Spacecraft Propulsion

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Every engine is a compromise: huge thrust or frugal fuel use. Click a bubble to meet the engine.

Engine map: thrust vs. specific impulse

flies in space tested on Earth concept* constant jet power

No engine gives you both

The exhaust jet carries kinetic energy. For a given power you can throw out a lot of mass slowly (high thrust) or a little mass very fast (frugally). Jet power is P = ½ F v_e, so at constant power F = 2P/v_e — that is why everything on the map lines up along diagonal lines.

High thrust: launch, landing, quick maneuvers

To lift off from Earth, thrust must exceed the rocket's weight. Only chemical engines do that (and, in tests, nuclear thermal ones): their propellant itself carries enormous power — the RS-25 delivers about 5 GW to its jet. But v_e ≈ 3–4.5 km/s, so a large Δv needs gigantic tanks.

High specific impulse: long voyages

Electric thrusters accelerate ions to 20–40 km/s, so they use 10 times less propellant. But they only have as much power as the solar panels provide — a few kilowatts — and thrust on the order of tenths of a newton. They are useless for launching from Earth; in a vacuum they push for months.

Tsiolkovsky calculator: how much propellant for a mission?

formula and basics: Rocket

Mission (departing from low Earth orbit, LEO)

Engine

Payload (without engines and tanks)20 t Number of engines1

required Δv—

engine v_e—

mass ratio m₀/m_f—

propellant—

initial mass in LEO—

engine burn time—

total thrust—

electric power—

payloadpower system (electric)tankspropellant

Task: deliver at least 20 t to Mars orbit. Budget: initial mass ≤ 60 t and engine burn time ≤ 3 years.

Simplifications: the Δv values are estimates for circular orbits without plane changes. High-thrust engines make short burns (a Hohmann-type transfer). Electric thrusters push continuously along a spiral, and that costs more Δv. For Mars: escape spiral from LEO ≈ 7.7 km/s + cruise ≈ 5.6 km/s + capture spiral into low orbit ≈ 3.4 km/s. Tanks are 10% of the propellant mass, and the electric power system (panels and power processing units) — 20 kg per kilowatt. We ignore the mass of the chemical and nuclear engines themselves (for nuclear propulsion that is a few tonnes). We also ignore planetary gravity while the engine is burning.

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Fuel and oxidizer burn in the chamber, and the de Laval nozzle turns the heat of the gas into the momentum of the jet.

Combustion chamber and de Laval nozzle

Mach number pressure p/p_c temperature T/T_c ambient pressure

Build an engine

Real engines

Chamber temperature T_c3,600 K Exhaust molar mass M13.5 g/mol Nozzle expansion A_e/A_*69 Chamber pressure p_c20.6 MPa Where does the engine fire?

exhaust v_e—

I_sp here—

exit Mach—

exit p—

exit T—

I_sp in vacuum—

Rocket propellants

What counts is the combustion temperature and the lightness of the exhaust molecules: v_e ∝ √T/M. Hydrogen gives the lightest exhaust (water vapor and excess H₂), so it wins — although it is troublesome: cold (−253 °C) and very low-density. The I_sp values are typical vacuum values.

LOX / LH₂ — hydrogen

I_sp ≈ 450–465 s

RS-25 (Space Shuttle, SLS), RL10, Vulcain. The most efficient chemistry, but hydrogen takes up huge tanks and leaks through the tiniest gaps.

LOX / RP-1 — kerosene

I_sp ≈ 300–350 s

Merlin (Falcon 9), F-1 (Saturn V), RD-180. Dense and easy to store at room temperature, but it leaves soot in the engine.

LOX / CH₄ — methane

I_sp ≈ 350–380 s

Raptor (Starship), BE-4 (Vulcan, New Glenn). Burns cleaner than kerosene, and methane can — in theory — be made on Mars from CO₂ and water.

Solid (APCP)

I_sp ≈ 250–290 s

Ammonium perchlorate + aluminum powder in a rubbery binder. The SLS boosters give about 16 MN of thrust, but once lit, they cannot be shut down.

Hypergolic N₂O₄ / UDMH (MMH)

I_sp ≈ 310–330 s

They ignite on contact and can wait in their tanks for years — ideal for probes and maneuvers. But they are highly toxic and carcinogenic.

