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speed of the rocket is this figure divided by its mass (10).
    In fact, this is a slight simplification. It assumes the mass of the rocket is constantly 10 kg. But its mass is actually changing continuously as fuel get burned. Initially the rocket weighs 11 kg because it has to carry all the fuel it needs for the burn—and this extra baggage makes the final speed slightly less. Konstantin Tsiolkovsky worked out a mathematical equation for determining the speed that a rocket can reach given the weight of the rocket body, the weight of propellant and the speed of its exhaust gas, taking into account the fact that the propellant burns gradually. In our example above, Tsiolkovsky’s rocket equation reveals that the rocket would actually accelerate to 238 m/s. Scientists call this total increase in velocity brought about by burning a given mass of fuel “delta-
v
”—which comes from the mathematician’s shorthand “delta,” meaning “a change in,” and the symbol for velocity, “
v
.”
Beating gravity
    So how much delta-
v
does it take to get a rocket into space? The answer to that question was provided centuries ago by the English physicist Isaac Newton. In 1687, Newton published his theory of gravity. It was a monumentalachievement for a scientist working in the 17th century: a single mathematical law that at a stroke explained the orbit of Jupiter and how apples fall from trees in Cambridge—phenomena separated by hundreds of millions of kilometers. Newton’s theory was a universal law of gravitation, revealing not only why objects fall downward in a gravitational field, but also how the planets circle the Sun. The mathematical description of orbits had been worked out 80 years earlier by the German astronomer Johannes Kepler. Newton’s theory neatly provided the physics underpinning all three of Kepler’s “laws of planetary motion.”
    However, Newton’s theory also revealed how fast a rocket needed to travel in order to reach orbit around Earth. Launch a projectile into the air and it arcs through the sky before falling back to the ground. Launch the projectile faster and the arc carries it higher and further. Orbit is achieved when the projectile is traveling so fast that the curved surface of the planet falls away at exactly the same rate the rocket falls under the attraction of gravity, meaning that the rocket circles around the planet continuously. (Some readers may have heard of the term “escape velocity”—the speed that a projectile, such as a cannon ball, must be given in a single kick at Earth’s surface in order to completely escape the planet’s gravity. However, escape velocity doesn’t apply to rockets because they burn their fuel gradually—theoretically, a rocket could leave the atmosphere traveling at any speed as long as it had enough fuel to keep accelerating.)
    Newton’s theory predicted that the minimum speed needed for a rocket to achieve a circular orbit around Earth is around 7,800 m/s (25,500 ft/s)—quite quick. In fact, the speed of the orbit itself is just part of the equation. After adding in air resistance, the energy spent climbing out of Earth’s gravitational field and other losses, the speed needed to get to orbit is actually more like 9,400 m/s (30,800 ft/s).
Multi-staging
    Imparting this much speed to a rocket is no mean feat. But Konstantin Tsiolkovsky came up with a neat trick to make life easier for the engineers—multi-staging. His idea was for the rocket to shed weight as it flew by jettisoning sections of itself that had served their purpose, such as empty fuel tanks. For example, his equations showed that for a rocket of fixed body mass and fuel load, and carrying a payload that makes up 0.1 percent of the total launch mass, splitting the rocket into three stages (each weighing 10 percent as much as the stage below it) would leave the payload ultimately traveling