It seems very exotic compared to something like RP1 or Methane, especially for a vehicle which should be flying a lot and around civilians. Why was this choice made?
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The Virgin Galactic design was originally based on Burt Rutan's SpaceShipOne design. Scaled Composites chose ("after a lengthy study") a N2O/HTPB hybrid motor for that vehicle because they felt it combined the handling simplicity of solid motors with the ability to terminate the thrust at will.
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$\begingroup$ I've just asked Why did Virgin Galactic switch back to HTPB after one launch using thermoplastic polyamide (i.e. nylon)? $\endgroup$ – uhoh Apr 6 '18 at 5:12