Protoplanetary disks (PPDs) have gained substantial attention due to their crucial role in planet formation. Observing their features in the far-infrared (FIR) spectrum has been challenging due to limitations in current optics and detectors, with proposed missions requiring a spectrometer with a spectral resolving power on the order of magnitude of 100,000. A promising solution is the virtually imaged phased array (VIPA), which could surpass the commonly used Fabry-Perot etalon and diffraction grating spectrometers. However, due to their novelty, VIPAs have seen limited applications in space and lack a numerically efficient model, preventing confi- dent recommendation for FIR spectroscopy. In this project, a one-dimensional (1D) analytical VIPA model with a numerically efficient implementation using Gaussian beam formalism was developed, showing close alignment with an advanced 2D model by Hu et al. (2015) based on the angular spectrum of plane waves. The new model demonstrated potential for VIPAs to meet the spectral resolving power required for space missions and showed the possibility to be further expanded to 2D for higher accuracy, while retaining high efficiency. An experimental setup for verifying the simulation results was proposed. The interplay between various device parameters, coupled with the numerous degrees of freedom required for aligning the optical setup, presented significant experimental challenges. Additionally, investigations into the design of inductive metal mesh mir- rors, supported by simulations in COMSOL and MATLAB, uncovered several difficulties that were thoroughly explored. The analytical VIPA model based on Gaussian beam propagation shows promise as a method for optimizing a VIPA for high-resolution far-infrared spectroscopy but further research and experimental validation are necessary to fully establish its efficiency and effectiveness. The project was a collaboration between TU Delft and the Netherlands Institute for Space Research (SRON).