  The Cosmological Advanced Survey Telescope for Optical and ultraviolet
Research (CASTOR) is a proposed Canadian-led 1m-class space telescope that will
carry out ultraviolet and blue-optical wide-field imaging, spectroscopy, and
photometry. CASTOR will provide an essential bridge in the post-Hubble era,
preventing a protracted UV-optical gap in space astronomy and enabling an
enormous range of discovery opportunities from the solar system to the nature
of the Cosmos, in conjunction with the other great wide-field observatories of
the next decade (e.g., Euclid, Roman, Vera Rubin). FORECASTOR (Finding Optics
Requirements and Exposure times for CASTOR) will supply a coordinated suite of
mission-planning tools that will serve as the one-stop shop for proposal
preparation, data reduction, and analysis for the CASTOR mission. We present
the first of these tools: a pixel-based, user-friendly, extensible,
multi-mission exposure time calculator (ETC) built in Python, including a
modern browser-based graphical user interface that updates in real time. We
then provide several illustrative examples of FORECASTOR's use that advance the
design of planned legacy surveys for the CASTOR mission: a search for the most
massive white dwarfs in the Magellanic Clouds; a study of the frequency of
flaring activity in M stars, their distribution and impacts on habitability of
exoplanets; mapping the proper motions of faint stars in the Milky Way; wide
and deep galaxy surveys; and time-domain studies of active galactic nuclei.
