How do rockets work?

Chapter 1Pushing on nothing: Newton's third law

Stand on a skateboard holding a heavy medicine ball and throw it forward as hard as you can. You roll backward. Nothing pushed you except the ball itself: as your arms shoved it one way, it shoved you the other way with exactly the same force. That is Isaac Newton's third law, usually stated as "for every action there is an equal and opposite reaction," and it is the entire principle of a rocket.

A rocket is a skateboarder who throws an enormous number of tiny medicine balls, very fast, without stopping. The "balls" are molecules of hot gas. Inside the engine, burning propellant produces gas at high pressure. That pressure presses on every inside wall of the combustion chamber. On the sides, the pushes cancel out. But at the back there is a hole, the nozzle, where gas escapes instead of pressing. So the pressure on the front wall of the chamber is not balanced by an equal pressure at the back, and the leftover push moves the rocket forward.

This is why rockets work in a vacuum, and in fact work a little better there. A rocket does not need air to push against. The thing it pushes against is its own exhaust. In 1920 a New York Times editorial mocked the physicist Robert Goddard for supposedly not understanding that a rocket in space would have "nothing to push against." The paper printed a correction on 17 July 1969, the day after Apollo 11 left for the Moon.

Goddard went on to launch the first liquid-fuelled rocket on 16 March 1926, from a cabbage field in Auburn, Massachusetts. It flew for about two and a half seconds and reached roughly 12 metres. Every rocket since works on the same principle; they just throw their gas much faster, and a great deal more of it.

So what: a rocket is a momentum machine. It gains momentum forward by giving the same amount of momentum backward to its exhaust. The faster the exhaust leaves, the more push you get from each kilogram of propellant. Hold on to that; it drives the whole story.

Chapter 2Thrust, exhaust velocity and specific impulse

Thrust is the force the engine produces. For most purposes it comes down to two numbers multiplied together: how much mass the engine throws out per second, and how fast that mass is going when it leaves.

Thrust ≈ (mass flow per second) × (exhaust velocity)

In symbols that is F = ṁ × v_e, where ṁ ("m-dot") is kilograms per second and v_e is metres per second. There is a second, smaller term for the difference between the pressure of the exhaust and the pressure of the surrounding air, which we will meet in Chapter 5. For now the main idea is enough: you can get more thrust by throwing more stuff, or by throwing it faster.

Those two routes are not equal. Throwing more stuff gives you more force right now, which you need to lift a heavy rocket off the pad. Throwing it faster gives you more push per kilogram, which matters for how far you can go in total. A weightlifter and a marathon runner are both strong in different ways, and rocket engineers keep the same distinction.

Specific impulse: miles per gallon for rockets

Engineers measure an engine's efficiency with a number called specific impulse, written I_sp. It answers: how long can one kilogram of propellant produce one kilogram's worth of thrust (that is, hold up its own weight against Earth's gravity)? The answer comes out in seconds, which is why you see engines described as "311 seconds" or "450 seconds."

Specific impulse and exhaust velocity are really the same thing in different units. Multiply I_sp by standard gravity, g₀ = 9.80665 m/s², and you get the effective exhaust velocity:

v_e = I_sp × g₀

An engine rated at 300 seconds has an effective exhaust velocity of about 2.9 km/s. One rated at 450 seconds blows its exhaust out at about 4.4 km/s, roughly thirteen times the speed of sound at sea level.

Typical numbers give a feel for the range:

• Solid rocket motors (like the Space Shuttle's boosters): about 250–280 seconds.
• Kerosene and liquid oxygen (SpaceX's Merlin engines): about 282 seconds at sea level and about 311 seconds in vacuum for the first-stage engine; the vacuum-optimised upper-stage version reaches about 348 seconds.
• Liquid hydrogen and liquid oxygen (the Space Shuttle main engine, RS-25): about 366 seconds at sea level and about 452 seconds in vacuum.
• Ion thrusters, which accelerate charged atoms with electric fields: 1,500–4,000 seconds or more, but with a thrust comparable to the weight of a sheet of paper.

So what: high thrust gets you off the ground; high specific impulse gets you far. Chemical rockets give you lots of thrust with moderate efficiency, which is why they are the only way to leave Earth, while electric propulsion is efficient but feeble and only useful once you are already in space.

