Planetesimal Formation and Planetary Evolution

Planetesimal Formation:

1. Initial Nebula: About 4600 million years ago, a rotating nebula of dust and gas, larger than our solar system, began to shrink.
2. Gravitational Collapse: This collapse formed a central mass and a rotating disk around it.
3. Protosun Formation: Particle collisions in the central mass released energy. Hydrogen nuclear fusion began, marking the birth of the protosun within the nebula.
4. Planetesimal Formation: Dust and gas particles in the disk around the protosun began to clump together. This process started with millimeter-sized granules, whose collisions and mergers formed larger bodies—planetesimals—ranging from hundreds of meters to kilometers in size.
5. Protoplanet Formation: Collisions and mergers of planetesimals, a process called accretion, formed protoplanets. During this process, each protoplanet swept its orbit clear of planetesimals.

Moon Formation:
The Moon may have formed alongside Earth. However, the Moon is about 100 million years younger than Earth, and despite being in the same area of the solar system, their densities differ significantly; Earth's density is greater. The most accepted theory, developed by Hartmann and Davis, proposes that early in Earth's existence, a planet collided with it. Part of this colliding body formed a cloud of debris that orbited Earth, eventually forming the Moon.

Earth Formation:

1. Protoplanet Earth Formation: Within the nebular disk surrounding the protosun, planetesimals accreted to form the protoplanet Earth. As its size increased, so did its gravitational field, which further favored the accretion of more planetesimals. The most abundant planetesimals in this area were silicates. During this phase, the temperature increased due to planetesimal impacts.
2. Differentiation by Density: The temperature of early Earth was high enough to partially melt it. This allowed the main components to distribute according to their density. Iron sank to form the core, a process called differentiation. Degassing released internal gases, forming the atmosphere, with abundant water vapor.
3. Surface Cooling and Ocean Formation: After the planetesimal bombardment decreased, Earth began to cool. Surface temperatures allowed water vapor to condense, forming oceans about 4200 million years ago.

Formulas:
Volume = 4/3πR³
Newton's Law of Universal Gravitation: F = G * M * m/d², where G is the gravitational constant (6.67 x 10^-11 m³/kg s²).
Mass of a planet: M = g * d²/G