CELESTIAL NAVIGATION

You are on the Earth on the unknown location at night with good seeing. This means you see all the stars over your horizon clearly.

You have a good angle measuring device (e.g., a sextant), a star catalogue, and a calculator. You know the date and the time precisely. You spot three stars well separated from each other.

Write a report on how to find your location (latitude and longitude) on the Earth with the following assumptions:

1. 1) Earth is perfectly spherical. Actually it has a very complex shape, but can be approximated with geoid or oblate spheroid. Here, you will assume that it is a perfect sphere.

2. 2) No atmospheric refraction. Actually when you observe a star other than in zenith direction, due to the atmospheric refraction the light coming from the star changes its direction and the deviation from the actual value should be taken into consideration.

3. 3) You measure the elevation angles (altitude) of the three known stars accurately. Known means that you can find their Right Ascension and Declination information from the Star Catalogue.

TASK: By using, the date (Year, Month, Day), the time, (Hour, Minute, Second), the Elevation angles of three known stars (assuming all have been measured at the same time) information, prepare a Matlab program to give the observers location (latitude and longitude). And prepare a report on how your algorithm works.