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Apache License
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http://www.apache.org/licenses/
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END OF TERMS AND CONDITIONS
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.PHONY: test release
_MOCHA=node_modules/.bin/_mocha
test:
npm run test-ci
release: test
ifeq ($(strip $(version)),)
@echo "\033[31mERROR:\033[0;39m No version provided"
@echo "\033[1;30mmake release version=1.0.0\033[0;39m"
else
ifneq ($(shell git diff --stat),)
@echo "Changes must be committed before running a release"
else
npm version $(version)
npm publish
git push origin master
git push origin --tags
endif
endif
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# geomagnetism
[![NPM version](http://img.shields.io/npm/v/geomagnetism.svg?style=flat)](https://www.npmjs.org/package/geomagnetism)
[![Coverage Status](http://img.shields.io/coveralls/naturalatlas/geomagnetism/master.svg?style=flat)](https://coveralls.io/r/naturalatlas/geomagnetism)
`geomagnetism` provides a convenient interface for retrieving the Earth's magnetic declination (variation between magnetic north and true north) at a given location and date. It leverages NOAA's [World Magnetic Model (WMM)](https://www.ngdc.noaa.gov/geomag/WMM/) to compute properties such as declination, inclination, horizontal intensity, and more.
``` sh
$ npm install geomagnetism --save
```
### Usage
The main entry point is the `model()` function. If you pass it a Date object, it will compute results for that specific date. If you do **not** pass a date, it will default to the current date. Once you have a model, you can query it using the `point()` method, which expects an array representing latitude and longitude. Optionally, you can provide an altitude as a third element in the array.
- Latitude and longitude are required: `[lat, lon]`
- Altitude (optional) can be provided: `[lat, lon, altitude_in_kilometers]`
**Example: Current Date**
```js
const geomagnetism = require('geomagnetism');
// If no date is passed, the current date is used
const currentModel = geomagnetism.model();
const info = currentModel.point([44.53461, -109.05572]); // only lat/lon
console.log('Declination (current date):', info.decl, 'degrees');
```
**Example: Specific Date**
```js
const geomagnetism = require('geomagnetism');
// If a date is passed, that specific date is used
const specificDateModel = geomagnetism.model(new Date('2020-10-05'));
const info = specificDateModel.point([44.53461, -109.05572]);
console.log('Declination on 2020-10-05:', info.decl, 'degrees');
```
**Example: Including Altitude**
```js
const geomagnetism = require('geomagnetism');
// Provide altitude as the third array item (in kilometers above mean sea level)
const model = geomagnetism.model(new Date('2022-01-01'));
const infoWithAltitude = model.point([44.53461, -109.05572, 1.5]);
console.log('Declination at altitude:', infoWithAltitude.decl, 'degrees');
```
## Handling Out-of-Range Dates
The `geomagnetism.model()` function determines the best available World Magnetic Model for the date you provide. If the given date falls outside the known range of the WMM data files, by default (`allowOutOfBoundsModel = false`), the function will throw an error indicating that no suitable model is found for the given date.
If you would prefer that the library "fall back" to the closest available model rather than throwing an error, you can explicitly pass true to allowOutOfBoundsModel option.
```js
geomagnetism.model(date, { allowOutOfBoundsModel: true });
```
- `date`: *(optional)* A JavaScript Date object. Defaults to the current date if not specified.
- `allowOutOfBoundsModel`: *(optional)* A boolean. If not specified or false, throws an error if the date is out of range. If true, falls back to the nearest available model.
**Examples:**
```js
const geomagnetism = require('geomagnetism');
// Strict behavior (default): If the date is out of range, an error is thrown
try {
let model = geomagnetism.model(new Date('1900-01-01')); // allowOutOfBoundsModel defaults to false
let info = model.point([44.53461, -109.05572]);
} catch (err) {
console.error('Error (strict mode):', err.message);
}
// Fallback behavior: If the date is out of range, it uses the closest model
let fallbackModel = geomagnetism.model(new Date('1900-01-01'), { allowOutOfBoundsModel: true });
let fallbackInfo = fallbackModel.point([44.53461, -109.05572]);
console.log('Declination using fallback model:', fallbackInfo.decl);
```
## Available Data & Models
`geomagnetism` ships with multiple versions of the WMM data, each valid for a certain time range. The library automatically picks the correct model based on the date you supply. Older models are included to gracefully handle historical dates when using the fallback behavior.
## License
Copyright © 2015–2024 [Natural Atlas, Inc.](https://naturalatlas.com/) & [Contributors](https://github.com/naturalatlas/geomagnetism/graphs/contributors)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at: http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
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var fs = require('fs');
var path = require('path');
/**
* Converts a coefficients file to a .json file that can be used to initialize a base model
*
* ex: node bin/convert WMM.COF wmm.json
*/
function exit(err){
console.log("Error: "+err);
process.exit(1);
}
var input_filename = process.argv[2];
var output_filename = process.argv[3];
if(!input_filename) exit("Input filename must be provided.");
if(!output_filename) exit("Output filename must be provided.");
// get parser by input file extension
var ext = path.extname(input_filename).toLowerCase().substr(1);
var parser;
try {
parser = require('../lib/parsers/'+ext);
} catch (err) {
exit("Unable to find parser for ."+ext+" file.");
}
var data = fs.readFileSync(input_filename, {encoding: 'utf8'});
var obj = parser(data);
