  We study the fundamental limits of detection for astrophysical observations
in the far infrared. Understanding these fundamental limits is critical to the
planning and analysis of experiments in this region. We specifically
characterize the difficulties associated with observing in the 0.1-10 THz
(30-3000 \mu m) regime including extraterrestrial, atmospheric, and optical
emission. We present signal, noise, and integration time models for selected
terrestrial, aircraft, balloon, and space missions. While ground based
telescopes offer the great advantage of aperture size, and hence angular
resolution, they suffer from the relatively low transmission and high radiance
of the atmosphere, particularly for wavelengths less than 500 \mu m. Space
telescopes are the inverse; they are limited by a small aperture, while an
airborne telescope is constrained by both. Balloon-borne telescopes provide an
option over much of the band. A quantitative understanding of this is critical
in comparing the sensitivity of various experiments and in planning the next
generation of missions. As representative sources we use the luminous far-IR
dusty galaxies NGC 958 and Mrk 231, but the same formalism can be applied to
any source. In this paper we focus on continuum emission but a future paper
will focus on line emission.