Hydrogen peroxide (HTP, 98%)

I_sp ≈ 150–190 s alone · about 300 s with fuel

It decomposes on a catalyst into steam and oxygen. In Poland, HTP engines are developed by the Łukasiewicz Research Network – Institute of Aviation (among others for the ILR-33 Bursztyn — “Amber” — suborbital rocket).

Throttling and restart

A liquid engine can be throttled down (Merlin about 40–100% thrust) and restarted in a vacuum — a must for orbital maneuvers and landing. A solid motor burns to the end.

Landing on the engine

The Falcon 9 first stage brakes with three burns and lands on a barge. That is engine braking in the atmosphere — more in Rocket.

Newton's third law

A rocket does not push against the air. It throws mass backward, and that mass pushes it forward with an equal force — in a vacuum it works even better (Motion and Forces).

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Electric propulsion: xenon ions accelerated by more than a thousand volts — feeble thrust, but it keeps pushing for years.

Inside the thruster

Neutralizer (cathode supplying electrons)

spacecraft potential0 V

ions that escaped100%

Power, voltage, thrust

Propellant gas

Electric power P2.3 kW Accelerating voltage U1,100 V Efficiency η60%

beam v √2eU/m—

I_sp (effective)—

thrust F = 2ηP/v_e—

gas consumption—

Thrust like the weight of a sheet of paper

The NSTAR thruster (Deep Space 1, Dawn) at its full power of 2.3 kW pushes with a force of about 92 mN. A sheet of A4 paper (80 g/m², about 5 g) lying on your palm presses with a force of about 0.05 N.

≈ 1.9sheets of A4 your thrust “weighs”

—Δv after a year of pushing a probe of mass 1,220 kg

Probe mass1,220 kg

We compute it from the Tsiolkovsky equation with constant thrust and dwindling gas. At launch, Dawn weighed about 1,220 kg, including 425 kg of xenon.

Electric propulsion in space

Deep Space 1 flies

1998: the first NASA probe powered mainly by an ion thruster (NSTAR). It flew past the asteroid Braille and the comet Borrelly.

Dawn (2007–2018) record

It entered orbit around Vesta, then flew on to Ceres and entered orbit around a second body — impossible with chemical propulsion. Its ion thrusters ran for almost 6 years in total and gave about 11.5 km/s of Δv — the most any probe has ever gained from its own propulsion.

BepiColombo and Psyche flies

BepiColombo (ESA/JAXA, launched 2018) is flying to Mercury on T6 ion thrusters. Psyche (NASA, 2023) uses SPT-140 Hall thrusters.

Starlink flies

Thousands of satellites with Hall thrusters running on krypton, and since 2023 on argon — cheaper than xenon. They are used to raise orbits, avoid collisions, and deorbit.

Poland: krypton at IFPiLM tests

The Institute of Plasma Physics and Laser Microfusion in Warsaw built, within an ESA program, a prototype krypton Hall thruster (KLIMT, 500 W class), tested among other places at the ESTEC center.

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Light has momentum. A mirror of thin foil catches it without propellant — and can tack around the Sun like a sailboat.

A sail around the Sun

Simulation speed

Set the sail

Sail angle α (← →)+35°

α > 0: the force has a forward component — the orbit grows. α < 0: a backward component — the sail brakes and falls toward the Sun. α = 0: only a push away from the Sun.

Sail

Areal density σ (whole craft)10 g/m²

distance from the Sun1.000 AU

flight time0 days

speed29.8 km/s

light pressure here9.08 µN/m²

characteristic accel. a_c—

fraction of solar gravity—

*The future 10 g/m² sail is a concept — today's sails with payload are about 100–1,600 g/m².

Light pressure

A photon with energy E carries momentum p = E/c. Near Earth the Sun delivers about 1,361 W/m², so absorbed light presses with a force of 4.54 µN on every square meter, and reflected light twice as hard, 9.08 µN/m² (the photon bounces like a ball off a wall).

P_rad = 2Sc cos²αa = 2Sσc·(1 AU)²r²S — solar flux · σ — mass per square meter · the force acts perpendicular to an ideal flat mirror

The pressure falls off as 1/r² — just like the Sun's gravity. That is why the ratio of the two forces is what matters: at σ ≈ 1.5 g/m² light would balance the Sun's pull, and the sail would “hover” in place.

