Lunar Resources proposes to NASA the Processing and Extraction of Metal Oxide Slag on the Moon (PEMOS) to extract rare earth elements, thorium and high temperature metal oxides on the Moon without any earth-based consumables. The global objective of PEMOS's Phase I project is to mature the PEMOS system to TRL 4 for the extraction of titanium, calcium, chromium, rare earth elements and thorium from regolith slag through experimentation and system design. In addition, an economic analysis will be developed whose objective is to determine if/when would the extraction of rare earth elements and thorium from lunar regolith be economical for use on Earth (i.e., to be extracted from the Moon and transported back from Earth).