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To install the mod, download the binaries for Ubuntu, macOS and Windows using the links found in the README file. KSP versions 1.8.1, 1.9.1, 1.10.1, 1.11.x, and 1.12.2 to 1.12.5 are supported.
Before using the mod we recommend that you read the concepts document which explains the most important parts of Principia. In particular, you should learn about the plotting frame and flight planning.
Even orbits that are nearly Keplerian are subject to perturbations, which makes them harder to describe than in stock. Principia provides a powerful orbit analysis tool to help you reach your desired orbit; as it requires a good understanding of the underlying concepts, it has extensive documentation.
To get started, you should take a look at @rsparkyc's nice tutorial for doing in interplanetary flyby of Eve and returning to Kerbin.
We also have a tutorial showing how to go to the Mun in an energy-efficient manner. It uses a rather ancient version of Principia and doesn't have all the bells and whistles of recent versions, but it illustrates how to optimize the Δv.
The FAQ explain how to install, how to report bugs and documents the known issues and limitations.
The change log gives a fairly detailed description of the new features in each release.
If you try to design your own solar system, e.g., using Kopernicus, you should be aware that the Jool system is unstable in the stock game and read our analysis of its stability. We have a detailed description of the configuration files that describe the gravity model, the initial state and the numerics parameters for a custom-made solar system.
For those interested about how things work behind the scenes, we recommend looking at the technical overview to understand the overall structure of the project.
We also expose an API to allow other mods to take Principia's effects into account.
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