> For the complete documentation index, see [llms.txt](https://docs.radiantdrift.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.radiantdrift.com/solar-eclipses/besselian-elements.md). # 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; y: Array; d: Array; l1: Array; l2: Array; mu: Array; 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.