var json = JSON.stringify(obj, null, 2);
fs.writeFileSync(output_filename, json);
console.log(output_filename + " successfully created");
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"n_max": 12,
"n_max_sec_var": 12,
"epoch": 2015,
"name": "WMM-2015",
"start_date": "2014-12-15T07:00:00.000Z",
"end_date": "2019-12-15T07:00:00.000Z"
}
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-29.6,
-17.3,
0,
6.5,
-0.8,
-2,
0,
-0.4,
5.8,
3.8,
-3.5,
0,
0.2,
2.3,
0,
3.3,
-0.6,
0,
0.3,
-1.5,
-1.2,
0.4,
0.2,
1.3,
0,
0.6,
0.5,
-0.8,
-0.2,
-1.1,
0.1,
0.2,
0,
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0.6,
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0.6,
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0.5,
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0,
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0.1,
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0.3,
0.1,
0,
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0.5,
0.2,
0,
0,
0.1,
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0.1,
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0.1,
0,
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0.2,
0,
0,
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0.1,
0,
0.1,
0,
0,
0.1,
0,
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0,
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0,
0,
0,
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0.1,
0,
0,
0,
0,
0,
0,
0,
-0.1
],
"n_max": 12,
"n_max_sec_var": 12,
"epoch": 2015,
"name": "WMM-2015v2",
"start_date": "2018-09-18T06:00:00.000Z",
"end_date": "2023-09-18T06:00:00.000Z"
}
+380
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@@ -0,0 +1,380 @@
{
"main_field_coeff_g": [
0,
-29404.5,
-1450.7,
-2500,
2982,
1676.8,
1363.9,
-2381,
1236.2,
525.7,
903.1,
809.4,
86.2,
-309.4,
47.9,
-234.4,
363.1,
187.8,
-140.7,
-151.2,
13.7,
65.9,
65.6,
73,
-121.5,
-36.2,
13.5,
-64.7,
80.6,
-76.8,
-8.3,
56.5,
15.8,
6.4,
-7.2,
9.8,
23.6,
9.8,
-17.5,
-0.4,
-21.1,
15.3,
13.7,
-16.5,
-0.3,
5,
8.2,
2.9,
-1.4,
-1.1,
-13.3,
1.1,
8.9,
-9.3,
-11.9,
-1.9,
-6.2,
-0.1,
1.7,
-0.9,
0.6,
-0.9,
1.9,
1.4,
-2.4,
-3.9,
3,
-1.4,
-2.5,
2.4,
-0.9,
0.3,
-0.7,
-0.1,
1.4,
-0.6,
0.2,
3.1,
-2,
-0.1,
0.5,
1.3,
-1.2,
0.7,
0.3,
0.5,
-0.2,
-0.5,
0.1,
-1.1,
-0.3
],
"main_field_coeff_h": [
0,
0,
4652.9,
0,
-2991.6,
-734.8,
0,
-82.2,
241.8,
-542.9,
0,
282,
-158.4,
199.8,
-350.1,
0,
47.7,
208.4,
-121.3,
32.2,
99.1,
0,
-19.1,
25,
52.7,
-64.4,
9,
68.1,
0,
-51.4,
-16.8,
2.3,
23.5,
-2.2,
-27.2,
-1.9,
0,
8.4,
-15.3,
12.8,
-11.8,
14.9,
3.6,
-6.9,
2.8,
0,
-23.3,
11.1,
9.8,
-5.1,
-6.2,
7.8,
0.4,
-1.5,
9.7,
0,
3.4,
-0.2,
3.5,
4.8,
-8.6,
-0.1,
-4.2,
-3.4,
-0.1,
-8.8,
0,
0,
2.6,
-0.5,
-0.4,
0.6,
-0.2,
-1.7,
-1.6,
-3,
-2,
-2.6,
0,
-1.2,
0.5,
1.3,
-1.8,
0.1,
0.7,
-0.1,
0.6,
0.2,
-0.9,
0,
0.5
],
"secular_var_coeff_g": [
0,
6.7,
7.7,
-11.5,
-7.1,
-2.2,
2.8,
-6.2,
3.4,
-12.2,
-1.1,
-1.6,
-6,
5.4,
-5.5,
-0.3,
0.6,
-0.7,
0.1,
1.2,
1,
-0.6,
-0.4,
0.5,
1.4,
-1.4,
0,
0.8,
-0.1,
-0.3,
-0.1,
0.7,
0.2,
-0.5,
-0.8,
1,
-0.1,
0.1,
-0.1,
0.5,
-0.1,
0.4,
0.5,
0,
0.4,
-0.1,
-0.2,
0,
0.4,
-0.3,
0,
0.3,
0,
0,
-0.4,
0,
0,
0,
0.2,
-0.1,
-0.2,
0,
-0.1,
-0.2,
-0.1,
0,
0,
-0.1,
0,
0,
0,
-0.1,
0,
0,
-0.1,
-0.1,
-0.1,
-0.1,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
-0.1
],
"secular_var_coeff_h": [
0,
0,
-25.1,
0,
-30.2,
-23.9,
0,
5.7,
-1,
1.1,
0,
0.2,
6.9,
3.7,
-5.6,
0,
0.1,
2.5,
-0.9,
3,
0.5,
0,
0.1,
-1.8,
-1.4,
0.9,
0.1,
1,
0,
0.5,
0.6,
-0.7,
-0.2,
-1.2,
0.2,
0.3,
0,
-0.3,
0.7,
-0.2,
0.5,
-0.3,
-0.5,
0.4,
0.1,
0,
-0.3,
0.2,
-0.4,
0.4,
0.1,
0,
-0.2,
0.5,
0.2,
0,
0,
0.1,
-0.3,
0.1,
-0.2,
0.1,
0,
-0.1,
0.2,
0,
0,
0,
0.1,
0,
0.2,
0,
0,
0.1,
0,
-0.1,
0,
0,
0,
0,
0,
-0.1,
0.1,
0,
0,
0,
0.1,
0,
0,
0,
-0.1
],
"n_max": 12,
"n_max_sec_var": 12,
"epoch": 2020,
"name": "WMM-2020",
"start_date": "2019-12-10T08:00:00.000Z",
"end_date": "2024-12-10T08:00:00.000Z"
}
+380
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@@ -0,0 +1,380 @@
{
"main_field_coeff_g": [
0,
-29351.8,
-1410.8,
-2556.6,
2951.1,
1649.3,
1361,
-2404.1,
1243.8,
453.6,
895,
799.5,
55.7,
-281.1,
12.1,
-233.2,
368.9,
187.2,
-138.7,
-142,
20.9,
64.4,
63.8,
76.9,
-115.7,
-40.9,
14.9,
-60.7,
79.5,
-77,
-8.8,
59.3,
15.8,
2.5,
-11.1,
14.2,
23.2,
10.8,
-17.5,
2,
-21.7,
16.9,
15,
-16.8,
0.9,
4.6,
7.8,
3,
-0.2,
-2.5,
-13.1,
2.4,
8.6,
-8.7,
-12.9,
-1.3,
-6.4,
0.2,
2,
-1,
-0.6,
-0.9,
1.5,
0.9,
-2.7,
-3.9,
2.9,
-1.5,
-2.5,
2.4,
-0.6,
-0.1,
-0.6,
-0.1,
1.1,
-1,
-0.2,
2.6,
-2,
-0.2,
0.3,
1.2,
-1.3,
0.6,
0.6,
0.5,
-0.1,
-0.4,
-0.2,
-1.3,
-0.7
],
"main_field_coeff_h": [
0,
0,
4545.4,
0,
-3133.6,
-815.1,
0,
-56.6,
237.5,
-549.5,
0,
278.6,
-133.9,
212,
-375.6,
0,
45.4,
220.2,
-122.9,
43,
106.1,
0,
-18.4,
16.8,
48.8,
-59.8,
10.9,
72.7,
0,
-48.9,
-14.4,
-1,
23.4,
-7.4,
-25.1,
-2.3,
0,
7.1,
-12.6,
11.4,
-9.7,
12.7,
0.7,
-5.2,
3.9,
0,
-24.8,
12.2,
8.3,
-3.3,
-5.2,
7.2,
-0.6,
0.8,
10,
0,
3.3,
0,
2.4,
5.3,
-9.1,
0.4,
-4.2,
-3.8,
0.9,
-9.1,
0,
0,
2.9,
-0.6,
0.2,
0.5,
-0.3,
-1.2,
-1.7,
-2.9,
-1.8,
-2.3,
0,
-1.3,
0.7,
1,
-1.4,
0,
0.6,
-0.1,
0.8,
0.1,
-1,
0.1,
0.2
],
"secular_var_coeff_g": [
0,
12,
9.7,
-11.6,
-5.2,
-8,
-1.3,
-4.2,
0.4,
-15.6,
-1.6,
-2.4,
-6,
5.6,
-7,
0.6,
1.4,
0,
0.6,
2.2,
0.9,
-0.2,
-0.4,
0.9,
1.2,
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0.3,
0.9,
0,
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-0.1,
0.5,
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-0.8,
-0.8,
0.8,
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0.2,
0,
0.5,
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0.3,
0.2,
0,
0.2,
0,
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0.1,
0.3,
-0.3,
0,
0.3,
-0.1,
0.1,
-0.1,
0.1,
0,
0.1,
0.1,
0,
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0,
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-0.1,
0,
0,
0,
0,
0,
0,
0,
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0,
0,
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0,
0,
0,
0,
0,
0,
0.1,
0,
0,
0,
