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Spaceflight

Spaceflight is travel beyond Earth's atmosphere, made possible by rockets that push themselves forward by throwing exhaust backwards. Reaching orbit means going sideways fast enough — about 8 km/s — to keep falling around Earth without hitting it, and the rocket equation shows why most of a rocket's launch weight must be propellant. Since Sputnik in 1957, spaceflight has carried satellites, telescopes and people into orbit and astronauts to the Moon.

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Deriving and Applying the Rocket Equation

In a short time a rocket of mass M ejects a small mass of exhaust. Conserving momentum for the rocket and exhaust, and using the effective exhaust velocity, gives the relation below; integrating it from the full mass to the empty mass gives the ideal rocket equation.

M du=−Veq dM  ⇒  Δu=Veqln⁡mfme,Veq=Isp g0M\,du = -V_{eq}\,dM \;\Rightarrow\; \Delta u = V_{eq}\ln\dfrac{m_f}{m_e}, \qquad V_{eq} = I_{sp}\,g_0

Momentum balance, its integral, and the link between effective exhaust velocity and specific impulse.

Inverting it, the mass ratio is e raised to the power Δu ÷ exhaust velocity. With an exhaust velocity of 3 km/s, gaining 8 km/s needs a mass ratio of about 14. NASA's example for a hydrogen–oxygen engine (specific impulse about 350 s) reaching a 200-mile orbit gives a mass ratio of about 10 — roughly 90% propellant and only about 1% payload.

Δu=Veqln⁡(MR)−g0 tb\Delta u = V_{eq} \ln(MR) - g_0\,t_b

Including gravity during the burn: the loss grows with the burn time.

Full explanation — the complete reference version every reading depth is based on

What it is

A rocket engine burns fuel with an oxidiser it carries on board and blasts the hot gas out of a nozzle. By Newton's third law, pushing the exhaust backwards pushes the rocket forwards. Because it brings its own oxidiser, a rocket works in the vacuum of space, unlike a jet engine or propeller, which needs air.

Getting into orbit

An orbit is not a place where gravity stops; it is a path of continuous falling. A spacecraft in low orbit moves sideways so fast that the curve of its fall matches the curve of Earth's surface, so it keeps falling but never hits the ground. The International Space Station does this at about five miles (8 km) per second, going round every 90 minutes. To leave Earth for good needs about 11.2 km/s, the escape velocity.

Δu=Veqln⁡ ⁣(mfullmempty)\Delta u = V_{eq} \ln\!\left(\dfrac{m_{\text{full}}}{m_{\text{empty}}}\right)

The ideal rocket equation: the change in velocity from the effective exhaust velocity and the full-to-empty mass ratio (lift and drag ignored).

Why rockets are mostly fuel

The velocity gain depends on the logarithm of the mass ratio, so each extra kilometre per second costs disproportionately more propellant. NASA's worked example for a hydrogen–oxygen rocket reaching a 200-mile-high orbit gives a mass ratio of about 10: roughly 90% of the launch weight is propellant, the remaining 10% is structure, engines and payload, and the payload is only about 1%.

Worked example

A rocket with an effective exhaust velocity of 3 km/s and a full-to-empty mass ratio of 4 gains Δu = 3 × ln 4 ≈ 4.2 km/s, ignoring drag and gravity (our own calculation with illustrative numbers). Turning the equation round shows that reaching 8 km/s with the same engine would need a mass ratio of about 14.

mfullmempty=eΔu/Veq=e8/3≈14\dfrac{m_{\text{full}}}{m_{\text{empty}}} = e^{\Delta u / V_{eq}} = e^{8/3} \approx 14

The rocket equation inverted to give the mass ratio needed for a chosen velocity change.

Milestones

  1. 4 October 1957: the Soviet Union launches Sputnik 1, the first artificial satellite, beginning the space age.
  2. April 1961: Yuri Gagarin becomes the first human in space, orbiting Earth in Vostok 1.
  3. July 1969: Apollo 11 makes the first crewed Moon landing; Neil Armstrong is the first person to set foot on the Moon.
  4. November 2000 onwards: the International Space Station has been continuously occupied, circling Earth 16 times a day.
Common misconception: A common misconception is that astronauts float because there is no gravity in space. At the space station's height gravity is about 90% as strong as on the ground; the crew float because they and the station are falling around Earth together.
Common misconception: Another is that a rocket needs air to push against. It pushes on its own exhaust, which is why rockets can work in the vacuum of space.

Where it connects

Spaceflight is applied physics: thrust is Newton's third law (Forces), the rocket equation follows from conservation of momentum (Momentum), and orbits are governed by gravity (Gravity) and Kepler's laws (Solar System). It carries space telescopes above the atmosphere (Telescopes), and satellite navigation must correct for relativity (Space-time).

Assumptions and limits

  • The ideal rocket equation ignores lift and drag; adding gravity subtracts g₀ multiplied by the burn time, so real rockets need even more propellant.
  • NASA's 1% payload figure is for its idealised example, not for any particular rocket.
  • The worked example's exhaust velocity and mass ratio are illustrative numbers, not data for a real engine.

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Sources and methodology

  • In a rocket engine, stored fuel and stored oxidiser burn in a combustion chamber and the hot exhaust is accelerated out through a nozzle; thrust is produced according to Newton's third law of motion. (awaiting scientific review)
  • Because a rocket carries its oxidiser on board, it can produce thrust in a vacuum, where jet engines and propellers, which rely on the surrounding air, cannot work. (awaiting scientific review)
  • The ideal rocket equation says a rocket's change in velocity equals its effective exhaust velocity multiplied by the natural logarithm of its full-to-empty mass ratio, neglecting lift and drag; including gravity subtracts g₀ multiplied by the burn time. (awaiting scientific review)
  • In NASA's worked example of the ideal rocket equation, a liquid hydrogen–liquid oxygen rocket with a specific impulse of about 350 seconds needs a mass ratio of about 10 to reach a 200-mile-high orbit, so about 90% of its launch weight is propellant and the payload only about 1%. (awaiting scientific review)
  • The International Space Station travels at about five miles per second and orbits Earth about every 90 minutes, making 16 orbits a day. (awaiting scientific review)
  • The escape velocity from Earth's surface is 11.186 kilometres per second. (awaiting scientific review)
  • Astronauts in orbit float not because gravity is absent — at the space station's altitude it is about 90 percent of its surface strength — but because they and their spacecraft are falling around Earth together. (awaiting scientific review)
  • On 4 October 1957 the Soviet Union launched Sputnik 1, humanity's first artificial satellite, into Earth orbit, beginning the space age. (awaiting scientific review)
  • In April 1961 Yuri Gagarin became the first human to travel into space, launching to orbit aboard Vostok 1. (awaiting scientific review)
  • Apollo 11 launched on 16 July 1969 and made the first crewed landing on the Moon, where Neil Armstrong became the first human to set foot on the lunar surface. (awaiting scientific review)
  • The International Space Station has been continuously occupied since November 2000. (awaiting scientific review)

Claims marked “awaiting scientific review” cite the sources listed but have not yet been signed off by a scientific reviewer.

Content status: published 1 October 2026.

  • Scientific review: this version has not yet been signed off by a scientific reviewer.
  • The Advanced explanation has not yet been reviewed for age suitability.