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How this mod works

When you are below 100K meters on Kerbin you are using the "inverse rotation" mode. This means that Kerbin is static and all the other planets and sun move around Kerbin. This is just part of how KSP works and cannot be avoided. If you don't switch to inverse rotation, then Kerbin moves and when you try to land your vessel explodes.

When you're above 100K meters (on Kerbin, but that altitude is different depending on the planet), then everything is back to normal and all the planets move around the sun.

You can see if you're in inverse rotation or not by checking the celestialbody.inverserotation on the current body you're orbiting.

While in tracking station, you're not in inverse rotation as you don't have an active vessel below the threshold altitude

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When you're NOT in inverse rotation, TiltEm just tilts the planet transform using a harmony patch and then you see the planet tilted.

When you're in inverse rotation, the whole planetarium must be tilted, so the orbit of the other planets are in the correct orbital plane. At the same time, the planet is tilted back to 0º as otherwise you'd have a tilted planet + tilted planetarium.

When you're tilting the planetarium, the vessels that are in track physics must be adjusted. This is done in another harmony patch that moves them around to the correct orbital parameters based on the planetarium tilt.