FORECASTOR -- I. Finding Optics Requirements and Exposure times for the Cosmological Advanced Survey Telescope for Optical and UV Research mission

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.