How orbits actually work

The most common thing people believe about orbit is that it is the place where gravity stops. It is not. At the altitude of the space station, gravity is still about ninety percent as strong as it is in your kitchen.

Newton explained the real answer with a thought experiment about a cannon on an impossibly tall mountain. Fire the cannonball gently and it arcs over and lands. Fire it harder and it lands further away, its path curving as it falls. Fire it hard enough and something strange happens: the ground curves away beneath the ball exactly as fast as the ball falls toward it. It never lands. It just keeps falling, all the way around.

That is an orbit, and there is nothing else to it. A satellite is not held up by anything. It is in permanent free fall, and the astronauts inside are weightless for the same reason someone in a falling lift is: they are falling too, at exactly the same rate. The only thing keeping the whole arrangement off the ground is sideways speed.

For low orbit, the required speed is about 7.7 kilometres per second. That is roughly 27,000 kilometres per hour, Paris to New York in about eight minutes, and it explains why getting to orbit is hard. Reaching the altitude of the space station is the easy part. A high-altitude balloon gets a third of the way. Almost all of a rocket's work goes into the sideways speed, not the height.

Because orbital speed is set by the balance between falling and moving sideways, and gravity weakens with distance, a higher orbit needs less speed, not more. It is also a longer way round. Both effects point the same way, so the further out you go, the longer a lap takes, and the effect is enormous.

The relationship has been known since 1619, when Kepler noticed that the square of a planet's orbital period is proportional to the cube of its distance from the body it circles. The same law governs everything around Earth, and it comes with a catch worth understanding: what matters is distance from the centre of the planet, not height above the ground.

Earth's radius is already 6,371 kilometres, so climbing from 400 to 800 kilometres barely changes how far from the centre you are, and barely changes the lap time. That is why everything in low orbit takes about an hour and a half, whether it is skimming at 300 kilometres or sitting at 1,000. Go far enough out that the extra distance actually counts, and the curve turns sharply upward.

Orbits are ellipses. A circle is just the special case where the ellipse is perfectly even. The closest point to Earth is called perigee, the furthest apogee, and how stretched the ellipse is between them is its eccentricity: zero for a circle, closer to one for a long thin cigar.

The shape changes the experience completely. A satellite falls toward perigee and picks up speed, then climbs away and slows down, so it races through the low part of its orbit in minutes and spends hours loitering out at the top. That is not a nuisance to be corrected. For some missions it is the entire point.

The classic example is the Molniya orbit, designed for a country too far north to see the geostationary ring well from the ground. Instead of hovering over the equator, a Molniya satellite dives past Earth low over the southern hemisphere and then hangs high over the north for most of its twelve-hour circuit.

The last thing that defines an orbit is how it is tilted relative to the equator, called its inclination. Zero degrees means orbiting exactly around the equator. Ninety degrees means passing over both poles. Anything above ninety means going around the planet against its rotation.

Inclination decides what a satellite can see and who it can talk to, and it is expensive to change once you are up there, so it is chosen carefully before launch. The result is that inclination is not spread evenly at all. Count what is in orbit degree by degree and it forms sharp spikes, each one a design decision made thousands of times over.

A satellite can only fly over the latitudes its tilt allows. An orbit inclined 51.6 degrees, like the space station's, passes over everything between 51.6 degrees north and south, which covers most of the inhabited world but never takes it over Iceland. To photograph the entire planet you need a near-polar orbit, and to serve high latitudes you need either a steep inclination or a Molniya-style ellipse.

Launch sites push back. A rocket gets a free head start from Earth's own rotation, up to 465 metres per second at the equator, but only if it launches roughly eastward. And a launch site cannot easily reach an inclination lower than its own latitude without an expensive turn. That is why equatorial spaceports are prized for geostationary missions, and why so many Russian satellites sit at high inclinations: Baikonur is at 46 degrees north.

The sun-synchronous trick. Earth is not a perfect sphere. It bulges at the equator, and that extra mass tugs at an orbit and makes its plane rotate slowly over months. Rather than fight it, mission designers use it: at about 98 degrees of tilt the rotation comes out to exactly one turn per year, matching Earth's trip around the Sun. The satellite then crosses the equator at the same local time every single pass, so a picture taken today has the same shadows as one taken next spring, and the solar panels never end up in the dark.

Put altitude and shape together and orbits fall into four families, each with its own economics and its own traffic.

A real orbit is never quite the neat ellipse of the textbook, because Earth is not a neat sphere and space is not quite empty. Three effects nudge every satellite, constantly.

The equatorial bulge makes the orbit plane rotate, degrees per day in low orbit. That is the effect the sun-synchronous orbits harness, and the one that makes constellation planning a three-dimensional puzzle.

Atmospheric drag steals energy from anything in low orbit and eventually brings it down. The space station loses altitude continuously and is reboosted several times a year; a satellite without propulsion simply comes home on its own schedule, which is exactly why the low shells stay clean.

Everything else tugs too: the Moon and Sun, the pressure of sunlight itself, and the lumpy gravity field of a planet whose mass is not evenly distributed. Geostationary satellites drift toward two stable longitudes and burn fuel every couple of weeks to stay in their assigned slot. When that fuel runs out, the mission is over regardless of how healthy the electronics are.

The counterintuitive part comes last. In orbit you cannot simply steer. Every change of path is a change of speed, paid for in propellant you had to carry up, and the currency has a name: delta-v, the total change in velocity a spacecraft can produce.

Raising an orbit takes two burns. Fire the engine forward and the far side of the orbit stretches outward; coast half a lap to the new high point, then fire again to round the orbit out there. That two-burn manoeuvre is the Hohmann transfer, and it is the cheapest way between two circular orbits. It is also why moving from low orbit to geostationary takes hours, not minutes.

Changing the tilt is far worse. Inclination is not something you can adjust gently: you have to swing the entire velocity vector sideways, and in low orbit that vector is 7.7 kilometres per second long. A 30 degree turn costs about as much propellant as launching to orbit in the first place. This is the single reason inclination is chosen on the launch pad and almost never revisited, and the reason the histogram above has such sharp spikes.

There is one elegant loophole. Do the turn at apogee, where the satellite is moving slowly, and the same change of direction costs a fraction as much. Missions heading for geostationary orbit use exactly that trick: climb out to 36,000 kilometres first, do the plane change up there where velocity is cheap, then circularise.