​Before we dive into the mathematics of orbital velocity, let's start with a simple question: When a rocket launches, does it go straight up, or does it go sideways?

If you pictured a rocket soaring vertically into the sky, you're not wrong—but you're not entirely right either. A rocket does initially launch vertically to efficiently escape the thickest part of the Earth's atmosphere and minimize drag. However, if it continued straight up, it would simply fall right back to Earth once its engines cut off. To achieve orbit, a rocket must perform a "gravity turn," gradually pitching over and accelerating horizontally. The ultimate goal is not to simply reach a high altitude, but to achieve such a high horizontal speed that the spacecraft continuously "falls around" the curve of the Earth.

This concept of falling while moving forward so fast that you miss the ground is the very essence of orbit. In this chapter, we will uncover the precise tangential speed required to perform this celestial balancing act at any given altitude.