Laser — laser-pushed sails Solar System Quanta — photons

Sails that have flown

IKAROS (JAXA, 2010) flies

The first solar sail in interplanetary space: a square 14 m on a side (about 200 m²), thinner than a hair. It flew past Venus and steered its course by changing the reflectivity of LCD panels along its edges.

LightSail 2 (2019) flies

The Planetary Society's satellite, about 5 kg with a 32 m² sail, showed that you can raise an orbit with light alone — by turning the sail twice on every orbit.

NASA ACS3 (2024) flies

Launched in April 2024, its 80 m² sail deployed in August 2024. A test of light composite booms that should make it possible to build sails of hundreds of square meters.

Breakthrough Starshot concept

Gram-scale probes on sails pushed by a ground-based laser of about 100 GW, up to 20% of the speed of light — Alpha Centauri in about 20 years. The problem: there is no way to brake, so it would be just a fast flyby.

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A reactor instead of combustion: heat from uranium fission warms hydrogen, and the lightest gas shoots out the fastest.

Nuclear thermal rocket (NTR)

Heat up the core

Gas temperature after the core2,700 K What flows through the core?

exhaust v_e (vacuum)—

I_sp—

compare: RS-25 (H₂/O₂)452 s

mass ratio for Δv = 5 km/s—

An ideal-nozzle model (expansion ratio 100, chamber pressure 7 MPa), without molecules breaking apart at high temperature. In reality hot hydrogen attacks the reactor fuel — one of the main engineering problems.

How much energy is in a kilogram of fuel?

If all the energy were turned into exhaust motion, ½v_e² = ε, that is v_max = √2ε. That is the upper limit on exhaust velocity — and the reason chemistry will never exceed about 5 km/s.

Logarithmic scale. Energy per kilogram of total propellant: H₂ + O₂ ≈ 1.3·10⁷ J/kg · U-235 fission ≈ 8·10¹³ J/kg · D–T fusion ≈ 3.4·10¹⁴ J/kg · annihilation ≈ 9·10¹⁶ J/kg (E = mc²). For fusion and annihilation the limit is relativistic.

Nuclear power in space: three different things

What it is	How it works	Thrust?	Status
RTG — radioisotope generator	Decay heat of plutonium-238 (half-life 87.7 years) turned into electricity by thermocouples. No reactor and no moving parts.	no — electricity only (about 110 W on Curiosity and Perseverance)	flies the Voyagers, Cassini, Mars rovers
NTR — nuclear thermal	A fission reactor heats hydrogen, which shoots out through a nozzle. I_sp about 850–900 s, thrust of hundreds of kilonewtons.	yes — high	tested on Earth 1959–1972 (NERVA)
NEP — nuclear electric	A reactor makes electricity (hundreds of kW to MW), which powers ion or Hall thrusters. High I_sp, low thrust, but independent of the Sun.	yes — low, continuous	concept design studies

Radioactivity — plutonium-238 and RTGs Power Plant — fission and fusion Particles — antimatter

NERVA and Rover tested on Earth

Between 1959 and 1972 the US tested more than 20 reactor engines in Nevada. The XE-Prime engine (1969) ran in a flight-like configuration and gave about 250 kN of thrust at an I_sp of about 840 s. The program was shut down in 1973 — not for technical reasons, but for budget ones.

DRACO canceled

A joint DARPA and NASA program was meant to put the first NTR engine into orbit in 2027. It was shut down in 2025 — partly because chemical rocket launches keep getting cheaper. As of 2026: no nuclear thermal engine has ever flown in space.

Project Orion (1958–1965) history

A ship pushed by small nuclear pulse charges detonating behind a pusher plate. Models powered by conventional explosives worked. The project was abandoned — partly after the 1963 treaty banning nuclear test explosions in the atmosphere and in space.

Fusion rocket* concept

Plasma from nuclear fusion released through a magnetic nozzle: I_sp on the order of 10⁴–10⁶ s. The problem: on Earth we do not even have a fusion power plant with net energy gain yet (see Power Plant).

Antimatter rocket* concept

Annihilation turns all of the mass into energy. But all the antiprotons produced in laboratories so far add up to a mass on the order of nanograms, and we store them one by one in traps (see Particles).

Why is there no NTR yet?

Tests that vent straight into the atmosphere, as in the 1960s, are not done today (the exhaust can carry radioactive particles), the reactor has to withstand more than 2,500 K in hot hydrogen, and liquid hydrogen is hard to store for months. The gain, according to NASA studies: a trip to Mars a few months shorter.