Chapter 3The rocket equation and the tyranny of mass

Here is the problem with carrying your own fuel. At launch, a rocket must lift not only itself but every kilogram of propellant it will burn later. Burning the first tonne of fuel has to accelerate all the fuel that remains. Burning the next tonne is a little easier, because there is less left to carry. The rocket gets lighter as it goes, and the maths of that steadily shrinking load has a famous answer.

In 1903 the Russian schoolteacher Konstantin Tsiolkovsky published the relationship now called the Tsiolkovsky rocket equation:

Δv = v_e × ln( m_full / m_empty )

In words: the total change in speed a rocket can achieve (Δv, said "delta-vee") equals its exhaust velocity multiplied by the natural logarithm of how much heavier it is full than empty. The ratio of full to empty mass is called the mass ratio.

You do not need to love logarithms to see what this means. A logarithm grows slowly. Doubling the mass ratio does not double your speed; it adds a fixed amount. Each extra helping of speed costs a multiple of propellant, not an additional amount. Engineers call this the tyranny of the rocket equation.

A worked number

Reaching low Earth orbit takes a delta-v of roughly 9.4 km/s once you count losses (Chapter 7 explains where that number comes from). Suppose your engine has an exhaust velocity of 3 km/s, typical for kerosene. Rearranging the equation:

mass ratio = e^{Δv / v_e} = e^{9.4 / 3} ≈ 23

The fully fuelled rocket must weigh about 23 times as much as the empty one. Put another way, about 96% of the rocket at liftoff must be propellant. Everything else, tanks, engines, pumps, wiring, computers, and the satellite you actually want to deliver, has to fit into the remaining 4%. For comparison, a soda can is about 4% aluminium by mass. A single-stage orbital rocket would have to be built more lightly, relative to its contents, than a drinks can.

Now run it with a hydrogen engine at 4.4 km/s. The mass ratio drops to e^9.4/4.4 ≈ 8.5, so propellant is "only" about 88% of the rocket. That looks like a big win, and it is part of why hydrogen is prized for upper stages. But liquid hydrogen is extremely light and bulky, so the tanks become huge and heavy, eating much of the advantage. Every choice in rocketry is a trade like this.

So what: the rocket equation is why launch is expensive, why rockets are mostly fuel tank, why engineers obsess over shaving kilograms, and why the next chapter's tricks, better propellants, better nozzles and staging, exist at all.

Chapter 4Propellants: solid, liquid, cryogenic

A chemical rocket needs two things: a fuel and an oxidiser to burn it. On Earth, fires take their oxygen from the air. A rocket climbing above the atmosphere cannot, so it carries its own oxidiser, which typically makes up most of the propellant mass. Together, fuel and oxidiser are called propellant.

Solid rockets

A solid rocket motor is a casing packed with a rubbery mixture that already contains both fuel and oxidiser. A common recipe uses ammonium perchlorate as the oxidiser and powdered aluminium as the fuel, held together by a synthetic rubber binder. Light it, and it burns from the inside out until it is gone.

Solids are simple, store for years, and produce huge thrust for their size. That is why they are used as strap-on boosters and in military missiles. Their weakness is control: once lit, a solid motor generally cannot be throttled precisely or switched off. Engineers shape the hollow core (often as a star) to set how fast the burning surface grows and therefore how thrust changes over time.

Liquid rockets

Liquid rockets keep fuel and oxidiser in separate tanks and pump them into a combustion chamber. That adds plumbing and complexity, but it means the engine can be throttled, shut down and often restarted. Common pairings:

• Kerosene (RP-1) and liquid oxygen: dense and relatively easy to handle. Used on the Saturn V's first stage and on Falcon 9.
• Liquid hydrogen and liquid oxygen: the highest specific impulse of any practical chemical pair, at the cost of enormous, super-cold tanks. Used on the Saturn V's upper stages, the Space Shuttle and NASA's SLS.
• Liquid methane and liquid oxygen: a newer middle ground. Denser than hydrogen, cleaner-burning than kerosene (which matters for reusing engines), and in principle makeable on Mars from carbon dioxide and water. Used by SpaceX's Raptor and Blue Origin's BE-4.
• Hypergolic propellants, such as hydrazine compounds with nitrogen tetroxide: they ignite on contact, with no spark needed, and store at room temperature. That reliability made them the choice for Apollo's service and lunar modules and for spacecraft thrusters today. They are also highly toxic.

