The Tyranny of the Rocket Equation

I've been a space nerd pretty much all my life, but it's been a long time since I dealt with the actual math involved in space exploration – since I was studying math and physics in university, actually. One of the key equations involved in space exploration is something called the rocket equation, developed by Konstantin Tsiolkovsky.

It's not an especially complex equation, but it has some important consequences. Astronaut and ISS Expedition 30/31 Flight Engineer, Don Pettit, has written an article for NASA's International Space Station site that clearly explains some of them, and without complex math. He explains how the rocket equation determines the amount of energy required to reach different destinations and how it affects the propellants used and the design of rockets.

I found one part of the article near the end especially interesting. It turns out that if the diameter of the Earth were only 50 percent larger, we wouldn't be able to use rockets to get into space. Assuming that the makeup of the larger Earth was roughly the same as what it is now, that translates to an increase in gravity of about 3.3 times.

If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport.

Imagine what life would be like on such a world, trapped forever in an impossibly deep gravity well.