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0,
-0.1
],
"secular_var_coeff_h": [
0,
0,
-21.5,
0,
-27.7,
-12.1,
0,
4,
-0.3,
-4.1,
0,
-1.1,
4.1,
1.6,
-4.4,
0,
-0.5,
2.2,
0.4,
1.7,
1.9,
0,
0.3,
-1.6,
-0.4,
0.9,
0.7,
0.9,
0,
0.6,
0.5,
-0.8,
0,
-1,
0.6,
-0.2,
0,
-0.2,
0.5,
-0.4,
0.4,
-0.5,
-0.6,
0.3,
0.2,
0,
-0.3,
0.3,
-0.3,
0.3,
0.2,
-0.1,
-0.2,
0.4,
0.1,
0,
0,
0,
-0.2,
0.1,
-0.1,
0.1,
0,
-0.1,
0.2,
0,
0,
0,
0.1,
0,
0.1,
0,
0,
0.1,
0,
0,
0,
0,
0,
0,
0,
-0.1,
0.1,
0,
0,
0,
0,
0,
0,
0,
-0.1
],
"n_max": 12,
"n_max_sec_var": 12,
"epoch": 2025,
"name": "WMM-2025",
"start_date": "2024-11-13T03:00:00.000Z",
"end_date": "2029-11-13T03:00:00.000Z"
}
+30
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declare module "geomagnetism" {
export interface GeomagnetismPoint {
x: number;
y: number;
z: number;
h: number;
f: number;
incl: number;
decl: number;
}
export interface GeomagnetismModel {
epoch: number;
start_date: Date;
end_date: Date;
name: string;
main_field_coeff_g: number[];
secular_var_coeff_h: number[];
n_max: number;
n_max_sec_var: number;
num_terms: number;
point(geoPoint: number[]): GeomagnetismPoint;
}
export interface GeomagnetismOptions {
allowOutOfBoundsModel: boolean;
}
export function model(date?: Date, options?: GeomagnetismOptions): GeomagnetismModel;
}
+54
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const Model = require('./lib/model.js');
const geomagnetism = module.exports = {};
const modelData = [
{
file: require('./data/wmm-2025.json'),
startDate: new Date("2024-11-13T03:00:00.000Z"),
endDate: new Date("2029-11-13T03:00:00.000Z")
},
{
file: require('./data/wmm-2020.json'),
startDate: new Date("2019-12-10T08:00:00.000Z"),
endDate: new Date("2024-12-10T08:00:00.000Z")
},
{
file: require('./data/wmm-2015v2.json'),
startDate: new Date("2018-09-18T06:00:00.000Z"),
endDate: new Date("2023-09-18T06:00:00.000Z")
},
{
file: require('./data/wmm-2015.json'),
startDate: new Date("2014-12-15T07:00:00.000Z"),
endDate: new Date("2019-12-15T07:00:00.000Z")
}
];
geomagnetism.model = function (date, options = {}) {
date = date || new Date();
const ts = date.getTime();
const allowOutOfBoundsModel = (options && options.allowOutOfBoundsModel) || false;
// Get the latest matching model
let matchingModelData = modelData.find((model) => {
return ts >= model.startDate.getTime() && ts <= model.endDate.getTime();
});
// Get if the date is before the first model or after the last model
if (!matchingModelData && ts < modelData[modelData.length - 1].startDate.getTime()) {
matchingModelData = modelData[modelData.length - 1];
} else if (!matchingModelData && ts > modelData[0].endDate.getTime()) {
matchingModelData = modelData[0];
}
// If no matching model found, use the latest
if (!matchingModelData) {
matchingModelData = modelData[0]; // latest (will throw error if allowOutOfBoundsModel is true)
}
const matchingModel = new Model(matchingModelData.file);
return matchingModel.getTimedModel(date, allowOutOfBoundsModel);
};
+46
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var GeodeticCoord = require('./geodetic.js');
module.exports = CartesianCoord;
function CartesianCoord(options){
this.x = options.x;
this.y = options.y;
this.z = options.z;
}
CartesianCoord.prototype.toGeodetic = function(ellipsoid){
var modified_b = this.z < 0 ? -ellipsoid.b : ellipsoid.b;
var x = this.x;
var y = this.y;
var z = this.z;
var r = Math.sqr(x*x + y*y);
var e = (modified_b*z - (ellipsoid.a*ellipsoid.a - modified_b*modified_b)) / (ellipsoid.a*r);
var f = (modified_b*z + (ellipsoid.a*ellipsoid.a - modified_b*modified_b)) / (ellipsoid.a*r);
var p = (4/3) * (e*f+1);
var q = 2 * (e*e + f*f);
var d = p*p*p + q*q;
var v;
if(d > 0) {
v = Math.pow(Math.sqrt(d) - q, 1/3) - Math.pow(Math.sqrt(d) + q, 1/3);
} else {
v = 2 * Math.sqrt(-p) * Math.cos(Math.acos(q / (p * Math.sqrt(-p)) ) / 3);
}
if(v*v < Math.abs(p)) {
v = -(v*v*v + 2*q) / 3*p;
}
var g = (Math.sqrt(e*e + v) + e) / 2;
var t = Math.sqrt(g*g + (f - v*g)/(2*g - e)) - g;
var rlat = Math.atan( (ellipsoid.a*(1 - t*t)) / (2*modified_b*t) );
var zlong = Math.atan2(y, x);
if(zlong < 0) zlong += 2*Math.PI;
var height_above_ellipsoid = (r - ellipsoid.a*t) * Math.cos(rlat) + (z - modified_b) * Math.sin(rlat);
var lambda = zlong * Math.PI/180;
if(lambda > 180) lambda -= 360;
return new GeodeticCoord({
lambda: lambda,
phi: rlat * Math.PI/180,
height_above_ellipsoid: height_above_ellipsoid,
ellipsoid: ellipsoid
});
};
+31
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var SphericalCoord = require('./spherical.js');
var Ellipsoid = require('../ellipsoid.js');
module.exports = GeodeticCoord;
function GeodeticCoord(options){
this.options = options;
this.lambda = options.lambda || options.lon; // longitude
this.phi = options.phi || options.lat; // geodetic latitude
this.height_above_ellipsoid = options.height_above_ellipsoid || 0;
this.ellipsoid = options.ellipsoid || new Ellipsoid();
}
GeodeticCoord.prototype.toSpherical = function() {
var ellipsoid = this.ellipsoid;
var coslat = Math.cos(this.phi*Math.PI/180);
var sinlat = Math.sin(this.phi*Math.PI/180);
var rc = ellipsoid.a / Math.sqrt(1 - ellipsoid.epssq * sinlat * sinlat);
var xp = (rc + this.height_above_ellipsoid) * coslat;
var zp = (rc * (1 - ellipsoid.epssq) + this.height_above_ellipsoid) * sinlat;
var r = Math.sqrt(xp*xp + zp*zp);
return new SphericalCoord({
r: r,
phig: 180/Math.PI*Math.asin(zp / r),
lambda: this.lambda
});
};
GeodeticCoord.prototype.clone = function(){
return new GeodeticCoord(this.options);
};
+5
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module.exports = {
Cartesian: require('./cartesian.js'),
Spherical: require('./spherical.js'),
Geodetic: require('./geodetic.js')
};
+54
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var CartesianCoord = require('./cartesian.js');
var LegendreFunction = require('../legendre.js');
module.exports = SphericalCoord;
function SphericalCoord(options){
this.lambda = options.lambda; // longitude
