Hanging still versus racing around

Why does one satellite hover over a single city while another must circle the world hourly?

A television dish bolted to a wall points at one fixed patch of sky and never moves again for twenty years. The satellite it is aimed at is genuinely parked there. Meanwhile a broadband satellite passing overhead is gone in a few minutes, and to get an uninterrupted signal you need thousands of them handing you off to one another like a relay team.

Both are satellites. Both are in free fall around the same planet. So the first thing to establish is whether the difference is a design choice at all — or whether the engineers had no say in it.

Consider what "hovering" even means for something in orbit. Nothing is holding it up; it is falling, continuously, and missing. So a satellite cannot hang still over a city in any absolute sense. The most it can do is go round the Earth at exactly the rate the Earth turns, so that from the ground it appears not to move.

Now the constraint that decides everything. For a circular orbit, the period is fixed by the radius alone — Kepler's third law, period squared proportional to radius cubed. You do not get to choose them separately. So how many altitudes give you a period equal to one rotation of the Earth?

Exactly one. Setting the period to a sidereal day, 23 hours 56 minutes and 4 seconds, gives an orbital radius of about 42,164 kilometres from the centre of the Earth — some 35,786 kilometres above the surface. And it must be circular, and it must lie in the equatorial plane, because any inclination makes the satellite trace a figure-of-eight in the sky rather than sitting still.

So "hovering" was never a capability that could be dialled in. It is a single point in the space of orbits, and everything else about that satellite follows from having chosen it.

What follows? Ask what 35,786 kilometres costs. Light covers it in about 0.12 seconds, so a signal that goes up and back down again arrives roughly a quarter of a second after it left, and a round trip — your request up and down, the reply up and down — takes about half a second before anything else happens. For a broadcast that is irrelevant. For a voice call it is the awkward pause everyone recognises; for anything interactive it is disqualifying.

There is a second cost that gets less attention. Signal strength falls with the square of distance. A geostationary satellite is roughly sixty-five times further away than one at 550 kilometres, which is a factor of several thousand in received power — paid for with large dishes, high power, and narrow beams.

And a third: from that height the satellite sees a huge cap of the Earth, close to two-fifths of the surface, so three of them nearly girdle the planet. But it sits over the equator, so from high latitudes it appears low on the horizon, and beyond about 81 degrees of latitude it is below the horizon entirely. The far north and the far south simply cannot be served this way.

Now run the reasoning the other way. Suppose you want the quarter-second gone. That means being close, which by the same law means a short period — about 95 minutes at 550 kilometres — and a ground speed of roughly 7.6 kilometres per second. Any given satellite is above your horizon for only a handful of minutes. So the price of low latency is not paid in altitude, it is paid in number: to have one always overhead everywhere, you need a constellation of thousands, plus continuous handover, plus the collision and disposal problems that come with a crowded shell.

Notice what has happened. We never made a trade between latency and coverage directly. We chose an altitude, and gravity handed us the rest as a package.

The misconception worth dislodging is that geostationary and low orbits are two points on a smooth dial that a mission planner tunes. They are not. Geostationary is a unique solution to an equation — one radius, one eccentricity, one inclination — and it is chosen when apparent stillness is the requirement, accepting a quarter-second delay, weak signal and no polar coverage as the fixed price.

It also helps to see that intermediate answers exist and are used, which shows the trade is real rather than binary. Navigation satellites sit in medium orbits with half-day periods: they move across the sky, so you need a couple of dozen rather than three or three thousand, and you get better geometry at high latitudes. Highly elliptical orbits do something cleverer still — a satellite near apogee moves slowly across the sky, so it dwells for hours over high latitudes that no equatorial satellite can reach, at the cost of needing a small relay of them and of crossing the radiation belts twice a lap.

One honest simplification: I have treated the orbit as ideal. Real geostationary satellites are not truly still. The Earth's equatorial bulge and the pull of the Sun and Moon drag them off station continuously, so they must burn fuel to hold position — and when the fuel runs out, that, rather than any failure of the hardware, usually ends the mission.

• Why highly elliptical orbits dwell over high latitudes, and what apogee has to do with it.
• How station-keeping fuel, rather than component failure, sets a satellite's working life.

Every term the collection defines is gathered in the glossary.