---
title: "Raw Besselian Elements"
method: GET
path: "/eclipse/besselian-elements"
tags: ["eclipse"]
---

# Raw Besselian Elements

`GET /eclipse/besselian-elements`

## Request

- Base URL: `https://api.openephemeris.com`
- URL: `https://api.openephemeris.com/eclipse/besselian-elements`
- Auth: one of:
  - HTTP bearer
  - API key in header `X-OpenEphemeris-API-Key`
  - API key in header `X-API-Key`
  - API key in header `X-Service-Key`

Raw Besselian elements (X, Y, d, μ, l₁, l₂, f₁, f₂) and their time derivatives for any eclipse. For researchers and advanced users.

## Query parameters

- `date` string, nullable
- `jd` number, double, nullable
- `delta_t_model` string

## Response `200`

Besselian elements for the eclipse

- BesselianElementsResponse
  - `elements` BesselianElements, required
    - `X` number, required: Shadow axis x in fundamental plane
    - `Xdot` number
    - `Y` number, required: Shadow axis y in fundamental plane
    - `Ydot` number
    - `d` number, required: Declination of shadow axis (degrees)
    - `ddot` number
    - `f1` number, required: Penumbral cone half-angle (radians)
    - `f2` number, required: Umbral cone half-angle (radians)
    - `l1` number, required: Penumbral shadow radius
    - `l2` number, required: Umbral shadow radius
    - `mu` number, required: Hour angle of shadow axis (degrees)
    - `mudot` number
    - `reference_jd` number, double, required
    - `reference_time_utc` string, required
  - `meta` CalculationMeta, required
    - `calculation_precision` string
    - `delta_t_model` string, required
    - `delta_t_seconds` number, required
    - `delta_t_uncertainty` number, required
    - `ephemeris` string, required
    - `julian_day` number, double, required

## Other responses

- `400`: Bad Request
- `422`: Validation Error
- `500`: Internal Server Error

---

[API](https://skmtc.dev/openephemeris/apis/open-ephemeris-api.md) · [All operations](https://skmtc.dev/openephemeris/apis/open-ephemeris-api/llms.txt) · [OpenAPI document](https://skmtc.dev/openephemeris/apis/open-ephemeris-api/revisions/d195a769cb89?raw)