# Besselian Elements

[Besselian elements](https://en.wikipedia.org/wiki/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*.

{% hint style="info" %}
Acknowledgement: 

* Eclipse Predictions by Fred Espenak, NASA's GSFC, [NASA/Goddard Space Flight Center](https://support.photoephemeris.com/hc/en-us/articles/eclipse.gsfc.nasa.gov)
  {% endhint %}

### 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](https://datacenter.iers.org/data/latestVersion/bulletinA.txt). 

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:

{% tabs %}
{% tab title="JavaScript" %}
{% code overflow="wrap" lineNumbers="true" %}

```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"
	}
})
```

{% endcode %}
{% endtab %}

{% tab title="cURL" %}
{% code overflow="wrap" lineNumbers="true" %}

```bash
curl "https://api.radiantdrift.com/solar-eclipse/elements/[JULIAN_DAY]?apiKey=[YOUR_API_KEY]" \
     -H 'Accept-Encoding: deflate, gzip, br'
```

{% endcode %}
{% endtab %}
{% endtabs %}

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:

{% code overflow="wrap" %}

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

{% endcode %}

The expected response is as follows:

{% code overflow="wrap" lineNumbers="true" %}

```json
{
  "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
  }
}
```

{% endcode %}

### Raw data

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

{% code overflow="wrap" %}

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

{% endcode %}

the expected response is:

{% code overflow="wrap" lineNumbers="true" %}

```json
{
  "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
  ]
}
```

{% endcode %}

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

{% code overflow="wrap" lineNumbers="true" %}

```typescript
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,
];
```

{% endcode %}

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

```typescript
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.


---

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