Orbiting is not floating above the Earth. It is falling, sideways, so fast that you keep missing. Everything about spaceflight follows from that, and from one equation that punishes every kilogram.
The International Space Station is only about 400 km up. At that height gravity is still 88% as strong as on the ground. The astronauts float because they and the station are in free fall, together, all the time. They are falling toward Earth at every moment, and moving sideways so fast that the Earth curves away beneath them as fast as they fall.
Isaac Newton described it in 1687. Imagine a cannon on top of a very tall mountain firing horizontally. Fire gently and the ball lands nearby. Fire faster and it lands farther. Fire fast enough and the ground curves away beneath the ball as it falls, and it never lands. That speed is the circular orbital velocity:
At 400 km it is about 7.7 km/s, which is 27,600 km/h. One lap takes about 92 minutes, so the ISS crew sees 16 sunrises a day. Go faster and your orbit stretches into an ellipse. At exactly √2 times the circular speed, the path stops curving back. This is escape velocity: about 11.2 km/s from Earth's surface, 10.9 km/s from 400 km up. Go any faster and you leave for good, though you never escape gravity entirely; it just fades away.
The lab on the next tab lets you fire the cannon yourself.
In 1903 a nearly deaf Russian schoolteacher named Konstantin Tsiolkovsky published the key result. A rocket moves by throwing mass backwards. The speed it gains, its delta-v, depends on how fast it throws the exhaust (ve) and on the ratio of its starting mass to its finishing mass:
The ln is a logarithm (there is a button for it on any scientific calculator), and it is the problem. To get a bit more speed you must carry exponentially more fuel. Fuel itself needs more fuel to carry it. Reaching low Earth orbit takes about 9.4 km/s of delta-v (7.7 for the orbit and the rest lost to gravity and air drag), and the best chemical rockets, with exhaust speeds of about 4.4 km/s, need roughly 88% of the launch mass to be propellant. A Saturn V managed to put about 5% of its launch mass into orbit, and about 1.6% on the way to the Moon.
The fixes are all clever ways around the same equation: staging (dropping empty tanks), reuse (landing the boosters; the first Falcon 9 landing was in December 2015), and better exhaust speed. An ion engine, such as the one on NASA's Dawn mission, throws charged atoms out at 30 km/s or more, many times faster than chemical fuel. But its thrust is only about the weight of a couple of sheets of paper, so it takes months of gentle pushing. Dawn became the first spacecraft to orbit two different bodies, Vesta and then Ceres.
If fuel is so expensive, can speed be had for free? Yes, by a gravity assist. A spacecraft that swings past a moving planet can leave with a different speed relative to the Sun. It takes a tiny amount of the planet's orbital momentum, and the planet slows by an amount too small to measure.
In 1964 a young aerospace student, Gary Flandro, noticed that the four giant planets would line up in the late 1970s in a way that happens only about once every 175 years. A spacecraft launched at the right moment could visit all four, using each planet to sling it on to the next. NASA launched two spacecraft in 1977. Voyager 2 visited Jupiter (1979), Saturn (1981), Uranus (1986) and Neptune (1989), and remains the only spacecraft ever to visit Uranus or Neptune. Voyager 1 took a faster path out of the plane of the planets.
Today both are in interstellar space (Voyager 1 crossed the boundary of the Sun's bubble in 2012, Voyager 2 in 2018). Voyager 1 travels at about 17 km/s, or 3.6 AU a year (an AU is the Earth–Sun distance, about 150 million km). NASA expects it to be one light-day from Earth, about 173 AU, around November 2026. Its radio signals, from a transmitter with the power of a refrigerator bulb, now take almost a day to arrive. It also carries a golden record of sounds and images from Earth.
The fastest object ever built is the Parker Solar Probe, which used repeated Venus flybys to lose orbital energy and fall closer and closer to the Sun. On 24 December 2024 it passed 6.1 million km from the Sun's surface at about 192 km/s (692,000 km/h).
The nearest star beyond the Sun, Proxima Centauri, is 4.24 light-years away, which is about 268,000 AU, or more than 1,500 times farther than Voyager 1 has travelled in nearly fifty years. At Voyager's speed the trip takes about 75,000 years. Even the Parker Solar Probe's speed would take more than 6,000.
The most serious proposal so far is Breakthrough Starshot, announced in 2016: chips weighing a gram, attached to light sails and pushed by a huge array of lasers to 20% of the speed of light, reaching Proxima in about 20 years. It is a concept, not a project. Dust grains hitting a chip at 60,000 km/s, building a laser array of that power, and sending back a signal are all unsolved. Every other idea (fusion rockets, antimatter, enormous generation ships) is even further out. Einstein's relativity adds one more twist: at very high speed, clocks aboard the ship run slow, so the trip feels shorter to the travellers than to people on Earth. Try it in the lab.
You launch a spacecraft sideways from 400 km above the Earth. Try different speeds. Air resistance is ignored. Speeds are in kilometres per second.
Choose an engine and how much of the rocket's mass is fuel. See the speed you can reach and how little is left at the end for payload.
Proxima Centauri is 4.24 light-years away. Pick a speed. Times ignore the time spent speeding up and slowing down.
Five questions.
A younger friend asks: “Why don't astronauts in the space station fall down?” Answer without using the word zero-gravity. Use falling, sideways speed and orbit. Then explain why a rocket needs so much fuel, using the rocket equation.