Besselian Elements

Returns Besselian elements as raw data or a structured response

Besselian elements are used to calculate data related to the circumstances and observation of solar eclipses. They are represented by a set of numeric values which can be used in conjunction with standard methods developed by Bessel, Chauvenet, Comrie, Meeus and others to perform a variety of eclipse related computations.

If you are performing your own eclipse calculations, the Besselian elements are almost certainly a required input.

For an explanation of the astronomical significance of the numbers included in the Besselian elements, please consult one of the standard sources, such as the Explanatory Supplement to the Astronomical Almanac.

Acknowledgement:

• Eclipse Predictions by Fred Espenak, NASA's GSFC, NASA/Goddard Space Flight Center

Availability

Besselian elements are available for all solar eclipses occurring between the years 1500 and 2500

Delta T Predictions

For eclipses occurring in within the coming 12 months, the Delta T values included in the Besselian elements are periodically updated from values predicted by IERS Bulletin-A.

As an eclipse approaches, the predicted value of Delta T may be subject to (typically) minor revisions of the order of a fraction of a second. Such changes, applied to eclipse calculations, change local circumstances timings, position angles, and the location of paths - however, such changes are usually relatively minor.

Request format

Given the midnight UTC on the date of the eclipse, converted to a Julian Day, the request is made as shown:

JavaScript

axios({
	"method": "GET",
	"url": "https://api.radiantdrift.com/solar-eclipse/elements/[JULIAN_DAY",
	"params": {
		"apiKey": [YOUR_API_KEY]
	},
	"headers": {
		"Accept-Encoding": "deflate, gzip, br"
	}
})

cURL

If no elements are available for the given JULIAN_DAY, a 404 Not Found response is given.

Example

The following request returns the Besselian elements for the total solar eclipse of Apr 20 2023:

GET https://api.radiantdrift.com/solar-eclipse/elements/2460054.5

The expected response is as follows:

{
  "query": {
    "name": "solar-eclipse/elements",
    "jd": 2460054.5,
    "credit": "Eclipse Predictions by Fred Espenak, NASA/Goddard Space Flight Center Emeritus, http://eclipse.gsfc.nasa.gov/"
  },
  "response": {
    "tMax": 2460054.67912,
    "t0": 4,
    "dT": 69.2,
    "x": [
      0.02685,
      0.49501821,
      0.0000135,
      -0.00000706
    ],
    "y": [
      -0.42736599,
      0.2441992,
      -0.0000494,
      -0.00000368
    ],
    "d": [
      11.41178989,
      0.013741,
      -0.000003,
      0
    ],
    "l1": [
      0.54680401,
      0.0001216,
      -0.0000116,
      0
    ],
    "l2": [
      0.000663,
      0.000121,
      -0.0000115,
      0
    ],
    "mu": [
      240.24293518,
      15.00341988,
      0,
      0
    ],
    "tanF1": 0.004655,
    "tanF2": 0.0046318,
    "latGreatestEclipse": -9.6,
    "lngGreatestEclipse": 125.8
  }
}

Raw data

By including the query parameter raw=1 in the request, the API will return raw data. For example for the request

GET https://api.radiantdrift.com/solar-eclipse/elements/2460231.5?raw=1

the expected response is:

{
  "query": {
    "name": "solar-eclipse/elements",
    "jd": 2460231.5,
    "credit": "Eclipse Predictions by Fred Espenak, NASA/Goddard Space Flight Center Emeritus, http://eclipse.gsfc.nasa.gov/"
  },
  "response": [
    2460232.25047,
    18,
    69.1,
    [
      0.16965801,
      0.45855331,
      0.0000278,
      -0.00000543
    ],
    [
      0.33485901,
      -0.2413671,
      0.000024,
      0.00000303
    ],
    [
      -8.24419022,
      -0.014888,
      0.000002,
      0
    ],
    [
      0.56431103,
      -0.0000891,
      -0.0000103,
      0
    ],
    [
      0.018083,
      -0.0000886,
      -0.0000103,
      0
    ],
    [
      93.50173187,
      15.00352955,
      0,
      0
    ],
    0.0046882,
    0.0046648,
    11.4,
    -83.1
  ]
}

In this case, the array included in the response property conforms to the following Typescript type:

export type BesselianElementsRaw = [
  number,
  number,
  number,
  [number, number, number, number],
  [number, number, number, number],
  [number, number, number, number],
  [number, number, number, number],
  [number, number, number, number],
  [number, number, number, number],
  number,
  number,
  number,
  number,
];

This, in turn can be mapped to the following type as follows:

export type Degrees = number;

export type BesselianElements = {
  tMax: number;
  t0: number;
  dT: number;
  x: Array<number>;
  y: Array<number>;
  d: Array<number>;
  l1: Array<number>;
  l2: Array<number>;
  mu: Array<number>;
  tanF1: number;
  tanF2: number;
  latGreatestEclipse: Degrees;
  lngGreatestEclipse: Degrees;
};

function createElements(rawElements: BesselianElementsRaw): BesselianElements | null {

  try {

    const result: BesselianElements = {
      tMax: rawElements[0],
      t0: rawElements[1],
      dT: rawElements[2],
      x: rawElements[3],
      y: rawElements[4],
      d: rawElements[5],
      l1: rawElements[6],
      l2: rawElements[7],
      mu: rawElements[8],
      tanF1: rawElements[9],
      tanF2: rawElements[10],
      latGreatestEclipse: rawElements[11],
      lngGreatestEclipse: rawElements[12],
    }

    return result;
  } catch (error: any) {
    console.log('createElements: %s', (error as Error)?.message);
  }

  return null;
}

You can request whichever format (raw or structured) is most suitable for your application and adapt the example code above to convert from raw to your own typed language implementation.