Q.What is the use of an erecting lens in a terrestrial telescope?

An astronomical telescope, used for viewing distant astronomical objects (stars, planets, the Moon), uses an objective of long focal length and large aperture together with an eyepiece of short focal length; the objective forms a real, inverted image of the distant object at its own second focal point (very nearly coinciding with the eyepiece's first focal point), and the eyepiece then acts as a simple microscope, magnifying that real image into a large final (still inverted) virtual image for the eye. In normal adjustment, the telescope's angular magnification is $m=f_o/f_e$, and its approximate overall length is $L\approx f_o+f_e$; since the final image is inverted, this design is perfectly acceptable for astronomy (where 'up' is arbitrary) …