gen-define-the-astronomical-unit-and-the-light-year-and-give-one-1609

Define the astronomical unit and the light-year and give one short worked example.

# Astronomical Unit (AU) **Definition:** The average distance from the Earth to the Sun, standardized as exactly **149,597,870,700 meters** (approximately 150 million km or 93 million miles). # Light-Year (ly) **Definition:** The distance light travels in vacuum in one Julian year (365.25 days), equal to approximately **9.461 × 10¹⁵ meters** (about 9.5 trillion km or 5.9 trillion miles). --- ## Worked Example **Question:** The nearest star system, Alpha Centauri, is 4.37 light-years away. Express this distance in astronomical units. **Solution:** First, find how many AU are in one light-year: 1 ly = 9.461 × 10¹⁵ m 1 AU = 1.496 × 10¹¹ m Therefore: $$1 \text{ ly} = \frac{9.461 \times 10^{15}}{1.496 \times 10^{11}} = 63,241 \text{ AU}$$ Now convert 4.37 ly: $$4.37 \text{ ly} = 4.37 \times 63,241 = \mathbf{276,000 \text{ AU}}$$ **Answer:** Alpha Centauri is approximately 276,000 AU away.