# How could a spacecraft be continuously propelled if it rotates to simulate gravity (by tether)?

For long term crewed space travel, gravity might be simulated by rotating a habitat in a long tether to a counter weight. Conventional chemical rocket engines give a spacecraft a brief initial impulse. Artificial gravity mode could be initiated afterwards by unfolding the tethers.

But some rocket engines are designed to give continuous propulsion over long periods of time. I think of for example nuclear thermal, ion electric and solar sails. How could such rocket engines be fitted on a spacecraft which has a long rotating tether? If placed at the center of mass, wouldn't such an engine bend the tethers and would that be a sound way to engineer it? Would rigid structures be required instead of a flexible unfoldable wire?

Some of the required rigidity could be provided by the rotation alone, by what's the simplest to describe as a centrifugal force (it really doesn't exist, it's merely a product of other forces), and it would be simplest to limit lateral wobble, if the thrust is applied perpendicular to the rotation vector from all its extremes simultaneously, i.e. your non-rigid wheel rotates 90° to your velocity vector.

My first edit was wrong. Rotating in the axis along your velocity vector would not only complicate engine design, but also eventually collapse the structure as one part of the wheel decelerates while the other accelerates during one single rotation. So unless you could compensate for the propulsive force with magnetic fields to keep the extreme parts of the wheel at a stable distance, this wouldn't work. But rotating the wheel perpendicular to the velocity vector could. If the two forces (centrifugal from our rotation and propulsive from our engines) are kept at exactly the 90° angle, they're non-interactive and the extreme ends of the wheel would keep exactly the same distance to each other as if the engines were off. That's true because the centrifugal force vector is equal in all directions along the wheel's plane of rotation, and the force on each of its parts is canceled out by its opposing end.

Problem is, that it would be imperative to keep the thrust vector (your normal) perpendicular to the wheel's rotational plane, the two (or more, but that's even harder to do then) engines would have to be perfectly synchronised, and run in a mutually compensating mode, where all the other engines would have to adjust to the worst of them. So while the engines perform exactly as expected, this could be relatively simple. Simply ignore that the whole structure rotates too and consider all its extreme parts with engines as individual spaceships flying in precision formation. If your velocity vector is exactly perpendicular to the plane of rotation, these forces don't have any influence on each other As one engine starts acting up though, all the rest of them have to follow suit and compensate, otherwise you end up with and out-of-plane rotation, precession of its extreme parts and eventual collision between them.

So, in my opinion; doable, but complicated. A rigid structure with a central engine would be simpler...

• "If the two forces (centrifugal from our rotation and propulsive from our engines) are kept at exactly the 90° angle, they're non-interactive and the extreme ends of the wheel would keep exactly the same distance to each other as if the engines were off. That's true because the centrifugal force vector is equal in all directions along the wheel's plane of rotation, and the force on each of its parts is canceled out by its opposing end" Very counter intuitive, might be because intuition assumes air resistance. So an acceleration in center of mass doesn't bend a perpendicular rotating wire? – LocalFluff May 26 '14 at 19:52
• @LocalFluff The idea here (with one central engine) is that your centrifugal force, the one I assumed you'd want it at ~ 1 g to simulate Earth-like gravity, is larger to your acceleration force along the velocity vector, so the centrifugal force flattens your whole configuration along its plane of rotation. If you'd use a non-rigid structure, the extreme ends would rotate inclined away from the velocity vector for more than 90° (i.e. the extreme ends would be closer), so also faster, but at the same distance to the central part that's easier to maintain orientation of than two engine config. – TildalWave May 26 '14 at 20:03
• E.g. if you rotate the non-rigid wheel with a central engine at such a rate that you end up with 1 g centrifugal force, if the central engine also accelerates at 1 g, you end up with the wheel's extreme ends rotating 90° to each other (45° to the central part) along the velocity vector. Re that counterintuitive part, yes, I imagine we automatically adjust for air resistance in our minds. But even then, it could be a stable config with sufficient rotation rate. That's how e.g. gyroscopes work. ;) – TildalWave May 26 '14 at 20:17
• So, with non-rigid wires the engine would be the tip of a cone with the wires rotating on the its mantel behind it? 1G acceleration and 1G rotational "gravity" gives 45 degrees angle of that "cone", I see! The continuous propulsion engines I've heard of are pretty much constant acceleration engines, so it might not be much of a problem to wire a habitable spaceship module, and its counterweight, perpendicular (well, trailing at some angle) to one of those? Given perfect engineering of balancing stuff ideally et c. If I understand your assesment of the basic physics of this correctly. – LocalFluff May 26 '14 at 20:30
• For the centrifugal force alone the cone radius, but you also get acceleration force from your engines. At 1 rpm, you'd need a radius of ~ 894.26 m for 1 g centrifugal acceleration (${\omega^2}r$). As you pull the extremes towards each other with acceleration force applied at the tether's center tho, the $r$ decreases but the rpm increases. Since the total energy of the rotating system didn't change, the centrifugal force didn't either, but you do have to add the acceleration force in the velocity vector. You'd want a long tether also to lower artificial gravity gradient head to toe. – TildalWave May 26 '14 at 21:47