tracking based positioning, navigation, and timing (PNT) with low Earth orbit (LEO) satellites has attracted considerable attention. However, as LEO satellites are not dedicated for PNT, we cannot obtain the crucial information, such as signals structure and clock synchronization from the LEO signals of opportunity (SOPs), bringing challenges to Doppler LEO-PNT. Moreover, Doppler signal acquisition is time-consuming, which implies that real-time target localization is not allowed. In this paper, LEO-PNT is studied from passive source localization point of view. A reduced-dimension MUSIC (RD-MUSIC) with uniform circular array (UCA) is proposed for target localization using LEO SOPs. UCA is adopted because it offers uniform coverage in all directions, resulting in highly effective signal detection from any angle-of-arrival. Additionally, both odd and even numbers of antenna elements are investigated. The devised method employs one-dimensional (1-D) search, and then establishes equations from which the target's coordinates can be solved in a computationally attractive manner. The efficiency and reliability of our RD-MUSIC are demonstrated via numerical simulations, where the data are generated by the systems tool kit (STK) of Analytical Graphics.