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Despite their importance to climate change, significant current and future source uncertainties remain for the most important carbon greenhouse gases (GHGs) methane (CH4) and carbon dioxide (CO2), particularly for the developing world. Mitigation by effective regulation and treaties requires accurate global GHG budgets, which only global-scale (satellite) remote sensing can deliver. A high spatial and spectral resolution spectrometer is needed; herein, we present the design concept for a Multi-Order Carbon Spectral Imager (MOCSI). MOCSI is designed for the global measurement of differential GHG column density and source fingerprinting from low Earth orbit. MOCSI includes three wavebands for CH4, CO2, and carbon monoxide (CO), whose altitude weighting functions emphasize the boundary layer, where the dominant GHG anthropogenic and natural sources are still unmixed and therefore most easily discerned against background levels. CO aids discrimination of megacity and fire GHG emissions from other sources and is also a precursor for ozone, which is also an important GHG. High spectral resolution ensures discrimination of target species from interferents, while high spatial resolution enhances sensitivity for discrete source identification and emission quantification. MOCSI is a compact, high-throughput shortwave-infrared push broom spectrometer that disperses multiple orders of a single grating onto a single focal plane array to minimize size, weight, and power of the instrument. MOCSI is specified to provide spatial and temporal resolution and sensitivity sufficient to address important global science questions related to megacity emissions, shifts in hydrocarbon production, and disaster response, as well as many others.