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The most important question of space travel: how do you stop?

There are no brakes in space

On Earth you brake by friction against the road or the air. In a vacuum there is nothing to “brace against”: the ship keeps going at the same speed (Newton's first law). To slow down, you have to throw mass forward — turn the ship around and fire the engine against the direction of motion. Braking costs as much propellant as speeding up. Unless along the way there is an atmosphere, a planet to fly past, or starlight.

Speed up, flip, brake

Forget to flip the ship

At speeds above about 0.1 c we use the formulas of special relativity (Relativity): time on the ship runs slower than on Earth.

Continuous-thrust trip calculator

Destination

Constant acceleration a0.01 g

Propulsion (for the propellant estimate)

trip time (Earth)—

ship time—

top speed—

Δv = a·t_ship—

mass ratio—

I_sp for a ratio of 10—

To Mars: how long does it take?

Distance 78 million km (Mars fairly close to Earth). Continuous-thrust trips are computed along a straight line, braking to zero. Logarithmic scale.

A Hohmann transfer is a flight along an ellipse, usually about 7–9 months, with two short burns (more: Rocket). The NTR estimates come from NASA studies — this is not a finished mission plan.

Game: stop at Mars

a ship with 0.01 g propulsion (concept*: high-power nuclear electric propulsion)

How do you brake at Mars?

Δv budget

to Mars—

speed—

Δv left—

mission time—

braking distance—

time warp—

Low-thrust spiral

Show Hohmann transfer

From LEO to GEO by spiral

Starting orbit

Engine acceleration0.001 g Shut off the engine on reaching GEO (or 400 km)

altitude—

speed—

orbits—

time—

Δv used—

Hohmann (2 burns)3.85 km/s

Gravity assist: braking by flyby

Relative to the planet, the ship leaves at the same speed it arrived with — only the direction changes. But relative to the Sun we add the planet's velocity. A flyby in front of the planet (on the side it is heading toward) slows the ship down. That is how MESSENGER and BepiColombo braked on their way to Mercury.

Speed relative to Venus v_∞6.0 km/s Altitude above Venus500 km

Other ways to brake

Aerobraking in use
The probe enters an elongated orbit and then skims the upper atmosphere hundreds of times, slowly circularizing it — it saves propellant but costs months. Magellan did this at Venus, and MGS, Mars Odyssey, MRO, and TGO at Mars (Atmosphere).
Atmospheric entry in use
The Curiosity rover plunged into the Martian atmosphere at about 5.8 km/s. A heat shield, a parachute, and a rocket-powered “sky crane” slowed it to zero in about 7 minutes.
Aerocapture* not flown yet
A single deep pass through the atmosphere instead of a braking burn — straight into orbit. It saves a lot of mass but demands precision and a heat shield. As of 2026: studied among others for missions to Uranus and Neptune, not yet performed.
Magnetic sail* concept
A superconducting loop tens of kilometers across repels the charged particles of the stellar wind or the interstellar medium. It could brake an interstellar ship over decades — with no propellant.
Braking with a sail at a star* concept
A very light sail could brake in the light of the target star — but only at speeds of a few percent of the speed of light, not 20% as in Starshot.

How does it work?

Rocket propulsion throws mass out at high speed in one direction, and the ship gains momentum in the other (Newton's third law). The force with which the engine pushes is the thrust. The speed at which the exhaust leaves is the exhaust velocity v_e. Engineers often quote it as the specific impulse I_sp in seconds: the number of seconds a kilogram of propellant could sustain a thrust equal to its own weight on Earth.

F = ṁ v_e + (p_e − p_a)A_ev_e = I_sp·g₀Δv = v_e ln(m₀/m_f)ṁ — propellant mass per second · g₀ = 9.806 65 m/s² · m₀, m_f — mass with and without propellant · e.g. Δv = 5 km/s at 450 s needs a mass ratio of 3.1, but at 3,000 s only 1.19

The Δv budget

Every maneuver — speeding up, changing orbit, braking — costs a certain change in velocity Δv. We add them up like expenses in a budget, and the Tsiolkovsky equation tells us how much propellant that takes. Braking costs as much as speeding up.

