UV-SCOPE is a mission concept to determine the causes of atmospheric mass loss in exoplanets, investigate the mechanisms driving aerosol formation in hot Jupiters, and study the influence of the stellar environment on atmospheric evolution and habitability. As part of these investigations, the mission will generate a broad-purpose legacy database of time-domain ultraviolet (UV) spectra for nearly 200 stars and planets. The observatory consists of a 60 cm, f/10 telescope paired to a long-slit spectrograph, yielding simultaneous, almost continuous coverage between 1203 Å and 4000 Å, with resolutions ranging from 6000 to 240. The efficient instrument provides throughputs > 4% (far-UV; FUV) and > 15% (near-UV; NUV), comparable to HST/COS and much better than HST/STIS, over the same spectral range. A key design feature is the LiF prism, which serves as a dispersive element and provides high throughput even after accounting for radiation degradation. The use of two delta-doped Electron-Multiplying CCD detectors with UV-optimized, single-layer anti-reflection coatings provides high quantum efficiency and low detector noise. From the Earth-Sun second Lagrangian point, UV-SCOPE will continuously observe planetary transits and stellar variability in the full FUV-to-NUV range, with negligible astrophysical background. All these features make UV-SCOPE the ideal instrument to study exoplanetary atmospheres and the impact of host stars on their planets. UV-SCOPE was proposed to NASA as a Medium Explorer (MidEx) mission for the 2021 Announcement of Opportunity. If approved, the observatory will be developed over a 5-year period. Its primary science mission takes 34 months to complete. The spacecraft carries enough fuel for 6 years of operations.