this.phig = options.phig; // geocentric latitude
this.r = options.r; // distance from center of ellipsoid
}
SphericalCoord.prototype.toCartesian = function(){
var radphi = this.phig * Math.PI/180;
var radlambda = this.lambda * Math.PI/180;
return new CartesianCoord({
x: this.r * cos(radphi) * cos(radlambda),
y: this.r * cos(radphi) * sin(radlambda),
z: this.r * sin(radphi)
});
};
SphericalCoord.prototype.toGeodetic = function(ellipsoid){
return this.toCartesian().toGeodetic(ellipsoid);
};
SphericalCoord.prototype.getHarmonicVariables = function(ellipsoid, n_max){
var m, n;
var cos_lambda = Math.cos(Math.PI/180 * this.lambda);
var sin_lambda = Math.sin(Math.PI/180 * this.lambda);
var cos_mlambda = [1.0, cos_lambda];
var sin_mlambda = [0.0, sin_lambda];
var relative_radius_power = [
(ellipsoid.re/this.r) * (ellipsoid.re/this.r)
];
for(n = 1; n <= n_max; n++){
relative_radius_power[n] = relative_radius_power[n-1] * (ellipsoid.re/this.r);
}
for(m = 2; m <= n_max; m++){
cos_mlambda[m] = cos_mlambda[m-1]*cos_lambda - sin_mlambda[m-1]*sin_lambda;
sin_mlambda[m] = cos_mlambda[m-1]*sin_lambda + sin_mlambda[m-1]*cos_lambda;
}
return {
relative_radius_power: relative_radius_power,
cos_mlambda: cos_mlambda,
sin_mlambda: sin_mlambda
};
};
SphericalCoord.prototype.getLegendreFunction = function(n_max) {
return new LegendreFunction(this, n_max);
};
+17
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@@ -0,0 +1,17 @@
module.exports = Ellipsoid;
function Ellipsoid(options) {
options = options || {
a: 6378.137,
b: 6356.7523142,
fla: 1 / 298.257223563,
re: 6371.2
};
this.a = options.a; // semi-major axis
this.b = options.b; // semi-minor axis
this.fla = options.fla; // flattening
this.re = options.re; // mean radius
this.eps = Math.sqrt(1-(this.b*this.b)/(this.a*this.a)); // first eccentricity
this.epssq = this.eps*this.eps; // first eccentricity squared
}
+168
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module.exports = LegendreFunction;
function LegendreFunction(coord_spherical, n_max){
var sin_phi = Math.sin(Math.PI/180 * coord_spherical.phig);
var result;
if(n_max <= 16 || (1 - Math.abs(sin_phi)) < 1e-10){
result = PcupLow(sin_phi, n_max);
} else {
result = PcupHigh(sin_phi, n_max);
}
this.pcup = result.pcup;
this.dpcup = result.dpcup;
}
function PcupLow(x, n_max){
var k, z, n, m, i, i1, i2, num_terms;
var schmidt_quasi_norm = [1.0];
var pcup = [1.0];
var dpcup = [0.0];
z = Math.sqrt((1-x)*(1+x));
num_terms = (n_max+1) * (n_max+2) / 2;
for(n = 1; n <= n_max; n++) {
for(m = 0; m <= n; m++) {
i = n*(n+1)/2 + m;
if(n == m){
i1 = (n-1)*n/2 + m - 1;
pcup[i] = z*pcup[i1];
dpcup[i] = z*dpcup[i1] + x*pcup[i1];
} else if (n == 1 && m == 0) {
i1 = (n-1)*n/2 + m;
pcup[i] = x*pcup[i1];
dpcup[i] = x*dpcup[i1] - z*pcup[i1];
} else if (n > 1 && n != m) {
i1 = (n-2)*(n-1)/2 + m;
i2 = (n-1)*n/2 + m;
if(m > n - 2){
pcup[i] = x*pcup[i2];
dpcup[i] = x*dpcup[i2] - z*pcup[i2];
} else {
k = ((n-1)*(n-1) - m*m) / ((2*n-1)*(2*n-3));
pcup[i] = x*pcup[i2] - k*pcup[i1];
dpcup[i] = x*dpcup[i2] - z*pcup[i2] - k*dpcup[i1];
}
}
}
}
for(n = 1; n <= n_max; n++) {
i = n*(n+1)/2;
i1 = (n-1)*n/2;
schmidt_quasi_norm[i] = schmidt_quasi_norm[i1] * (2*n-1) / n;
for(m = 1; m <= n; m++){
i = n*(n+1)/2 + m;
i1 = n*(n+1)/2 + m - 1;
schmidt_quasi_norm[i] = schmidt_quasi_norm[i1] * Math.sqrt(((n - m + 1) * (m == 1 ? 2 : 1)) / (n + m));
}
}
for(n = 1; n <= n_max; n++) {
for(m = 0; m <= n; m++) {
i = n*(n+1)/2+m;
pcup[i] *= schmidt_quasi_norm[i];
dpcup[i] *= -schmidt_quasi_norm[i];
}
}
return {
pcup: pcup,
dpcup: dpcup
};
}
function PcupHigh(x, n_max){
if(Math.abs(x) == 1.0){
throw new Error("Error in PcupHigh: derivative cannot be calculated at poles");
}
var n, m, k;
var num_terms = (n_max + 1) * (n_max + 2)/2;
var f1 = [];
var f2 = [];
var pre_sqr = [];
var scalef = 1.0e-280;
for(n = 0; n <= 2*n_max + 1; ++n){
pre_sqr[n] = Math.sqrt(n);
}
k = 2;
for(n = 0; n <= n_max; n++){
k++;
f1[k] = (2*n - 1) / n;
f2[k] = (n - 1) / n;
for(m = 1; m <= n - 2; m++){
k++;
f1[k] = (2*n - 1) / pre_sqr[n+m] / pre_sqr[n-m];
f2[k] = pre_sqr[n-m-1] * pre_sqr[n+m-1] / pre_sqr[n+m] / pre_sqr[n-m];
}
k += 2;
}
var z = Math.sqrt((1-x)*(1+x));
var plm;
var pm1 = x;
var pm2 = 1;
var pcup = [1.0, pm1];
var dpcup = [0.0, z];
if(n_max == 0){
throw new Error("Error in PcupHigh: n_max must be greater than 0");
}
k = 1;
for(n = 2; n <= n_max; n++)
{
k = k + n;
plm = f1[k] * x * pm1 - f2[k] * pm2;
pcup[k] = plm;
dpcup[k] = n * (pm1 - x * plm) / z;
pm2 = pm1;
pm1 = plm;
}
var pmm = pre_sqr[2] * scalef;
var rescalem = 1/scalef;
var kstart = 0;
for(var m = 1; m <= n_max - 1; ++m){
rescalem *= z;
//calculate pcup(m,m)
kstart = kstart + m + 1;
pmm = pmm * pre_sqr[2*m+1] / pre_sqr[2*m];
pcup[kstart] = pmm * rescalem / pre_sqr[2*m+1];
dpcup[kstart] = -( m*x*pcup[kstart] /z );
pm2 = pmm / pre_sqr[2*m + 1];
//calculate pcup(m+1,m)
k = kstart + m + 1;
pm1 = x * pre_sqr[2*m+1] * pm2;
pcup[k] = pm1*rescalem;
dpcup[k] = (pm2*rescalem *pre_sqr[2*m+1] - x*(m+1)*pcup[k]) / z;
//calculate pcup(n,m)
for(n = m + 2; n <= n_max; ++n){
k = k + n;
plm = x*f1[k]*pm1 - f2[k]*pm2;
pcup[k] = plm*rescalem;
dpcup[k] = (pre_sqr[n+m]*pre_sqr[n-m]*pm1*rescalem - n*x*pcup[k]) / z;
pm2 = pm1;
pm1 = plm;
}
}
//calculate pcup(n_max,n_max)
rescalem = rescalem*z;
kstart = kstart + m + 1;
pmm = pmm / pre_sqr[2*n_max];
pcup[kstart] = pmm * rescalem;
dpcup[kstart] = -n_max * x * pcup[kstart] / z;
return {
pcup: pcup,
dpcup: dpcup
};
}
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module.exports = MagneticElements;
function MagneticElements(options){
this.x = options.x;
this.y = options.y;
this.z = options.z;
this.h = options.h;
this.f = options.f;
this.incl = options.incl;
this.decl = options.decl;
this.gv = options.gv;
this.xdot = options.xdot;
this.ydot = options.ydot;
this.zdot = options.zdot;
this.hdot = options.hdot;
this.fdot = options.fdot;
this.incldot = options.incldot;
this.decldot = options.decldot;
this.gvdot = options.gvdot;
}
