Lesson 3: Kepler's Laws

🎯 Objectives

• State Kepler's three laws
• Verify them with an N-body simulation
• Understand why a numerical integrator can be trusted (energy conservation)

🧪 Exercise

1. Using P² = a³ (years and AU), calculate the period of a planet 4 AU from the Sun.
2. Using (1+e)/(1−e), calculate how much faster Earth moves at perihelion (January) than at aphelion (July). Use e = 0.0167.
3. If you have MHD-INT PRO, open N-body mode and measure Mars's period.

⚠️ Model limits

• The simulation includes only the Sun and four planets; the rest are left out to keep it fast.
• The starting positions are chosen (each planet begins at its perihelion), not the real positions on a given date; MHD-INT PRO's Ephemerides mode uses the real JPL ones.
• It is Newtonian gravity: it does not include general relativity, which explains a small extra precession of Mercury's perihelion (43 arcseconds per century).