Why "cryogenic" matters

Liquid oxygen boils at about −183 °C, liquid methane at about −162 °C and liquid hydrogen at about −253 °C, only 20 degrees above absolute zero. These cryogenic propellants have to be loaded shortly before launch and constantly topped up as they boil off, which is why rockets on the pad vent white clouds. The frost you see on a rocket's side is moisture from the air freezing onto tanks of liquid oxygen.

So what: propellant choice is a balance between efficiency (specific impulse), density (how big the tanks must be), handling (temperature, toxicity) and control (can you throttle or restart it). No pairing wins on all four, which is why big rockets often use different propellants in different stages.

Chapter 5Engines and nozzles

Burning propellant produces hot, high-pressure gas, but heat and pressure are not yet thrust. The job of a rocket engine is to turn as much of that energy as possible into fast, orderly motion pointed straight out of the back. Most of that work is done by the bell-shaped nozzle.

The de Laval nozzle

A rocket nozzle narrows to a tight throat and then flares out into a wide bell. That shape is called a de Laval nozzle, after the Swedish engineer Gustaf de Laval, who developed it for steam turbines in the 1880s. Goddard was among the first to apply it to rockets.

It works in a way that seems backwards at first. When gas is moving slower than sound, squeezing it through a narrowing pipe speeds it up, the way water speeds up when you put your thumb over a hose. At the throat the gas reaches exactly the speed of sound. Past that point the rules flip: for gas moving faster than sound, a widening channel makes it accelerate further, because the gas expands and cools, turning its heat energy into speed. By the time the exhaust leaves the bell it can be travelling several times the speed of sound.

Why bells come in different sizes

Remember the second term in the thrust equation? It comes from the pressure of the exhaust as it leaves the nozzle compared with the pressure of the air outside. The fuller version is:

F = ṁ v_e + (p_exit − p_outside) × A_exit

A nozzle works best when the exhaust leaves at the same pressure as its surroundings. At sea level, air pressure is high, so a first-stage nozzle must stay fairly short; a very wide bell would over-expand the gas below air pressure, and the atmosphere would push back in, wasting thrust and even causing the flow to separate from the walls. In vacuum, outside pressure is zero, so a larger bell can keep expanding and accelerating the gas. That is why upper-stage engines have strikingly huge nozzles and why the same engine has a higher specific impulse in vacuum than at sea level.

Pumps, heat and steering

Large liquid engines need to push hundreds of kilograms of propellant per second into a chamber at very high pressure. They do this with turbopumps: turbines spun by hot gas, driving pumps that can be as powerful as a locomotive while fitting in a space the size of a barrel. How engineers drive those turbines (burning a little propellant on the side and dumping it, or routing everything through the main chamber) is one of the major differences between engine designs.

Chamber gas can reach around 3,000 °C, hotter than the melting point of the metal walls. Many engines survive by regenerative cooling: running cold propellant through channels in the nozzle and chamber walls before burning it, so the propellant soaks up heat that would otherwise melt the engine.

Finally, to steer, most rockets gimbal their engines, tilting the whole engine a few degrees on a pivot so its thrust points slightly off-centre and turns the rocket. Rockets have no wings to bank on; they balance on a column of fire the way you balance a broom on your palm, with computers making constant tiny corrections.

So what: the engine is a machine for turning heat into directed speed. Its nozzle is tuned for the air pressure it will fly in, its pumps fight to feed it, its own propellant keeps it from melting, and its pivot lets it steer.

Chapter 6Staging: throwing the rocket away

Chapter 3 showed that a single-stage rocket would need to be about 96% propellant to reach orbit, with everything else squeezed into the last 4%. Real tanks, engines and structures can just about meet that, but leave almost nothing for a payload. The way out is to stop carrying the empty parts.