MagneticElements.prototype.clone = function(){
return new MagneticElements(this);
};
MagneticElements.prototype.scale = function(factor){
return new MagneticElements({
x : this.x * factor,
y : this.y * factor,
z : this.z * factor,
h : this.h * factor,
f : this.f * factor,
incl : this.incl * factor,
decl : this.decl * factor,
gv : this.gv * factor,
xdot : this.xdot * factor,
ydot : this.ydot * factor,
zdot : this.zdot * factor,
hdot : this.hdot * factor,
fdot : this.fdot * factor,
incldot : this.incldot * factor,
decldot : this.decldot * factor,
gvdot : this.gvdot * factor
});
};
MagneticElements.prototype.subtract = function(subtrahend){
return new MagneticElements({
x : this.x - subtrahend.x,
y : this.y - subtrahend.y,
z : this.z - subtrahend.z,
h : this.h - subtrahend.h,
f : this.f - subtrahend.f,
incl : this.incl - subtrahend.incl,
decl : this.decl - subtrahend.decl,
gv : this.gv - subtrahend.gv,
xdot : this.xdot - subtrahend.xdot,
ydot : this.ydot - subtrahend.ydot,
zdot : this.zdot - subtrahend.zdot,
hdot : this.hdot - subtrahend.hdot,
fdot : this.fdot - subtrahend.fdot,
incldot : this.incldot - subtrahend.incldot,
decldot : this.decldot - subtrahend.decldot,
gvdot : this.gvdot - subtrahend.gvdot
});
};
MagneticElements.fromGeoMagneticVector = function(magnetic_vector){
var bx = magnetic_vector.bx;
var by = magnetic_vector.by;
var bz = magnetic_vector.bz;
var h = Math.sqrt(bx*bx + by*by);
return new MagneticElements({
x: bx,
y: by,
z: bz,
h: h,
f: Math.sqrt(h*h + bz*bz),
decl: 180/Math.PI * Math.atan2(by, bx),
incl: 180/Math.PI * Math.atan2(bz, h)
});
};
MagneticElements.fromSecularVariationVector = function(magnetic_variation){
var bx = magnetic_variation.bx;
var by = magnetic_variation.by;
var bz = magnetic_variation.bz;
return new MagneticElements({
xdot: bx,
ydot: by,
zdot: bz,
hdot: (this.x*bx + this.y*by) / this.h,
fdot: (this.x*bx + this.y*by + this.z*bz) / this.f,
decldot: 180/Math.PI * (this.x*this.ydot - this.y*this.xdot) / (this.h*this.h),
incldot: 180/Math.PI * (this.h*this.zdot - this.z*this.hdot) / (this.f*this.f),
gvdot: this.decldot
});
};
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module.exports = MagneticVector;
function MagneticVector(options){
this.bx = options.bx;
this.by = options.by;
this.bz = options.bz;
}
MagneticVector.prototype.rotate = function(coord_spherical, coord_geodetic) {
var psi = Math.PI/180 * (coord_spherical.phig - coord_geodetic.phi);
return new MagneticVector({
bz: this.bx*Math.sin(psi) + this.bz*Math.cos(psi),
bx: this.bx*Math.cos(psi) - this.bz*Math.sin(psi),
by: this.by
});
};
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var GeodeticCoord = require('./coords/geodetic.js');
var MagneticElements = require('./magnetic_elements.js');
var MagneticVector = require('./magnetic_vector.js');
module.exports = Model;
function Model(options){
this.epoch = options.epoch;
this.start_date = new Date(options.start_date);
this.end_date = new Date(options.end_date);
this.name = options.name || "";
this.main_field_coeff_g = options.main_field_coeff_g || [0];
this.main_field_coeff_h = options.main_field_coeff_h || [0];
this.secular_var_coeff_g = options.secular_var_coeff_g || [0];
this.secular_var_coeff_h = options.secular_var_coeff_h || [0];
this.n_max = options.n_max || 0;
this.n_max_sec_var = options.n_max_sec_var || 0;
this.num_terms = this.n_max*(this.n_max+1)/2 + this.n_max;
}
Model.prototype.getTimedModel = function(date, allowOutOfBoundsModel = false){
var year_int = date.getUTCFullYear();
var fractional_year = (date.valueOf() - Date.UTC(year_int)) / (1000*3600*24*365);
var year = year_int + fractional_year;
var dyear = year - this.epoch;
if(date < this.start_date || date > this.end_date){
if(allowOutOfBoundsModel) {
console.error("Model is only valid from "+this.start_date.toDateString()+" to "+this.end_date.toDateString());
} else {
throw new Error("Model is only valid from "+this.start_date.toDateString()+" to "+this.end_date.toDateString());
}
}
var model = new Model({
epoch: this.epoch,
n_max: this.n_max,
n_max_sec_var: this.n_max_sec_var,
name: this.name,
start_date: this.start_date,
end_date: this.end_date,
});
var a = model.n_max_sec_var;
var b = a*(a + 1)/2 + a;
for(var n = 1; n <= this.n_max; n++){
for(var m = 0; m <= n; m++){
var i = n * (n + 1)/2 + m;
var hnm = this.main_field_coeff_h[i];
var gnm = this.main_field_coeff_g[i];
var dhnm = this.secular_var_coeff_h[i];
var dgnm = this.secular_var_coeff_g[i];
if(i <= b){
model.main_field_coeff_h[i] = hnm + dyear*dhnm;
model.main_field_coeff_g[i] = gnm + dyear*dgnm;
model.secular_var_coeff_h[i] = dhnm;
model.secular_var_coeff_g[i] = dgnm;
} else {
model.main_field_coeff_h[i] = hnm;
model.main_field_coeff_g[i] = gnm;
}
}
}
return model;
};
Model.prototype.getSummation = function(legendre, sph_variables, coord_spherical){
var bx = 0;
var by = 0;
var bz = 0;
var n, m, i, k;
var relative_radius_power = sph_variables.relative_radius_power;
var cos_mlambda = sph_variables.cos_mlambda;
var sin_mlambda = sph_variables.sin_mlambda;
var g = this.main_field_coeff_g;
var h = this.main_field_coeff_h;
for(n = 1; n <= this.n_max; n++){
for(m = 0; m <= n; m++){
i = n*(n+1)/2 + m;
bz -= relative_radius_power[n] *
(g[i]*cos_mlambda[m] + h[i]*sin_mlambda[m]) *
(n+1) * legendre.pcup[i];
by += relative_radius_power[n] *
(g[i]*sin_mlambda[m] - h[i]*cos_mlambda[m]) *
(m) * legendre.pcup[i];
bx -= relative_radius_power[n] *
(g[i]*cos_mlambda[m] + h[i]*sin_mlambda[m]) *
legendre.dpcup[i];
}
}
var cos_phi = Math.cos(Math.PI/180 * coord_spherical.phig);
if(Math.abs(cos_phi) > 1e-10){
by = by / cos_phi;
} else {
//special calculation around poles
by = 0;
var schmidt_quasi_norm1 = 1.0, schmidt_quasi_norm2, schmidt_quasi_norm3;
var pcup_s = [1];
var sin_phi = Math.sin(Math.PI/180 * coord_spherical.phig);
for(n = 1; n <= this.n_max; n++){
i = n*(n+1)/2 + 1;
schmidt_quasi_norm2 = schmidt_quasi_norm1 * (2*n-1) / n;
schmidt_quasi_norm3 = schmidt_quasi_norm2 * Math.sqrt(2*n/(n+1));
