Spaceship Physics

Introduction

The current central problem with space travel is summed up by the Tsiolkovsky rocket equation: $$\Delta v = v_e \ln \left( \frac{m_0}{m_f} \right)$$ Here, $\Delta v$ is the difference between the rocket's initial and final speed, $v_e$ is the exhaust speed, $m_0$ is the initial total mass (including propellant, payload, and the rest), and $m_f$ is the final total mass, which is everything except propellant. An efficient rocket can have an exhaust speed near $4000 \frac{\textrm{m}}{\textrm{s}}$, meaning that it would need a mass ratio of around $10.5$ to reach orbital speed, given drag and other losses. The ratio of structural mass to payload mass can also easily be in excess of $10$, so the amount of payload a rocket can carry is really miniscule compared to its total mass.

There are a few potential approaches to this problem:

Engineering

We can divide a rocket into stages, jettisoning empty tanks and other stuff on the way. This is the most popular approach.

Design

We can find a use for the large empty pressure vessels that a single-stage-to-orbit vehicle would bring with it. For example, on a long-term crewed mission, you could live in one. Even relatively small rockets, like the Falcon 9, have oxidizer tanks with comparable width to International Space Station modules.

Theoretical Physics

We can try to determine the maximum possible $v_e$, then go from there.

Ion Engines