the moon and the sun causes ocean tides on Earth.
4. Astrophysics:
   • Understanding the behavior of stars, galaxies, and the large-scale structure of the universe.
5. General Relativity:
   • Einstein's theory of general relativity builds on Newton's law by describing gravity as the curvature of spacetime caused by mass.

Newton's Insights

• Newton realized that the same force that causes an apple to fall to the ground also governs the motion of the moon and planets.
• He unified terrestrial and celestial mechanics, showing that the same set of physical laws applies universally.

Limitations

• Newton's law of gravity works extremely well for most practical purposes but breaks down in extremely strong gravitational fields or at very large scales, where Einstein's theory of general relativity provides a more accurate description.

Summary

Newton's law of universal gravitation is fundamental in understanding how masses interact through the force of gravity. It describes how the gravitational force between two objects is proportional to their masses and inversely proportional to the square of the distance between them. This law has wide-ranging applications from predicting the motion of celestial bodies to understanding tidal forces and satellite orbits.