If the moon is observed at 30 degrees azimuth seen from -say meridian 77 in New York- Is the moon said to be also at 30 degrees azimuth at meridian 77 for an observer in Lima ?

 

Sorry, not a subject of my expertise.

No azimuth is a property of both the moon's position and the position of the observer.

It is not a property of either the observer or the object alone but a combiantion of the two.

It is the angle between the position of something and true North, or if you had aligned your theodolite telescope to true North it is the angle you would have to swing through to point at the object.

 

I note you have another thread about Field Astronomy terms but I will try to answer them here.

 

There are two axis passing through the earthly and celestial spheres.

 

One is the axis ot rotation and it passes from North pole to South Pole, through the centre of the Earth and Celestial sphere, which have the same centre and NS axis.

 

The other is a plumb line from the observer on the Earth's surface to the centre of the earth.

If this line is extended to the celestial sphere it meets that sphere in the Zenith and Nadir

 

So the zenith and nadir are properties of the observer alone, they are not properties of the observed object.

 

A plane throught he centre of the earth at right angles to this axis is the horizontal plae for the observer.

 

A theodolite measures the angle from this horizontal plane to the object in the sky ie on the celestial sphre as the altitude.

 

The terms you were seeking for the elliptical path taken by objects on the celestial sphere are upper and lower transit or culmination for the highest and lowest altitudes.

 

The left and right ends of the ellipse are called elongation.

 

We can find some pictures if you wish.