How rockets reach orbit: why going sideways matters more than going up

Newton imagined a cannon on a high mountain firing a ball horizontally. The faster the ball leaves, the farther it lands, and at a high enough speed the Earth's surface curves away as fast as the ball drops, so the ball never lands. For a low Earth orbit at around 400 kilometres, that speed is about 7.8 kilometres a second. Astronauts are weightless not because gravity is absent but because they and their craft are in continuous free fall.

A rocket accelerates by throwing mass backwards, and the relationship between the speed it can gain, the speed of its exhaust and the share of its mass that is fuel was worked out by the Russian schoolteacher Konstantin Tsiolkovsky, who published it in 1903. The relationship is logarithmic, which is bad news: to get a little more speed you need a great deal more fuel, and the extra fuel itself has to be lifted.

The result is that a launch vehicle is mostly propellant. At lift-off, around nine-tenths of the mass of a typical rocket is fuel and oxidiser, and the satellite on top is a small fraction of the total.

To make the best of this, rockets are built in stages. When the first stage has burned its fuel, it is dropped, and the second stage lights, no longer carrying the weight of the empty tanks. India's workhorse Polar Satellite Launch Vehicle has four stages, alternating solid and liquid fuel. Larger vehicles such as the LVM3 use a cryogenic upper stage, which burns liquid hydrogen and liquid oxygen, a combination that gives more thrust for each kilogram of propellant.

Strap-on boosters are fitted alongside the first stage to give extra thrust at the start, and a streamlined fairing protects the satellite through the thick air and is thrown off once the rocket has climbed above most of the atmosphere.

A rocket rises vertically at first to get out of the densest air, then tilts over gradually, in what is called a gravity turn, and picks up speed horizontally. The moment of greatest stress on the vehicle, called max-Q, comes about a minute in, when it is moving fast in air that is still fairly thick. After the stages have done their work, the final burn puts the satellite into the orbit that was planned for it.

Low Earth orbit, a few hundred kilometres up, is used for crewed stations and for many imaging and communications satellites. Sun-synchronous orbits pass over each place at the same local time every day, which suits Earth observation. Geostationary orbit, at 35,786 kilometres above the equator, is the one altitude at which a satellite takes exactly a day to circle the Earth, so it appears fixed in the sky, which suits broadcasting and weather satellites.

India's launches take place at the Satish Dhawan Space Centre on the island of Sriharikota, on the east coast, at about 14 degrees north. Launching east lets rockets use the Earth's rotation, which at that latitude gives them about 0.45 kilometres a second for free, and the sea to the east is the safest place for dropped stages to fall.

Because most of the cost of a launch is the vehicle that is thrown away, reusing it is the biggest lever on cost. SpaceX landed an orbital-class booster for the first time in December 2015, and India has tested a winged reusable vehicle in landing experiments. In a launch headline, the numbers to look for are the payload mass and the orbit it is going to, because carrying one tonne to low Earth orbit is far easier than carrying it to geostationary transfer orbit. And a successful launch is not a successful mission: it is only the first step.

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