# How to compute satellite coordinates (lat,long) given antenna's coordinates, angles and satellite height

Given an Earth station (antenna) coordinates (in lat,long) ant its Elevation (El) and Azimuth (Az), how to compute the satellite coordinates (lat,long), known its height?

For simplification purposes, the Earth can be considered as an sphere.

So its given:

Earth Radius = 6371000 meters
Satellite Height, in meters (perpendicular to the Earth's)

Station lat, long (as parameters)
Station height (0 = Zero, for simplification purposes)
Station Elevation (angle, radius or degrees)
Station Azimuth (angle, radius or degrees)


In summary: I'm trying to calculate satellite's coordinates projected on celestial sphere. I.e. it's current ground track position from the horizontal coordinate system values and the position of the observation.

The problem can be shown in this two figures:

• If I try to use kepler's Law, I get some strange results, due the quadrant changing in some situations... Commented Oct 23, 2014 at 15:24
• Do you mean the satellite's altitude and azimuth?
– user21
Commented Oct 26, 2014 at 6:37
• No. Its Latitude and Longitude. I have the altitude (given by the satellite spce) and azimuth (from Antenna) Commented Nov 3, 2014 at 16:50
• OK, so you're trying to compute the point on Earth that is directly below the satellite? In other words, the point on Earth that intersects the line between the satellite and the center of the Earth?
– user21
Commented Nov 3, 2014 at 16:52
• It is what I'm looking for. Commented Nov 3, 2014 at 16:53