Explain briefly the difference between Geocentric, Geographic and Plane coordinates?

Question

(Just the main points, do not need too long)

Answer 1

Well, "geocentric" means "earth-centered," so for that, you could locate something below, on, or above the surface of the earth. Most likely you'd use a coordinate system with r for radius, angle theta (0-360) zeroed at the Greenwich Prime Meridian, and angle phi (0-180) zeroed at the North Pole.

"Geographic" is simply the latitude and longitude system used for locating points on the surface of the earth.

"Plane coordinates" are in x-y-z format (3 dimensions) or just x-y format in 2 dimensions.

Conversion between spherical and plane (Cartesian) coordinates uses these formulae:

z = r cos phi
rho = r sin phi (where rho is the projection of r onto the x-y plane)
y = rho sin theta = r sin phi sin theta
x = rho cos theta = r sin phi cos theta

It's not hard to get conversion formulae to and from geographic coordinates (latitude and longitude) also.