Moon Phases

The phase cycle

JavaScript — moon phases

// Synodic vs sidereal months
const SYNODIC = 29.530;  // days
const SIDEREAL = 27.322;  // days
const TROPICAL_YEAR = 365.2422;
const synodic_per_year = TROPICAL_YEAR / SYNODIC;

console.log(`Synodic months per year: ${synodic_per_year.toFixed(3)}`);  // 12.37

// Moon orbital speed
const a_MOON = 384400;
const v_moon = 2 * Math.PI * a_MOON / (SIDEREAL * 86400) * 1000;
console.log(`Moon orbital speed: ${(v_moon/1000).toFixed(1)} km/s`);

// Phase angle from time since new moon
function phaseAngle(days_since_new) {
  return (days_since_new / SYNODIC) * 360;  // degrees
}

console.log(`At day 7: ${phaseAngle(7).toFixed(0)}°`);  // ~85° = first quarter
console.log(`At day 14.75: ${phaseAngle(14.75).toFixed(0)}°`);  // 180° = full

// Illuminated fraction
function illuminatedFraction(phase_angle_deg) {
  return 0.5 * (1 - Math.cos(phase_angle_deg * Math.PI / 180));
}

console.log(`At first quarter: ${(illuminatedFraction(90) * 100).toFixed(1)}%`);
console.log(`At full: ${(illuminatedFraction(180) * 100).toFixed(1)}%`);

// Tide amplitude
function tideAmplitude(phase_deg, basemoon = 1.0, baseSun = 0.46) {
  // Spring tide at new/full; neap at quarters
  const moon = basemoon;
  const sun = baseSun * Math.cos(phase_deg * Math.PI / 180);
  return moon + sun;
}

console.log(`New/full tide: ${tideAmplitude(0).toFixed(2)} (max)`);
console.log(`Quarter tide: ${tideAmplitude(90).toFixed(2)} (min)`);

Why moon phases matter

• Tides. Spring/neap cycle (twice monthly).
• Calendars. Lunar and lunisolar systems still in use.
• Eclipses. Predicting when alignments work for solar/lunar eclipses.
• Astronomy timing. New moon best for deep-sky observation (no Moon glare).
• Wildlife behavior. Many species respond to lunar cycles.
• Public awareness. Most accessible astronomical phenomenon.
• Cultural significance. Holidays, religious dates often lunar-based.

Common misconceptions

• Moon phases caused by Earth's shadow. NO — phases are due to angle between Sun and Moon. Earth's shadow only causes lunar eclipses (rare events).
• Same Moon face always lit. Same FACE always faces Earth (tidal locking). But different parts ARE lit at different phases.
• Moon visible only at night. Visible during day too — about half the time.
• Phase determines weather. No causation. Lunar weather effects (if any) are tiny.
• Full moons cause "lunatic" behavior. Studies show no statistical effect on crime, hospital admissions, etc.
• New moon is invisible. Yes, by definition — Sun and Moon align; no reflected sunlight reaches us.