Overview
The lecture covered creating a scale model of the Earth, Moon, and Sun system to help visualize relative sizes and distances, and introduced astronomical units and light-years for measuring vast distances in space.
Building a Scale Model
- The real Earth's diameter is 12,742 km.
- The model Earth used is a 6 cm (0.06 m) ball.
- Scale factor = 6 cm ÷ 12,742 km (converted to same units).
- 1 km = 100,000 cm, so 12,742 km = 1,274,200,000 cm.
- Scaling factor ≈ 4.71 × 10⁻⁹.
Scaled Sizes and Distances
- Real Moon’s diameter = 3,474 km.
- Scaled Moon’s diameter ≈ 1.64 cm.
- Real Earth-Moon distance = 384,400 km.
- Scaled Earth-Moon distance ≈ 1.81 meters.
- Real Sun's diameter = 1,391,980 km.
- Scaled Sun’s diameter ≈ 6.55 meters.
- Scaled Sun-Earth distance (1 Astronomical Unit, AU) ≈ 704 meters.
- Pluto’s scaled distance would be about 17.5 miles from the model Earth.
Astronomical Units and the Solar System
- 1 Astronomical Unit (AU) = 149.6 million km (distance from Earth to Sun).
- Venus is about 0.7 AU from the Sun; Mercury about 0.4 AU.
- Pluto’s orbit is about 80 AU from the Sun.
Measuring Interstellar Distances
- Proxima Centauri, the nearest star, is ~271,936 AU from the Sun.
- In the scale model, Proxima Centauri is about 119,000 miles away from the model Earth.
- Astronomers use light-years for very large distances.
- 1 light-year ≈ 63,240 AU.
Speed of Light and Light Travel Time
- Speed of light = 186,000 miles/second.
- Light circles Earth ~7 times in one second.
- Light travels from Earth to Moon in ~1.25 seconds.
- Light travels from Earth to Sun in ~8 minutes.
- Voyager 1 can be reached by light in about 17 hours.
- Proxima Centauri is 4.3 light-years away; its light takes 4.3 years to reach Earth.
Communication Across Distances
- A message to Proxima Centauri takes 4.3 years one way, 8.6 years round trip.
Key Terms & Definitions
- Astronomical Unit (AU) — Average Earth-Sun distance, ~149.6 million km.
- Light-year — Distance light travels in one year (~9.46 trillion km or 63,240 AU).
- Scaling Factor — Ratio used to create a proportional model of real objects.
Action Items / Next Steps
- Review the definitions of AU and light-year.
- Practice scaling calculations with different planets or distances.
- Prepare questions about astronomical distance measurements for next class.