schmidt_quasi_norm1 = schmidt_quasi_norm2;
if(n == 1){
pcup_s[n] = pcup_s[n-1];
} else {
k = ((n-1)*(n-1) - 1) / ((2*n-1)*(2*n-3));
pcup_s[n] = sin_phi * pcup_s[n-1] - k*pcup_s[n-2];
}
by += relative_radius_power[n] *
(g[i]*sin_mlambda[1] - h[i]*cos_mlambda[1]) *
pcup_s[n] * schmidt_quasi_norm3;
}
}
return new MagneticVector({
bx: bx, by: by, bz: bz
});
};
Model.prototype.point = function(coords) {
// Extract altitude if provided, otherwise default to 0
var altitude = (coords.length > 2 && typeof coords[2] === 'number') ? coords[2] : 0;
var coord_geodetic = new GeodeticCoord({
lat: coords[0],
lon: coords[1],
height_above_ellipsoid: altitude
});
var coord_spherical = coord_geodetic.toSpherical();
var legendre = coord_spherical.getLegendreFunction(this.n_max);
var harmonic_variables = coord_spherical.getHarmonicVariables(coord_geodetic.ellipsoid, this.n_max);
var magnetic_vector_sph = this.getSummation(legendre, harmonic_variables, coord_spherical);
var magnetic_vector_geo = magnetic_vector_sph.rotate(coord_spherical, coord_geodetic);
return MagneticElements.fromGeoMagneticVector(magnetic_vector_geo);
};
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module.exports = function(str){
var result = {
main_field_coeff_g: [0],
main_field_coeff_h: [0],
secular_var_coeff_g: [0],
secular_var_coeff_h: [0],
n_max: 0,
n_max_sec_var: 0
};
var lines = str.split(/\r?\n/);
for(var i = 0; i < lines.length; i++) {
var line = lines[i];
var vals = line.match(/\S+/g);
if(!vals) continue;
if(vals.length === 3){
result.epoch = parseFloat(vals[0]);
result.name = vals[1];
result.start_date = new Date(vals[2]);
result.end_date = new Date(vals[2]);
var year = result.start_date.getFullYear();
result.end_date.setFullYear(year + 5);
}
if(vals.length === 6){
var n = parseInt(vals[0]);
var m = parseInt(vals[1]);
if(m <= n) {
var i = (n*(n+1)/2+m);
result.main_field_coeff_g[i] = parseFloat(vals[2]);
result.main_field_coeff_h[i] = parseFloat(vals[3]);
result.secular_var_coeff_g[i] = parseFloat(vals[4]);
result.secular_var_coeff_h[i] = parseFloat(vals[5]);
}
if(n > result.n_max){
result.n_max = n;
result.n_max_sec_var = n;
}
}
}
return result;
};
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{
"name": "geomagnetism",
"types": "geomagnetism.d.ts",
"version": "0.2.0",
"description": "Computes geomagnetic field information",
"main": "index.js",
"scripts": {
"test": "mocha test",
"test-ci": "mocha -R tap"
},
"repository": {
"type": "git",
"url": "https://github.com/naturalatlas/geomagnetism.git"
},
"keywords": [
"geomag",
"geomagnetic",
"magnetic",
"field",
"north",
"declination",
"wmm"
],
"devDependencies": {
"mocha": "~5.x",
"chai": "~4.2.0"
},
"author": "Brandon Reavis",
"license": "Apache-2.0",
"bugs": {
"url": "https://github.com/naturalatlas/geomagnetism/issues"
},
"homepage": "https://github.com/naturalatlas/geomagnetism"
}
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var geomagnetism = require('../index.js');
var assert = require('chai').assert;
var fs = require('fs');
var tolerances = {
incl: 0.01, //deg
decl: 0.01, //deg
x: 5, //nT
y: 5, //nT
z: 5, //nT
h: 5, //nT
f: 5 //nT
};
function loadTestValues(){
var str = fs.readFileSync(__dirname + '/values.csv', {encoding: 'utf8'});
var lines = str.split(/\r?\n/);
var header = lines[0].split(',');
var values = [];
for(var i = 1; i < lines.length; i++){
var l = lines[i].split(',');
var v = {};
for(var j = 0; j < header.length; j++){
v[header[j]] = parseFloat(l[j]);
}
values.push(v);
}
return values;
}
function getModel(test){
var t0, t1;
var year = test.date;
var year_int = Math.floor(year);
var year_fpart = year - year_int;
var dms = 1000*3600*24*365*year_fpart;
t0 = new Date(year_int, 0, 1);
t1 = new Date(t0.valueOf() + dms);
return geomagnetism.model(t1);
}
var values = loadTestValues();
describe("model", function(){
describe("point()", function(){
it("should return expected values", function(){
values.forEach(function(test){
var model = getModel(test);
var info = model.point([test.lat, test.lon, test.alt]);
assert.closeTo(info.incl, test.incl, tolerances.incl, 'inclination ' + test.date);
assert.closeTo(info.decl, test.decl, tolerances.decl, 'declination ' + test.date);
assert.closeTo(info.x, test.x, tolerances.x, 'x');
assert.closeTo(info.y, test.y, tolerances.y, 'y');
assert.closeTo(info.z, test.z, tolerances.z, 'z');
assert.closeTo(info.h, test.h, tolerances.h, 'h');
assert.closeTo(info.f, test.f, tolerances.f, 'f');
});
});
it("should return value for current date", function(){
var date = new Date();
geomagnetism.model(date).point([44.53461, -109.05572]);
});
it("should return value for current date + 1 year", function(){
var date = new Date();
date.setFullYear(date.getFullYear() + 1);
geomagnetism.model(date).point([44.53461, -109.05572]);
});
});
describe("getTimedModel()", function(){
it("should throw error if date is outside of valid range and allowOutOfBoundsModel is false", function(){
assert.throws(function(){
geomagnetism.model(new Date("1/1/1999"));
}, Error);
});
it("should log error if date is outside of valid range below and allowOutOfBoundsModel is true", function(){
var model = geomagnetism.model(new Date("1/1/1999"), { allowOutOfBoundsModel: true });
assert.equal(model.start_date.getFullYear(), 2014);
});
it("should log error if date is outside of valid range above and allowOutOfBoundsModel is true", function(){
var model = geomagnetism.model(new Date("1/1/2030"), { allowOutOfBoundsModel: true });
assert.equal(model.start_date.getFullYear(), 2024);
});
it("should get a different model for a different date", function(){
var pt = [44.53461, -109.05572];
var model0 = geomagnetism.model();
var model1 = geomagnetism.model(new Date("3/22/2018"));
var decl0 = model0.point(pt).decl;
var decl1 = model1.point(pt).decl;
assert.notEqual(model0, model1);
assert(Math.abs(decl1 - decl0) > 0.001, 'declination should be different');
});
});
});
