Navigation, Astronavigation, Positioning and Geodesy

Great Circle Navigation on Sphere and on WGS84 Ellipsoid
Course and Distance from Origin to Destination

This Javascript-program asks the Latitude and the Longitude of two Locations and calculates great circle distance, the initial course and the arrival course. In the Homepage of National Geospatial-Intelligence Agency is Nautical Calculator which calculates only on Sphere. Look "Nautical Calculators" , from there "Sailings".
My Javascript calculates by Vincent's iteration method on WGS84 Ellipsoid the distance on accuracy of one millimeter. Thus it is suitable also for geodetic calculations.

Great Circle Sailing on WGS84 Ellipsoid

Javascipt program asks the Origin, the Initial Course and the Distance. It calculates the Destination. Program uses by Vincenty's iteration method.

Great Circle Mathematics of Sphere

Vincenty's iteration method of Ellipsoid, accuracy of one millimeter

Loxodrome (Rhumb Line, Mercator) Sailing on WGS84 Ellipsoid

This Jacascript-program asks the latitude and the longitude of the two locations and calculates constant Course between locations.

Loxodrome (Rhumb Line, Mercator) on WGS84 Ellipsoid: Destination

Javascipt program asks the Origin, the Constant Course and the Distance. It calculates the Destination.

Mathematics of Loxodrome - Rhumb Line, Mercator Sailing

An Article Celestial Positioning using two stars (finnish language)

Celestial Positioning using Two Stars:

Javascript program asks the altides of two stars, their declinations and right ascentions, Greenwich Mean Time (UT) and assumed location of the measurement place. After that the program calculates the exact Latitude and Longitude using Newton's iteration method. The accuracy is as good as the accuracy of measurements. The best assumed location is obtained from dead reckoning, but it also can be very inexact. It is enough to know being somewhere on Atlantic or somewhere on Pacific Ocean...:-) The Newton Iteration method very quickly finds exact position corresponding measurements.

The Positioning using One Star's Altitude and Azimuth

This is not so exact as two star's altitude method.
It is suitable in emergency situations when only one star is visible.
First you can recognize the star from altitude and azimuth. After that you get exact declination and right ascention of the star from navigation or astronomical table.
Latitude and Longitude is calculated using Newton's iteration method.

Calculate Altitude, Azimuth, Hour Angle, etc of Star

Recognize Star by Azimuth and Altitude

Julian Day, Julian Date, UT, GMT, GMST, LST, GHA, LHA, RA, SHA?

Calculate Julian Day Number, Julian Date, Greenwich Mean Sidereal Time GMST, Hour Angle, Local Hour Angle LHA, Greenwich Hour Angle GHA. Calculate Sidereal Hour Angle from Right Ascention.

Calculation of Easter Sunday - Protestant, Catholic, Orthodox, Finnish Orthodox)

Juhani Kaukoranta

Last changes 14.10.2022