Staging means stacking two or more rockets on top of each other. The bottom stage, the biggest, lifts everything off the pad. When its propellant is gone, it detaches and falls away, and the next stage lights. Now the rocket is not dragging a huge empty tank and a set of heavy engines through the rest of the climb. Each stage only has to provide part of the total delta-v, so each can live with a much gentler mass ratio.

The Saturn V that sent astronauts to the Moon was a three-stage rocket. At liftoff it weighed about 2,900 tonnes and stood about 111 metres tall. Its first stage burned for under three minutes; the third stage eventually sent the Apollo spacecraft, under 2% of the rocket's original mass, on its way to the Moon. SpaceX's Falcon 9 uses two stages and weighs about 550 tonnes at liftoff. Configured to be thrown away rather than landed, it can carry about 22 tonnes to low Earth orbit, around 4% of its liftoff weight.

Staging comes with costs: every separation is a moment when something can go wrong, every stage needs its own engines, and every extra engine is weight and money. Two or three stages usually hit the sweet spot. Strap-on boosters, like the Shuttle's twin solids or the side cores of Falcon Heavy, are a variation called parallel staging: they burn alongside the core from liftoff and drop off early.

So what: staging is the main way engineers beat the rocket equation. It is also why, until recently, almost every rocket was a pile of very expensive hardware that ended up in the ocean.

Chapter 7Getting to orbit: it is mostly sideways

Space, by the most common convention, starts at the Kármán line, 100 km up. A rocket could reach that height with a speed of only about 1.4 km/s straight up, then fall straight back down, as suborbital tourist flights do. Reaching orbit is a completely different and much harder problem, because orbit is not about height. It is about sideways speed.

An orbiting spacecraft is falling the whole time. It is just moving sideways so fast that as it falls, the curved Earth drops away beneath it at the same rate, so it never hits the ground. In low Earth orbit, a couple of hundred kilometres up, that takes about 7.8 km/s, roughly 28,000 km/h, or once around the planet in about 90 minutes. Our daily explainer on satellites covers this falling-around idea in more detail.

The delta-v budget

If orbital speed is 7.8 km/s, why did Chapter 3 use 9.4 km/s? Because a rocket pays extra on the way up:

• Gravity loss, typically 1–1.5 km/s. Every second the rocket spends thrusting upward against gravity, some of its thrust is spent just holding itself up rather than adding speed. The longer the climb, the bigger the loss.
• Drag loss, typically around 0.1–0.3 km/s. Air resistance is a smaller penalty than most people expect, because rockets rise through the thick lower atmosphere quickly.
• Steering loss: any thrust that is pointed away from the direction of travel to change course is not adding speed.

Add those to orbital speed and the total lands around 9.3–10 km/s, depending on the rocket and the orbit. Earth helps a little, too: it spins eastward at about 0.46 km/s at the equator. Launching east, and as close to the equator as possible, gives a free head start. That is why Florida and French Guiana are favourite launch sites and why most rockets head out over the ocean to the east.

The gravity turn

A rocket leaves the pad going straight up, to clear the tower and get out of the thickest air quickly. Within seconds it begins to tip over slightly toward the horizon, and from then on gravity does much of the steering. Pulling down on a rocket that is already tilted, gravity gradually bends its path from vertical toward horizontal. This manoeuvre is called a gravity turn.

The gravity turn is a compromise. Climbing too steeply wastes propellant fighting gravity for too long. Turning over too early keeps the rocket in thick air at high speed. The worst of that air stress comes about a minute after launch at a point called Max Q, maximum dynamic pressure, which is why launch commentators call it out; many rockets throttle down briefly to get through it. By the time the second stage is burning, the rocket is far above most of the atmosphere and pointed almost horizontally, piling on the sideways speed that orbit demands.

So what: getting to space is easy; staying there is hard. Around 80% of the effort of reaching orbit goes into going sideways, not up.

Chapter 8Coming back: reentry and reusability

A spacecraft in low orbit is carrying a ferocious amount of energy. Each kilogram moving at 7.8 km/s has about 30 megajoules of kinetic energy, more than the chemical energy in a kilogram of TNT several times over. To land, almost all of that has to go somewhere, and the only practical place for it to go is into the air as heat.