The de Laval nozzle

The gas in the chamber is hot and slow. In the constriction it accelerates to the speed of sound (Mach 1), and in the expanding section it keeps going, supersonically, as it cools. The ideal exhaust velocity grows with temperature and falls with molecular mass:

v_e = √2γγ − 1·RT_cM·[1 − (p_e/p_c)^(γ−1)/γ]γ ≈ 1.2–1.4 — adiabatic index · R = 8.314 J/(mol·K) · M — exhaust molar mass

Electric propulsion and the sail

v = √2qU/mF = 2ηPv_eP_rad = 2Sc ≈ 9.08 µN/m²at 2.3 kW, η = 0.6, and 3,100 s: F ≈ 91 mN (NSTAR: 92 mN) · light pressure near Earth for an ideal mirror

Continuous thrust and the flip maneuver

The ship accelerates at a constant a for the first half of the way, turns 180°, and brakes for the second half. The fastest path at a given acceleration is called a brachistochrone.

t = 2√d/av_max = √a dΔv = a t78 million km at 1 g: about 2.1 days, v_max ≈ 875 km/s, Δv ≈ 1,750 km/s

At high speeds we compute relativistically (τ — time on the ship, d — the whole distance):

τ = 2ca arcosh(1 + a d2c²)t = 2ca sinh(aτ2c)m₀m_f = e^aτ/v_e4.24 light-years at 1 g: about 3.5 years on the ship and 5.9 years on Earth

A spiral instead of a jump

A weak engine cannot do a Hohmann transfer. So it pushes along its motion nonstop, and the orbit slowly grows. Such a spiral costs more Δv (LEO to GEO: |v_LEO − v_GEO| ≈ 4.6 km/s instead of 3.85 km/s), but at an I_sp of 3,000 s it uses several times less propellant.

Simplifications: the engine map shows typical ranges, not every engine model. The nozzle is computed as isentropic flow of an ideal gas with constant γ (the result is usually a few percent better than a real engine). The plume and shock diamonds are drawn schematically. For the ion thruster we take an effective v_e = 0.8 of the beam speed (part of the gas is not ionized, and the beam diverges). The sail is an ideal flat mirror in a single orbital plane; the Sun is a point, and the planets do not attract the sail. The continuous-thrust trip is computed along a straight line (no solar gravity and no planetary motion), and the game is one-dimensional. The spiral is a numerical integration (RK4) of motion in the field of a point-mass Earth with no atmosphere and no oblateness. Engine values are based on data from manufacturers, NASA, and ESA (as of 2026).

Engine map: thrust vs. specific impulse

No engine gives you both

High thrust: launch, landing, quick maneuvers

High specific impulse: long voyages

Tsiolkovsky calculator: how much propellant for a mission?

Combustion chamber and de Laval nozzle

Build an engine

Rocket propellants

LOX / LH₂ — hydrogen

LOX / RP-1 — kerosene

LOX / CH₄ — methane

Solid (APCP)

Hypergolic N₂O₄ / UDMH (MMH)

Hydrogen peroxide (HTP, 98%)

Throttling and restart

Landing on the engine

Newton's third law

Inside the thruster

Power, voltage, thrust

Thrust like the weight of a sheet of paper

Electric propulsion in space

Deep Space 1 flies

Dawn (2007–2018) record

BepiColombo and Psyche flies

Starlink flies

Poland: krypton at IFPiLM tests

A sail around the Sun

Set the sail

Light pressure

Sails that have flown

IKAROS (JAXA, 2010) flies

LightSail 2 (2019) flies

NASA ACS3 (2024) flies

Breakthrough Starshot concept

Nuclear thermal rocket (NTR)

Heat up the core

How much energy is in a kilogram of fuel?

Nuclear power in space: three different things

NERVA and Rover tested on Earth

DRACO canceled

Project Orion (1958–1965) history

Fusion rocket* concept

Antimatter rocket* concept

Why is there no NTR yet?

There are no brakes in space

Speed up, flip, brake

Continuous-thrust trip calculator

To Mars: how long does it take?

Game: stop at Mars

Low-thrust spiral

From LEO to GEO by spiral

Gravity assist: braking by flyby

Other ways to brake

Aerobraking in use

Atmospheric entry in use

Aerocapture* not flown yet

Magnetic sail* concept

Braking with a sail at a star* concept

How does it work?

The Δv budget

The de Laval nozzle

Electric propulsion and the sail

Continuous thrust and the flip maneuver

A spiral instead of a jump

See also

Challenges

Did you know…?

Keys