Hubble's Law reveals the universe's expansion, showing distant galaxies moving away faster. This groundbreaking discovery changed our understanding of cosmic structure and evolution, linking galaxy distances to their speeds.

Redshift, universe age calculations, and expansion implications stem from Hubble's work. These concepts help us grasp the universe's past, present, and potential futures, from the Big Freeze to the Big Rip.

Understanding Hubble's Law and the Expanding Universe

Hubble's law and mathematical formulation

• Hubble's Law relates galaxy distance to recessional velocity showing farther galaxies move away faster
• Mathematical formulation $v = H_0 \times d$ calculates recessional velocity ($v$) using Hubble constant ($H_0$) and galaxy distance ($d$)
• Hubble constant approximates 70 km/s/Mpc measures expansion rate (kilometers per second per megaparsec)

Redshift and universe expansion

• Redshift increases light wavelength from distant objects due to Doppler effect and cosmic expansion
• Cosmological redshift stretches light wavelength as space itself expands
• Greater redshift indicates faster recession and increases with distance
• Redshift formula $z = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}}$ quantifies wavelength change

Universe age and size calculations

• Hubble time $t_H = \frac{1}{H_0}$ approximates universe age at 13.8 billion years
• Hubble radius $R_H = \frac{c}{H_0}$ estimates observable universe size at 14.4 billion light-years
• Calculations assume constant expansion rate and neglect dark energy and matter effects

Implications of cosmic expansion

• Future scenarios include:
  1. Big Freeze: continued expansion leading to heat death
  2. Big Crunch: gravity-driven reversal of expansion
  3. Big Rip: accelerating expansion tearing apart structures
• Dark energy drives accelerated expansion affecting universe's long-term fate
• Cosmic microwave background cools as universe expands providing early expansion evidence
• Galaxy evolution sees increasing intergalactic distances and reduced merger rates
• Future observability limited as galaxies beyond cosmic horizon become undetectable