gen-define-the-formation-of-the-solar-system-and-give-one-short-bc8c

Define the formation of the solar system and give one short worked example.

# Formation of the Solar System ## Definition The **solar system formation** refers to the process by which the Sun, planets, moons, and other celestial bodies formed approximately **4.6 billion years ago** from a rotating cloud of gas and dust called the **solar nebula**. ### Key Stages: 1. **Nebular collapse** - A giant molecular cloud collapses under gravity (possibly triggered by a nearby supernova shockwave) 2. **Disk formation** - Conservation of angular momentum causes the collapsing cloud to flatten into a rotating protoplanetary disk with a dense center 3. **Protosun formation** - The center becomes hot and dense enough to form the protosun 4. **Planetesimal accretion** - Dust grains collide and stick together, forming larger bodies called planetesimals 5. **Planetary formation** - Planetesimals collide and merge to form protoplanets, then planets 6. **Differentiation** - Inner rocky planets form where it's hot; outer gas giants form beyond the "frost line" where ices can condense --- ## Worked Example: Conservation of Angular Momentum **Problem:** A nebular cloud with radius R₁ = 10¹⁵ m rotates once every T₁ = 1 million years. It collapses to R₂ = 10¹³ m. Find the new rotation period T₂. **Solution:** Angular momentum is conserved: I₁ω₁ = I₂ω₂ For a uniform sphere: I ∝ MR² Since mass is conserved: R₁²ω₁ = R₂²ω₂ ω = 2π/T, so: R₁²/T₁ = R₂²/T₂ T₂ = T₁(R₂/R₁)² = 10⁶ years × (10¹³/10¹⁵)² **T₂ = 100 years** This demonstrates why the collapsing nebula spins much faster!