{
  "address": "50c3bad5c412f4d5e24dc6aae5db9a98",
  "category": "other",
  "question": "Using Cooper's formula, what is the sun's declination on day 172 of the year?",
  "answer": "23.45 degrees",
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  "madeAt": "2026-09-30T22:39:30.722Z",
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  "validityClass": "forever",
  "sources": [
    {
      "label": "The absorption of solar radiation in solar stills",
      "url": null
    }
  ],
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  "answerMethod": "method",
  "unsourced": false,
  "source": {
    "kind": "doi",
    "value": "Cooper, P.I. (1969). The absorption of solar radiation in solar stills. Solar Energy, 12(3), 333-346.",
    "retrieved_utc": "2026-09-30T19:42:00Z"
  },
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  "method": {
    "name": "Solar declination from day of year",
    "version": "1",
    "source_url_or_file": "methods/sun-declination-by-day-of-year.cjs",
    "sha256_of_method_file": "a6af02cd8d353d406268573d578db6f231daea12f6f34710c0875bedcec108c3"
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  },
  "method_deck": {
    "inputs": [
      {
        "name": "day_of_year",
        "type": "integer",
        "unit": "day (1-366)",
        "required": true,
        "description": "Day of the year, January 1 = 1.",
        "min": 1,
        "max": 366
      }
    ],
    "outputs": [
      {
        "name": "declination_degrees",
        "unit": "degrees",
        "description": "Solar declination, positive north of the celestial equator."
      }
    ],
    "steps": [
      "Cooper's formula: declination = 23.45 * sin( (360/365) * (284 + N) ), where N is the day of year and the sine argument is in degrees.",
      "Convert the argument to radians before taking the sine, since standard math libraries use radians.",
      "Round the result to 2 decimals.",
      "This is a smooth approximation to Earth's actual declination curve (accurate to roughly within 1 degree); it does not model leap-year or orbital-eccentricity irregularities."
    ],
    "constants": [
      {
        "name": "max_declination_degrees",
        "value": 23.45,
        "unit": "degrees",
        "source": 0
      },
      {
        "name": "days_in_year",
        "value": 365,
        "unit": "days",
        "source": 0
      },
      {
        "name": "phase_offset_days",
        "value": 284,
        "unit": "days",
        "source": 0
      }
    ],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "day_of_year": 172
        },
        "expected": {
          "answer": "23.45 degrees"
        },
        "check": "Day 172 is on or near the June solstice; Earth's axial tilt is a well known fact of 23.45 degrees, and it is the known maximum of the declination curve, so the formula should return a value essentially equal to that maximum, which it does (23.4499 rounds to 23.45)."
      },
      {
        "name": "test vector: December solstice",
        "inputs": {
          "day_of_year": 355
        },
        "expected": {
          "answer": "-23.45 degrees"
        },
        "check": "Day 355 is on or near the December solstice, the known minimum of the declination curve at -23.45 degrees (Earth's axial tilt with the opposite sign), which the formula reproduces (-23.4498 rounds to -23.45)."
      }
    ],
    "disclaimer": null,
    "deck_category": "astronomy"
  },
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  "kind": "method",
  "provenanceClass": "own_question",
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        "source": {
          "kind": "doi",
          "value": "Cooper, P.I. (1969). The absorption of solar radiation in solar stills. Solar Energy, 12(3), 333-346.",
          "retrieved_utc": "2026-09-30T19:42:00Z"
        },
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        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Solar declination from day of year",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
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}