[shagie]

It certainly is that book.

The wiki https://en.wikipedia.org/wiki/King_David%27s_Spaceship

It's been a long time since I read it... but the specifics of that part of the story:

> Back in Haven, Dougal's men used the acquired knowledge to build a primitive crewed spaceship, adopting a low-tech design of Robert Goddard—a rapid firing cannon using high-explosive shells detonating behind the ship to provide propulsion (but which might blow up the ship). Because the ship would not be airtight, only members of MacKinnie's company (who still had their space suits) could pilot it, and because it would only be able to carry a minimal payload, Graham (the lightest of the company) volunteered and was chosen as pilot. Before the launch, MacKinnie proposed to her, and she accepted. As soon as Prince Samual's World was unified, and in the presence of unsuspecting Imperial witnesses, Graham's ship was launched and achieved orbit, although it could not re-enter the atmosphere (meaning that the Imperials had to rescue Graham). King David then immediately requested that Prince Samual's World be admitted to the Second Empire as a self-governing world capable of crewed space travel, not as a colony.