Gravity

Beginner

Gravity is an invisible pull that attracts objects with mass toward one another.

It is the force that keeps your feet firmly on the ground, makes apples fall from trees, and holds the Earth in orbit around the Sun. The more massive an object is, the stronger its gravitational pull. For example, because Jupiter is much larger and more massive than Earth, you would weigh significantly more if you were standing on Jupiter. Conversely, because the Moon is smaller than Earth, astronauts can bound in the air easily.

Intermediate

In Classical Mechanics, gravity was described by Sir Isaac Newton in 1687 with his Law of Universal Gravitation.

Newton proposed that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The mathematical formula is:
$$
F = G \frac{m_1 m_2}{r^2}
$$

Where:

• $F$ is the gravitational force between two objects.
• $m_1$ and $m_2$ are the masses of the objects.
• $r$ is the distance between the centers of their masses.
• $G$ is the gravitational constant ($6.67430 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2$).

This equation was revolutionary because it unified the heavens and the Earth: the same force pulling an apple down was the exact same force keeping the moon in orbit.

Advanced

While Newton's equations are incredibly accurate for most practical purposes (including sending rockets to the moon), they break down when dealing with extremely massive objects or speeds approaching the speed of light.

General Relativity

In 1915, Albert Einstein published his General Theory of Relativity, fundamentally redefining gravity. According to Einstein, gravity is not a "force" that reaches across space, but rather a consequence of the curvature of spacetime caused by the uneven distribution of mass and energy.

Imagine spacetime as a trampoline. If you place a heavy bowling ball in the center, it creates a dip. If you roll a marble across the trampoline, its path will curve around the bowling ball. The marble isn't being "pulled" by a mysterious force; it is simply following the straightest possible path (a geodesic) through a curved space.

This is governed by the Einstein Field Equations:
$$
R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
$$

Where:

• $R_{\mu\nu}$ and $R$ describe the curvature of spacetime.
• $g_{\mu\nu}$ is the metric tensor.
• $\Lambda$ is the cosmological constant.
• $T_{\mu\nu}$ is the stress-energy tensor (representing the distribution of mass and energy).

In short, John Archibald Wheeler perfectly summarized General Relativity: "Spacetime tells matter how to move; matter tells spacetime how to curve."