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date,alt,lat,lon,x,y,z,h,f,incl,decl,gv
2015.0,0,80,0,6627.1,-445.9,54432.3,6642.1,54836.0,83.04,-3.85,-3.85
2015.0,0,0,120,39518.2,392.9,-11252.4,39520.2,41090.9,-15.89,0.57,0.57
2015.0,0,-80,240,5797.3,15761.1,-52919.1,16793.5,55519.8,-72.39,69.81,309.81
2015.0,100,80,0,6314.3,-471.6,52269.8,6331.9,52652.0,83.09,-4.27,-4.27
2015.0,100,0,120,37535.6,364.4,-10773.4,37537.3,39052.7,-16.01,0.56,0.56
2015.0,100,-80,240,5613.1,14791.5,-50378.6,15820.7,52804.4,-72.57,69.22,309.22
2017.5,0,80,0,6599.4,-317.1,54459.2,6607.0,54858.5,83.08,-2.75,-2.75
2017.5,0,0,120,39571.4,222.5,-11030.1,39572.0,41080.5,-15.57,0.32,0.32
2017.5,0,-80,240,5873.8,15781.4,-52687.9,16839.1,55313.4,-72.28,69.58,309.58
2017.5,100,80,0,6290.5,-348.5,52292.7,6300.1,52670.9,83.13,-3.17,-3.17
2017.5,100,0,120,37585.5,209.5,-10564.2,37586.1,39042.5,-15.70,0.32,0.32
2017.5,100,-80,240,5683.5,14808.8,-50163.0,15862.0,52611.1,-72.45,69.00,309.00
2015.21096,0,44.5364,-109.0461,18702.1,3663.7,50812.2,19057.5,54268.5,69.44104,11.08386,0
2020.0,28,89,-121,-575.7,-1396.0,56082.3,1510.0,56102.7,88.46,-112.41,0
2020.0,48,80,-96,1518.0,-1160.5,55671.9,1910.8,55704.7,88.03,-37.40,0
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2028.000000,86,-85,-79,12713.115116,11085.480728,-46988.258092,16867.459172,49924.018042,-70.25,41.09,0
2028.000000,30,-36,-64,17341.333537,-1411.102609,-14639.967305,17398.651081,22738.551012,-40.08,-4.65,0
2028.000000,75,79,125,2447.595900,-823.235047,57308.751756,2582.332595,57366.902212,87.42,-18.59,0
2028.000000,21,6,-32,27567.094260,-7045.034525,-4352.046687,28453.070088,28783.980055,-8.70,-14.34,0
2028.000000,1,-76,-75,16993.742946,9761.147808,-42479.847250,19597.635210,46782.525885,-65.23,29.87,0
2028.000000,45,-46,-41,13609.973828,-2812.623735,-19816.196211,13897.562372,24203.798713,-54.96,-11.68,0
2028.000000,11,-22,-21,12430.606447,-5337.987778,-21373.837958,13528.270036,25295.356080,-57.67,-23.24,0
2028.500000,28,54,-120,14735.145798,4066.959949,52393.678137,15286.094495,54578.037650,73.74,15.43,0
2028.500000,68,-58,156,6944.959164,6159.591995,-62264.415929,9282.943032,62952.605366,-81.52,41.57,0
2028.500000,39,-65,-88,17946.905687,10131.662696,-35982.872979,20609.270068,41466.964689,-60.20,29.45,0
2028.500000,27,-23,81,24940.672257,-5883.907569,-41948.733657,25625.329284,49156.421313,-58.58,-13.27,0
2028.500000,11,34,0,29078.234597,798.434048,30945.577813,29089.194286,42471.284539,46.77,1.57,0
2028.500000,72,-62,65,6567.891205,-16150.440331,-44267.327811,17434.847799,47576.992646,-68.50,-67.87,0
2028.500000,55,86,70,901.741754,2192.139033,55926.154052,2370.361097,55976.363930,87.57,67.64,0
2028.500000,59,32,163,28217.104175,75.200106,26405.862611,28217.204381,38645.571587,43.10,0.15,0
2028.500000,65,48,148,23365.167010,-3931.047029,44177.553125,23693.546804,50130.233993,61.79,-9.55,0
2028.500000,95,30,28,29692.133298,2367.965026,29039.808439,29786.406936,41599.765773,44.27,4.56,0
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2029.000000,95,-70,42,10426.249753,-14920.796381,-38237.047006,18202.660480,42348.655378,-64.54,-55.06,0
2029.000000,50,87,-154,257.877420,-869.484879,55992.308183,906.920459,55999.652503,89.07,-73.48,0
2029.000000,58,32,19,29359.395781,2108.188210,30508.465542,29434.989012,42393.219362,46.03,4.11,0
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2029.500000,63,88,26,2041.140972,1511.567287,55286.620082,2539.900024,55344.931586,87.37,36.52,0
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1 date alt lat lon x y z h f incl decl gv
2 2015.0 0 80 0 6627.1 -445.9 54432.3 6642.1 54836.0 83.04 -3.85 -3.85
3 2015.0 0 0 120 39518.2 392.9 -11252.4 39520.2 41090.9 -15.89 0.57 0.57
4 2015.0 0 -80 240 5797.3 15761.1 -52919.1 16793.5 55519.8 -72.39 69.81 309.81
5 2015.0 100 80 0 6314.3 -471.6 52269.8 6331.9 52652.0 83.09 -4.27 -4.27
6 2015.0 100 0 120 37535.6 364.4 -10773.4 37537.3 39052.7 -16.01 0.56 0.56
7 2015.0 100 -80 240 5613.1 14791.5 -50378.6 15820.7 52804.4 -72.57 69.22 309.22
8 2017.5 0 80 0 6599.4 -317.1 54459.2 6607.0 54858.5 83.08 -2.75 -2.75
9 2017.5 0 0 120 39571.4 222.5 -11030.1 39572.0 41080.5 -15.57 0.32 0.32
10 2017.5 0 -80 240 5873.8 15781.4 -52687.9 16839.1 55313.4 -72.28 69.58 309.58
11 2017.5 100 80 0 6290.5 -348.5 52292.7 6300.1 52670.9 83.13 -3.17 -3.17
12 2017.5 100 0 120 37585.5 209.5 -10564.2 37586.1 39042.5 -15.70 0.32 0.32
13 2017.5 100 -80 240 5683.5 14808.8 -50163.0 15862.0 52611.1 -72.45 69.00 309.00
14 2015.21096 0 44.5364 -109.0461 18702.1 3663.7 50812.2 19057.5 54268.5 69.44104 11.08386 0
15 2020.0 28 89 -121 -575.7 -1396.0 56082.3 1510.0 56102.7 88.46 -112.41 0
16 2020.0 48 80 -96 1518.0 -1160.5 55671.9 1910.8 55704.7 88.03 -37.40 0
17 2020.0 54 82 87 1555.6 1941.4 56520.5 2487.8 56575.2 87.48 51.30 0
18 2020.0 65 43 93 24375.3 303.2 49691.4 24377.2 55348.7 63.87 0.71 0
19 2020.0 51 -33 109 21556.3 -2183.2 -52676.0 21666.6 56957.9 -67.64 -5.78 0
20 2020.0 39 -59 -8 14369.9 -4063.3 -24679.0 14933.4 28845.4 -58.82 -15.79 0
21 2020.0 3 -50 -103 19684.4 10512.2 -31883.6 22315.5 38917.2 -55.01 28.10 0
22 2020.0 94 -29 -110 23467.8 6650.9 -19320.7 24392.0 31116.9 -38.38 15.82 0
23 2020.0 66 14 143 34916.8 70.2 8114.9 34916.9 35847.5 13.08 0.12 0
24 2020.0 18 0 21 29311.2 536.0 -14589.0 29316.1 32745.6 -26.46 1.05 0
25 2020.5 6 -36 -137 23948.6 8791.9 -32897.6 25511.4 41630.3 -52.21 20.16 0
26 2020.5 63 26 81 34737.7 259.2 30023.4 34738.7 45914.9 40.84 0.43 0
27 2020.5 69 38 -144 22647.3 5390.0 35831.9 23279.9 42730.3 56.99 13.39 0
28 2020.5 50 -70 -133 8943.1 13981.7 -51628.5 16597.2 54230.7 -72.18 57.40 0
29 2020.5 8 -52 -75 19571.7 5387.5 -23769.0 20299.7 31257.7 -49.50 15.39 0
30 2020.5 8 -66 17 15247.0 -9734.8 -31062.0 18089.7 35945.6 -59.78 -32.56 0
31 2020.5 22 -37 140 21429.0 3451.3 -55415.6 21705.2 59514.7 -68.61 9.15 0
32 2020.5 40 -12 -129 28773.9 5503.9 -8221.8 29295.6 30427.4 -15.68 10.83 0
33 2020.5 44 33 -118 23414.3 4748.3 38184.5 23890.9 45042.6 57.97 11.46 0
