How Do Rockets Work? Throwing Mass Backwards to Reach Orbit

Newton's third law says that every force has an equal and opposite one, and a rocket is that law made into a vehicle. When the engine throws exhaust gas out of the nozzle at several kilometres a second, the gas pushes back on the engine with the same force, and the rocket accelerates forward. Nothing outside is involved; a rocket works better in a vacuum than in air, since there is no atmosphere in the way. The thrust depends on two things, how much mass is thrown out per second and how fast, and the second matters more: doubling the exhaust speed doubles the thrust for the same fuel, while doubling the fuel flow uses fuel twice as fast.

The engine's job is therefore to make the exhaust as fast as possible. Burning fuel and oxidiser in a chamber at high pressure produces hot gas, and the bell-shaped nozzle lets it expand and accelerate, converting heat into directed speed. The best chemical rockets, burning liquid hydrogen with liquid oxygen, reach exhaust speeds of about 4.4 kilometres a second, and that number, which chemistry sets, is the reason rockets are the shape they are.

Because a rocket has to carry the mass it will throw, and has to accelerate that mass before throwing it, the fuel needed grows exponentially with the speed required. Konstantin Tsiolkovsky wrote the equation down in 1903: the change in a rocket's speed equals the exhaust speed times the natural logarithm of the ratio of its full mass to its empty mass. To reach orbit a rocket needs about 9.4 kilometres a second, including losses to gravity and drag, which with an exhaust speed of 4.4 means a mass ratio of about 8, and with more typical kerosene engines at 3 kilometres a second a ratio above 20. That is why nearly everything on the pad is propellant and why the structure has to be made of the thinnest possible metal. Staging helps: dropping empty tanks and used engines on the way up means the upper stages do not have to accelerate dead weight, and almost every orbital rocket ever flown has had at least two stages. The main terms:

• •Thrust: mass flow through the engine times exhaust speed, the force pushing the rocket
• •Specific impulse: exhaust speed expressed as seconds, the measure of an engine's efficiency
• •Delta-v: the total change in speed a rocket can achieve, fixed by the rocket equation
• •Mass ratio: full mass over empty mass; higher is better and hard to raise
• •Staging: shedding structure as propellant is used, which multiplies the achievable delta-v

The hard part of spaceflight is not getting high but getting fast. A rocket that climbs straight up to 100 kilometres and stops falls straight back down. To stay up, a spacecraft must be moving sideways so fast that as it falls towards the Earth, the Earth's surface curves away beneath it at the same rate, and it falls around the planet for ever; at 400 kilometres, the height of the International Space Station, that speed is 7.7 kilometres a second, about 28,000 kilometres an hour, a lap of the Earth every ninety minutes. That is why rockets tilt over within seconds of launch and spend most of their burn accelerating horizontally. Astronauts float not because gravity is absent, since it is ninety percent as strong as on the ground, but because they and their vehicle are falling together. Leaving Earth altogether takes 11.2 kilometres a second, and the rocket equation makes every extra kilometre a second expensive.

Solid rockets, the oldest kind, are a tube packed with fuel and oxidiser mixed into a rubbery block that burns from the inside out; they are simple, powerful and cannot be throttled or shut down, which is why they are used as boosters and in missiles. Liquid rockets pump fuel and oxidiser from separate tanks into the chamber, can be throttled, stopped and restarted, and power every crewed vehicle; the pumps, spinning at tens of thousands of revolutions a minute to feed a Saturn V's engines at the rate of a swimming pool every few seconds, are the hardest part to build. Ion engines, used on deep-space probes, throw out a thin stream of charged atoms at 30 kilometres a second or more, giving a thrust no stronger than the weight of a sheet of paper but sustaining it for years; they cannot lift anything off a planet but can reach speeds no chemical rocket can.

The Chinese were launching gunpowder rockets by the thirteenth century, and the rocket's red glare in the American anthem is British Congreve rockets over Baltimore in 1814. Robert Goddard flew the first liquid-fuelled rocket in Massachusetts in 1926, a flight of two and a half seconds; the German V-2 of 1944 was the first to reach space; and its designers, in Soviet and American hands, built the rockets that launched Sputnik in 1957 and carried Apollo to the Moon on a Saturn V whose first stage burned 2,000 tonnes of propellant in two and a half minutes. The recent change is reuse. A rocket whose first stage flies back and lands, as the Falcon 9 began doing in 2015, throws away far less hardware per launch, and the cost of putting a kilogram into orbit has fallen by roughly a factor of ten as a result. The equation has not changed; the accountancy has.

The Earth spins eastward, and everything on its surface is carried along with it. At the equator that motion is about 465 metres a second; at the latitude of London it is only around three fifths of that. A rocket launched towards the east starts with that speed already in hand, and given how the rocket equation punishes every extra metre a second, the free boost is valuable. That is why most launches head east, and why Europe launches its rockets from Kourou in French Guiana, close to the equator, rather than from Europe itself.

Safety shapes the map too. Rockets drop spent stages and sometimes fail, so launch sites are placed where the flight path heads out over sea or empty land, which is why Cape Canaveral sits on the Florida coast with the Atlantic to its east. Some orbits need a different trade. Satellites that must pass over the whole Earth, such as weather and mapping satellites in polar orbits, are launched north or south and get little help from the spin, while a westward launch works against the rotation and costs extra fuel, which is why it is rarely done.

In January 1920 an editorial in The New York Times mocked Robert Goddard for suggesting that a rocket could travel through space. A rocket, the writer argued, needs something to push against, and Goddard seemed to lack the basic physics taught in every high school. The mistake was the one Newton's third law corrects: the rocket pushes against its own exhaust, not against the air. On 17 July 1969, the day after Apollo 11 set off for the Moon, the newspaper printed a short correction, accepting that a rocket can work in a vacuum and saying that it regretted the error.

In fact the air gets in the way, and the reason lies in the nozzle. A nozzle works best when the exhaust leaves it at roughly the same pressure as its surroundings. Near the ground the atmosphere presses on the exhaust, so first-stage nozzles are kept relatively small; make them too wide and the outside air pushes the flow away from the walls, causing instability and lost thrust. In a vacuum nothing presses back, so the gas can keep expanding and speeding up, which is why upper-stage engines carry enormous bells and why the same engine gives more thrust above the atmosphere than at sea level.

Launch footage often surprises people by how slowly a rocket seems to rise. At lift-off its thrust is typically only somewhat greater than its weight, perhaps 1.2 to 1.5 times. A rocket with thrust 1.3 times its weight has three tenths of its weight left over to accelerate it, so it climbs at about 0.3 g, gaining roughly three metres per second every second, which looks leisurely beside a sports car. Engines powerful enough to make the rocket leap off the pad would themselves be heavier, and every kilogram of engine is a kilogram that must be carried all the way up.

The slow start has a cost, known as gravity loss. For every second a rocket spends climbing vertically, gravity takes away about 9.8 metres per second of the speed its engines provide, so lingering near the pad wastes propellant. The acceleration then rises steeply, because the thrust stays much the same while the mass shrinks as propellant burns away. A stage that starts at 0.3 g can finish at around four g, which is why engines are throttled back or shut down one at a time late in a burn, keeping the load within what the structure and any crew can bear.

A rocket moves by expelling its own mass at high speed, so that the reaction pushes it the other way, which is the only way to accelerate in a vacuum. Because it must carry and accelerate everything it will throw, the propellant needed grows exponentially with the speed required, which is why rockets are mostly fuel, are built in stages and shed them as they climb. Reaching orbit means reaching about 7.7 kilometres a second sideways, so that the vehicle falls around the Earth rather than back to it.