How a rocket works

The first liquid-fuelled rocket flew for two and a half seconds and rose about 12.5 m.

The engine throws gas downward (lower arrow); the gas pushes the rocket upward with an equal force (upper arrow). No air or ground is needed to push against.

Push something away and it pushes back

Stand on a skateboard and throw a heavy ball forward: you roll backwards. Let go of a blown-up balloon and it shoots off as the air rushes out of the neck. Both are Newton's third law at work: when one object pushes on another, the second pushes back on the first just as hard, in the opposite direction. A rocket engine burns fuel to make a great deal of hot gas and throws it out of the nozzle at high speed. The rocket pushes the gas backwards, and the gas pushes the rocket forwards.

A common mistake is to think the exhaust needs air to push against. It does not. The push happens inside the engine, between the rocket and its own gas, which is why rockets work even better in the vacuum of space, where no air gets in the way. The quantity that matters is momentum, mass times velocity. If the engine throws out 1 kg of gas at 3,000 m/s, the rocket gains 3,000 kg·m/s of momentum in the other direction, whatever is around it.

The rocket equation

In 1903 the Russian schoolteacher Konstantin Tsiolkovsky published a treatise on using rocket engines in space, and with it the equation every rocket designer still uses. It says how much a rocket can change its speed, Δv, from two numbers: the exhaust speed v_e and the mass ratio, the starting mass m₀ divided by the final mass m_f after the fuel is gone. Δv = v_e × ln(m₀ ÷ m_f). The logarithm is the bad news. With an exhaust speed of 3 km/s, a rocket that is three-quarters fuel (mass ratio 4) gains 4.16 km/s; making it 90% fuel (ratio 10) only gets you 6.91 km/s.

Reaching orbit takes about 7.7 km/s of sideways speed plus extra to fight gravity and air on the way up, which is more than one simple rocket can manage. The answer is staging. A big first stage lifts everything, then drops away when empty so its heavy tanks and engines stop being dead weight; a second stage starts with a fresh, much better mass ratio. NASA's Saturn V for the Apollo flights had three stages: the first lifted the rocket to about 68 km, the second carried it almost to orbit, and the third finished the job and then pushed the spacecraft towards the Moon.

BackgroundOn 16 March 1926, on a snowy farm in Auburn, Massachusetts, Robert Goddard launched the world's first liquid-fuelled rocket. According to the Town of Auburn, it reached an altitude of 41 feet (about 12.5 m), flew for two and a half seconds and landed 184 feet (about 56 m) from its launching frame. Goddard had published "A Method of Reaching Extreme Altitudes" in 1919 and was mocked for suggesting a rocket could reach the Moon. Today the launch site, now part of a golf course, is a National Historic Landmark.

Saturn V (NASA)	Value
Height	111 m (363 ft)
Mass at liftoff	2.8 million kg
Thrust at launch	34.5 million newtons
To Earth orbit	about 118,000 kg
To the Moon	about 43,500 kg
Stages	3

Liftoff also needs thrust greater than weight. The Saturn V weighed 2.8 million kg × 9.81 m/s² ≈ 27.5 million newtons on the pad and its engines gave 34.5 million, a ratio of about 1.26. The leftover 7 million newtons, shared over 2.8 million kg, gives an upward acceleration of only about 2.5 m/s² at first, which is why big rockets seem to rise so slowly. As fuel burns away the mass falls and the acceleration climbs.

Which law explains why a rocket moves?
- Newton's third law
- The law of conservation of mass
- Ohm's law
Does a rocket engine need air to push against?
- Yes
- No, it pushes against its own exhaust
An engine throws out 2 kg of gas at 3,000 m/s. How much momentum (kg·m/s) does the rocket gain?
Exhaust speed 3 km/s, mass ratio 10. What is Δv in km/s? (two decimals)
Exhaust speed 4.4 km/s, mass ratio 10. What is Δv in km/s? (one decimal)
Why do rockets use stages?
- To drop empty tanks and engines so the rest has a better mass ratio
- Because one engine cannot be made big enough to light
- To make the rocket taller
Goddard's rocket reached 41 feet. How many metres is that? (one decimal; 1 ft = 0.3048 m)
Saturn V: thrust 34.5 MN, weight 27.5 MN. What is the thrust-to-weight ratio? (two decimals)
In what year did Tsiolkovsky publish his work on rockets in space?
- 1903
- 1926
- 1957
Why does a large rocket seem to rise slowly at first?
- Its thrust is only a little larger than its weight
- The air is thick and stops it
- The engines warm up slowly

Key points

A rocket pushes exhaust back and is pushed forward (Newton's third law); no air is needed.
Rocket equation: Δv = vₑ × ln(m₀ ÷ m_f).
Staging drops dead weight so each stage starts with a better mass ratio.
Goddard flew the first liquid-fuelled rocket on 16 March 1926.
Saturn V: 111 m, 2.8 million kg, 34.5 MN thrust, three stages.

Sources for this course (17)

Town of Auburn MA, Robert Goddard (auburnma.gov/693/Robert-Goddard)
History.com This Day in History, 16 March 1926 (Tsiolkovsky 1903 treatise)
NASA "What Was the Saturn V?" (nasa.gov/learning-resources/for-kids-and-students/what-was-the-saturn-v-grades-5-8)
NASA Earth Fact Sheet (nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html, GM 0.39860 × 10⁶ km³/s², escape velocity 11.186 km/s, sidereal rotation 23.9345 h)
NASA History "The Dawn of the Space Age" (nasa.gov/history/dawn-of-the-space-age)
NASA "April 1961, First Human Entered Space" (nasa.gov/image-article/april-1961-first-human-entered-space)
GPS.gov Space Segment (gps.gov/space-segment)
KARI (kari.re.kr: KOMPSAT-1 1999, Chollian, Nuri launch dates, Danuri contents/193, 194, 196 and news release 2022-12-28)
Korea.kr policy news on the Nuri second launch, 21 June 2022 (korea.kr/news/policyNewsView.do?newsId=148902762)
Korea AeroSpace Administration (kasa.go.kr, founded 27 May 2024)
NASA International Space Station Facts and Figures (nasa.gov/international-space-station/space-station-facts-and-figures)
ISS National Lab on Zarya and Expedition 1 (issnationallab.org/iss360/celebrating-the-20th-anniversary-of-the-first-international-space-station-module)
Korea Herald and Korea.net on Yi So-yeon, 8 April 2008 (koreaherald.com/article/10711787, korea.net/NewsFocus/HonoraryReporters/view?articleId=264742)
NASA Apollo pages (nasa.gov/the-apollo-program, nasa.gov/history/apollo-11-mission-overview, nasa.gov/mission/artemis-ii)
NASA Voyager 1 (science.nasa.gov/mission/voyager/voyager-1) and "What is a light-day" (science.nasa.gov/mission/voyager/voyager-1/voyager-1-what-is-a-light-day)
NASA Stennis Lagniappe July 2015 on New Horizons at Pluto (nasa.gov/wp-content/uploads/2015/05/julylagniappe.pdf)
NASA SVS 5534 Parker Solar Probe (svs.gsfc.nasa.gov/5534).

Checked: 2026-10-18