34 2020.5 50 -81 -67 16087.9 8788.9 -44780.8 18332.1 48387.8 -67.74 28.65 0
35 2021.0 74 -57 3 13228.0 -5423.3 -23859.2 14296.6 27814.7 -59.07 -22.29 0
36 2021.0 46 -24 -122 26037.0 6501.8 -18297.4 26836.5 32480.6 -34.29 14.02 0
37 2021.0 69 23 63 34450.4 646.9 24869.2 34456.5 42493.9 35.82 1.08 0
38 2021.0 33 -3 -147 30690.1 5265.7 -1277.4 31138.6 31164.8 -2.35 9.74 0
39 2021.0 47 -72 -22 18352.8 -1946.6 -33665.0 18455.7 38392.0 -61.27 -6.05 0
40 2021.0 62 -14 99 33213.0 -990.3 -33354.0 33227.7 47080.5 -45.11 -1.71 0
41 2021.0 83 86 -46 2408.8 -1796.2 54184.7 3004.8 54268.0 86.83 -36.71 0
42 2021.0 82 -64 87 2249.5 -13907.0 -53526.9 14087.8 55349.8 -75.25 -80.81 0
43 2021.0 34 -19 43 19327.6 -4933.5 -25969.5 19947.3 32746.2 -52.47 -14.32 0
44 2021.0 56 -81 40 9198.0 -15323.4 -45453.8 17872.0 48841.2 -68.54 -59.03 0
45 2021.5 14 0 80 39246.6 -2338.9 -12258.0 39316.2 41182.8 -17.32 -3.41 0
46 2021.5 12 -82 -68 15995.1 9368.5 -46308.7 18536.8 49880.9 -68.18 30.36 0
47 2021.5 44 -46 -42 14159.0 -2889.8 -19762.2 14450.9 24482.1 -53.82 -11.54 0
48 2021.5 43 17 52 35896.1 773.7 15885.6 35904.4 39261.7 23.87 1.23 0
49 2021.5 64 10 78 39294.0 -1172.2 5088.1 39311.5 39639.4 7.37 -1.71 0
50 2021.5 12 33 -145 24301.2 5327.4 32429.3 24878.3 40872.8 52.51 12.36 0
51 2021.5 12 -79 115 -9403.6 -8972.3 -58271.0 12997.3 59702.9 -77.43 -136.34 0
52 2021.5 14 -33 -114 23592.3 7712.3 -24163.1 24820.9 34640.0 -44.23 18.10 0
53 2021.5 19 29 66 32618.0 1215.2 33763.7 32640.6 46961.7 45.97 2.13 0
54 2021.5 86 -11 167 32676.0 5828.1 -20299.1 33191.7 38906.8 -31.45 10.11 0
55 2022.0 37 -66 -5 16404.3 -5011.2 -28849.5 17152.6 33563.5 -59.27 -16.99 0
56 2022.0 67 72 -115 4532.7 1254.7 55923.4 4703.2 56120.8 85.19 15.47 0
57 2022.0 44 22 174 28671.0 3294.9 17967.2 28859.7 33995.6 31.91 6.56 0
58 2022.0 54 54 178 20624.8 514.8 45076.8 20631.2 49573.8 65.41 1.43 0
59 2022.0 57 -43 50 11344.6 -12349.5 -32850.3 16769.3 36883.0 -62.96 -47.43 0
60 2022.0 44 -43 -111 20646.1 9330.1 -29747.5 22656.4 37392.8 -52.71 24.32 0
61 2022.0 12 -63 178 6292.0 9718.1 -61429.1 11577.2 62510.5 -79.33 57.08 0
62 2022.0 38 27 -169 25896.5 3991.3 24097.4 26202.3 35598.4 42.60 8.76 0
63 2022.0 61 59 -77 10098.3 -3208.9 54735.3 10595.8 55751.4 79.04 -17.63 0
64 2022.0 67 -47 -32 12663.7 -3178.2 -20600.9 13056.5 24389.9 -57.63 -14.09 0
65 2022.5 8 62 53 12336.1 4236.6 54498.1 13043.3 56037.2 76.54 18.95 0
66 2022.5 77 -68 -7 16604.7 -4741.2 -29908.6 17268.3 34535.8 -60.00 -15.94 0
67 2022.5 98 -5 159 33613.6 4601.1 -14426.9 33927.0 36867.1 -23.04 7.79 0
68 2022.5 34 -29 -107 23739.9 6662.3 -19023.5 24657.0 31142.6 -37.65 15.68 0
69 2022.5 60 27 65 32938.8 1025.8 30561.3 32954.8 44944.6 42.84 1.78 0
70 2022.5 73 -72 95 -2661.0 -13095.2 -55423.4 13362.8 57011.5 -76.44 -101.49 0
71 2022.5 96 -46 -85 19136.4 6358.2 -21915.4 20165.1 29781.1 -47.38 18.38 0
72 2022.5 0 -13 -59 21797.3 -6520.6 -5425.9 22751.7 23389.8 -13.41 -16.65 0
73 2022.5 16 66 -178 13804.5 463.2 54055.4 13812.2 55792.1 75.67 1.92 0
74 2022.5 72 -87 38 7132.3 -15063.2 -48550.5 16666.4 51331.5 -71.05 -64.66 0
75 2023.0 49 20 167 30099.4 2737.4 15301.2 30223.6 33876.1 26.85 5.20 0
76 2023.0 71 5 -13 28217.7 -3592.6 -8905.8 28445.5 29807.1 -17.38 -7.26 0
77 2023.0 95 14 65 36804.1 -356.8 11616.0 36805.8 38595.3 17.52 -0.56 0
78 2023.0 86 -85 -79 12598.0 11248.0 -47331.2 16888.7 50254.0 -70.36 41.76 0
79 2023.0 30 -36 -64 17694.8 -1198.1 -14566.5 17735.3 22950.5 -39.40 -3.87 0
80 2023.0 75 79 125 2605.8 -676.0 57085.9 2692.1 57149.3 87.30 -14.54 0
81 2023.0 21 6 -32 27630.5 -7515.0 -3646.9 28634.3 28865.6 -7.26 -15.22 0
82 2023.0 1 -76 -75 16998.9 9958.1 -42873.8 19700.9 47183.6 -65.32 30.36 0
83 2023.0 45 -46 -41 13880.3 -2936.1 -19853.0 14187.4 24401.3 -54.45 -11.94 0
84 2023.0 11 -22 -21 12752.8 -5710.4 -21372.4 13972.9 25534.7 -56.82 -24.12 0
85 2023.5 28 54 -120 14556.6 4230.3 52945.6 15158.8 55072.9 74.02 16.20 0
86 2023.5 68 -58 156 7015.1 5987.8 -62459.5 9223.1 63136.8 -81.60 40.48 0
87 2023.5 39 -65 -88 18024.0 10347.2 -36415.6 20783.0 41928.8 -60.29 29.86 0
88 2023.5 27 -23 81 24811.0 -6176.1 -41759.2 25568.2 48965.0 -58.52 -13.98 0
89 2023.5 11 34 0 29033.7 545.3 30807.0 29038.8 42335.9 46.69 1.08 0
90 2023.5 72 -62 65 6836.8 -16092.9 -44111.8 17485.0 47450.8 -68.38 -66.98 0
91 2023.5 55 86 70 1168.7 2124.7 55750.6 2424.9 55803.4 87.51 61.19 0
92 2023.5 59 32 163 28170.0 176.0 26318.3 28170.6 38551.7 43.05 0.36 0
93 2023.5 65 48 148 23356.8 -3861.2 43968.0 23673.8 49936.3 61.70 -9.39 0
94 2023.5 95 30 28 29663.3 2331.2 28857.6 29754.7 41450.1 44.12 4.49 0
95 2024.0 95 -60 -59 18099.3 2821.2 -26193.2 18317.9 31962.9 -55.03 8.86 0
96 2024.0 95 -70 42 10615.3 -14769.3 -38293.4 18188.3 42393.4 -64.59 -54.29 0
97 2024.0 50 87 -154 80.9 -592.4 55904.6 597.9 55907.8 89.39 -82.22 0
98 2024.0 58 32 19 29331.6 2019.5 30329.8 29401.0 42241.2 45.89 3.94 0
99 2024.0 57 34 -13 28158.7 -1290.8 29015.5 28188.3 40453.4 45.83 -2.62 0
100 2024.0 38 -76 49 8218.0 -16491.7 -44260.7 18425.8 47942.9 -67.40 -63.51 0
101 2024.0 49 -50 -179 15431.4 9482.7 -53818.3 18112.2 56784.4 -71.40 31.57 0
102 2024.0 90 -55 -171 12918.7 10118.6 -53373.5 16409.7 55839.2 -72.91 38.07 0
103 2024.0 41 42 -19 24317.3 -2127.0 36981.3 24410.2 44311.1 56.57 -5.00 0
104 2024.0 19 46 -22 22384.7 -2590.4 40713.3 22534.0 46533.4 61.04 -6.60 0
105 2024.5 31 13 -132 28046.9 4548.8 17417.2 28413.4 33326.9 31.51 9.21 0
106 2024.5 93 -2 158 33858.1 4253.5 -10940.3 34124.3 35835.1 -17.78 7.16 0
107 2024.5 51 -76 40 10459.6 -15294.7 -42141.5 18529.2 46035.2 -66.27 -55.63 0
108 2024.5 64 22 -132 25808.9 4792.5 25239.1 26250.1 36415.3 43.88 10.52 0
109 2024.5 26 -65 55 8607.6 -16603.5 -41366.0 18702.1 45397.3 -65.67 -62.60 0
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112 2024.5 63 88 26 2189.6 1254.6 55156.1 2523.6 55213.8 87.38 29.81 0
113 2024.5 33 17 5 34060.9 362.9 8230.6 34062.9 35043.1 13.58 0.61 0
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