Reentry heating is often described as friction, but most of it comes from compression. A spacecraft moving at many times the speed of sound slams into air faster than the air can move out of the way, forming a shock wave in front of it. Air crushed in that shock layer heats to thousands of degrees, far hotter than the surface of the Sun in the case of capsules returning from the Moon at around 11 km/s.

Blunt is better

In the 1950s, NASA researchers H. Julian Allen and Alfred Eggers worked out a counterintuitive answer: make the front of the vehicle blunt, not pointed. A blunt shape pushes the shock wave out ahead of it, so most of the scorching air flows around the spacecraft instead of touching it. That is why capsules from Mercury to Apollo to Dragon and Orion look like gumdrops with their wide end forward.

The rest of the heat is handled by a heat shield. Capsules typically use ablative shields, which char and slowly erode, carrying heat away as they burn off. The Space Shuttle used tens of thousands of silica tiles that were such poor conductors of heat that one could be held by its edges moments after coming out of a furnace. Damage to that thermal protection is what doomed Columbia in 2003.

Bringing the rocket back too

For most of the space age, the rocket that launched a spacecraft was thrown away. Reusing it is hard because, as the rocket equation insists, every kilogram of landing legs, fins and reserved propellant is a kilogram not spent on payload. Falcon 9's first stage keeps back part of its propellant, flips around after separation, relights its engines to slow down, steers with grid fins, and lands on its own legs, either back near the launch site or on a drone ship at sea. The first landing after an orbital launch came on 21 December 2015; landings are now routine and individual boosters have flown many times.

Reuse costs payload capacity, but if a booster can fly again after inspection and refuelling, it saves building a new one. The economics, not the physics, are what changed: the rocket equation still takes its cut, and reusable designs simply decide the cut is worth paying.

So what: going up means building energy; coming down means getting rid of it safely. Blunt shapes and sacrificial heat shields protect spacecraft, and propulsive landing has turned the most expensive part of a rocket into something that can be flown again.

Chapter 9Common misconceptions

"Rockets push against the air."

They push against their own exhaust. Air is a hindrance, not a help: it causes drag, and its pressure reduces an engine's thrust compared with vacuum. (Chapter 1.)

"Getting to space is mostly about going up."

Reaching 100 km is comparatively easy. Orbit requires about 7.8 km/s of sideways speed, and that is where most of the propellant goes. (Chapter 7.)

"Astronauts float because there is no gravity in space."

At the International Space Station's altitude, gravity is still about 90% as strong as on the ground. Astronauts float because they and their station are falling together around Earth, so nothing presses them against the floor.

"Reentry heat is caused by friction."

Mostly it is compression: air piled up in a shock wave ahead of the vehicle heats sharply. Friction along the surface contributes, but it is not the main source. (Chapter 8.)

"A more powerful engine always means a better rocket."

Thrust gets you off the ground, but specific impulse and the mass ratio decide how far you can go. A huge engine on a heavy rocket can be worse than a modest, efficient engine on a light one. (Chapters 2 and 3.)

"Rockets burn up most of their fuel getting out of the atmosphere."

A rocket typically clears the densest air in the first couple of minutes, but it keeps burning for several more, accelerating sideways. Drag costs only a few per cent of the total delta-v budget.

Chapter 10Further reading

Go shorter on Daily Explainer

• How do satellites stay in orbit?
• What was the space race?
• What is gravity, really?
• What is energy?

Sources and deeper reading

• NASA Glenn Research Center, Beginner's Guide to Rockets: thrust, specific impulse, nozzles and the rocket equation, with interactive simulators.
• George P. Sutton and Oscar Biblarz, Rocket Propulsion Elements (Wiley): the standard engineering textbook for propulsion.
• NASA, Saturn V flight manuals and press kits (NASA History Office), for stage masses, burn times and performance.
• SpaceX, Falcon 9 vehicle page and user's guide, for liftoff mass, Merlin engine performance and payload figures.
• H. Julian Allen and A. J. Eggers Jr., A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth's Atmosphere at High Supersonic Speeds, NACA Report 1381 (1958): the blunt-body insight.
• Konstantin Tsiolkovsky, Exploration of Outer Space by Means of Reaction Devices (1903): the original rocket equation.