Nano-satellites have a cost advantage due to their low mass and usage of commercial-off-the-shelf technologies. However, the low mass also restricts the functionality of a nano-satellite's payload. Typically, this would imply instruments with very low to low resolution and accuracy, essentially ruling out applications such as remote sensing. However, multiple nano-satellites can cooperate to improve the overall system performance, for example by increasing the frequency of the observations. The objective of this study is to design a radar system that can be accommodated in a nano-satellite, and investigate the feasibility of using multiples of these nano-satellites to perform high temporal resolution remote sensing. In this paper therefore, the concept of a nano-satellite sized Synthetic Aperture Radar (Nano-SAR) is investigated. Nano-satellites have very constrained power and volume budgets, and there are limits to how much surface area they can unfold for use in radar. Given these constraints, a SAR system for use in a nano-satellite in a 350 km orbit was sized, and approaches to tackle the deficits in the radar link budget are proposed. When applying state-of-the-art technologies, both on the component level, as well as on an architectural level, one arrives at a closed link budget. The proposed radar system consists of a patch antenna array with a span of 1.14 m by 0.18 m, operating at a frequency of 5.8 GHz. Power amplification and phase shifting is performed on the panel, using digital radio frequency (RF) integrated Complementary Metal Oxide Semiconductor (CMOS) circuits. This results in a swath width of 60 km, with pixel sizes of 10 m in elevation direction. Given these performance values, coupled with the increased revisit times, it was obvious this radar, when flown in a larger swarm of nano-satellites, would allow faster now-casting for weather prediction. With significant investment in technology development, it could be possible to use this system for SAR interferometry, for near-real-time monitoring of fast ground deformation phenomena such as earthquakes and volcanoes. Other applications could lie in the field of near-real-time ship motion detection and oil spill spread detection. Many technical challenges need to be solved still and platforms need to be designed, capable of supporting this system, before this payload would be ready for deployment. Preliminary design suggests the cost of such an instrument is substantially higher than what is common for nano-satellite components. However, the potential of such a system is extremely promising, and merits further investigation.