Cosmic Rays

What cosmic rays are

Energy spectrum features

JavaScript — cosmic ray calculations

// Energy of "Oh-My-God particle"
const eV = 1.602e-19;
const c = 3e8;
const m_p = 1.673e-27;  // proton

const E_OMG = 3.2e20 * eV;  // joules
console.log(`OMG energy: ${(E_OMG / eV / 1e20).toFixed(1)} × 10²⁰ eV`);

// Equivalent in everyday terms
console.log(`OMG energy: ${E_OMG.toFixed(2)} J`);
// ~50 J — a baseball at 60 mph has ~140 J of KE
console.log(`Baseball at 30 m/s: ${0.5 * 0.145 * 30 * 30} J`);  // 65 J

// Lorentz factor
function lorentzFactorFromEnergy(E_J, mass_kg = m_p) {
  const E_rest = mass_kg * c * c;
  return E_J / E_rest;
}

console.log(`OMG γ: ${lorentzFactorFromEnergy(E_OMG).toExponential(2)}`);
// γ ~ 3.4 × 10¹¹ — proton appears slowed by factor of 10¹¹

// Time dilation
function travelTime(distance_ly, gamma) {
  // From proton's frame, distance is contracted
  const ly = 9.461e15;  // m per ly
  const c_speed = 3e8;
  return distance_ly * ly / (c_speed * gamma);
}

console.log(`OMG to cross galaxy (100,000 ly) in proper time: ${travelTime(1e5, 3.4e11).toExponential(2)} s`);
// Microsecond — proton "experiences" galaxy crossing in microseconds!

// Atmospheric depth (g/cm²)
const atm_depth = 1033;  // g/cm² at sea level
function depthAtAltitude(altitude_km) {
  // Exponential approximation
  return atm_depth * Math.exp(-altitude_km / 8);
}

console.log(`Sea level: ${depthAtAltitude(0)} g/cm²`);
console.log(`Cruising altitude (10 km): ${depthAtAltitude(10).toFixed(0)} g/cm²`);
// ~150 g/cm²

// Annual cosmic ray dose
const doses = {
  'Sea level': 0.4,           // mSv/year
  'Mile high (Denver)': 0.5,
  'Aircraft cruising': 0.0036,  // mSv/hour
  'ISS (LEO)': 150,           // mSv/year
  'Mars surface': 250,        // mSv/year
  'Mars transit': 660         // mSv/year (no shielding)
};
console.log(doses);

Where cosmic rays matter

• Astrophysics. Probes of high-energy processes in supernovae, pulsars, AGN.
• Particle physics. Ultra-high energies inaccessible to accelerators; muon discovery (1936) was from cosmic rays.
• Earth's radiation environment. Background dose, aviation health, satellite design.
• Space exploration. Major risk for human Mars missions; need shielding.
• Atmospheric chemistry. Cosmic rays produce C-14 (used in dating), Be-10, etc.
• Climate. Some studies link CR flux to cloud formation; controversial.
• Foundations. Tests of special relativity (muon time dilation observed at sea level).

Common mistakes

• Calling them "rays." Originally thought to be EM rays; they're particles. "Cosmic ray" is historical.
• Believing they're mostly photons. ~99% are charged particles (mostly protons). Gamma rays from cosmic sources exist but are different category.
• Underestimating energies. Highest CR have macroscopic-particle energies (joules per particle).
• Thinking atmosphere fully blocks them. Most secondary muons reach ground (and pass through us). Atmospheric shielding is partial.
• Confusing primary and secondary cosmic rays. Primary — original from space. Secondary — created in atmospheric showers. Most ground detections are secondary.
• Treating cosmic ray dose as negligible. Adds significantly at altitude, on long-haul flights, in space.