On the one hand, satellites in geosynchronous orbits look, from afar, like they're orbiting

the earth just like any other satellite.

But from down here, they appear to be floating, stationary, thirty-six thousand kilometers

above our heads [a tenth of the way to the moon].

Because by definition, a geosynchronous orbit is in sync with the rotation of the earth

- it takes the same amount of time for one orbit as the earth takes for one full rotation

[aka a day] - so even though it's orbiting like normal around the earth's center of mass,

it's stationary with respect to the earth's surface.

[Fullscreen onscreen footnote: \* Ok technically only the geo*stationary* orbits are actually

stationary above you, because they orbit around the equator.

Geo*synchronous* orbits take the same time as the earth to rotate, but are at other angles

and so appear to drift up and down in latitude [\*and longitude] while while floating overhead.

But regardless of whether they're geosynchronous or geostationary, they're possible because

of two things:]

Geosynchronous orbits are possible because of two things: Kepler's laws, and the fact

that we live on a pile of rock.

Kepler's third law is the observation that the farther you are from a planet or dog or

whatever, the longer it takes to complete an orbit.

The reasons are partly that you have to travel a longer distance to orbit around a bigger

circle [ellipse - or near-ellipse in GR], compounded by the fact that gravity is weaker

farther out so you can't go as fast along the circle [centripetal force & all that].

But anyway, the point is that a super big orbit takes basically forever, and the closer

you get the less and less time an orbit takes.

So [by the intermediate value theorem,] somewhere in there is a time that's exactly in sync

with the amount of time it takes the planet itself to spin around once.

Hence, "geosynchronous" [or dog-synchronous, or whatever.]

And when you orbit in exactly the same time it takes the planet to spin, for someone on

the planet, you appear to just float overhead.

[*onscreen note: again, technically that's only true for geostationary orbits... geosynchronous

ones have a bit of side-to-side drift]

[If you're in an orbit that's bigger than a geosynchronous orbit, you appear to travel

"backwards" through the sky (to the west on earth), and if you're closer in, then you

speed ahead to the east.

The fact that geosynchronous orbits don't move relative to the surface is why they're

useful:] And that's the reason geosynchronous orbits are useful - if you can put a satellite

just floating above you at all times, it'll also be floating above most other people and

places on your side of the earth, too, and you can use it to send messages or television

signals to them.

While mountains might block the view between you, the satellite will always be up there

with a clear line of sight.

But there are two potential problems with geosynchronous orbits.

The first is: they don't always exist.

The faster a planet is rotating, the closer you have to be to it in order to be in a geosynchronous

orbit, so what if the planet is spinning so fast you'd have to be inside it to be in sync?

Well that's certainly a potential problem if you're orbiting a ball or a dog or something

held together by internal tension forces [electromagnetic forces]: a solid steel ball with a 1meter

radius spinning once per hour has geosynchronous orbits that are inside it.

But most things you can orbit are held together by gravity - the same force that causes you

to orbit - and a planet that's held together by gravity can only spin so fast before bits

of the planet itself start getting flung off.

When a planet is spinning at this maximum speed, the physics works out that a geosynchronous

orbit would exactly coincide with the surface of the planet.

For any slower spin rate, a geosynchronous orbit is farther from the planet's surface.

So if you're orbiting something like the earth, which is basically a pile of rock held together

by gravity, there will always technically be geosynchronous orbits.

And this brings us to the second potential problem with geosynchronous orbits: even if

they exist, they're not guaranteed to be useful.

If a planet is spinning quickly, geosynchronous orbits around it might be too close to see

much of the planet's surface.

For example, if earth took 90 minutes to spin instead of 24 hours, geosynchronous orbits

would be at an altitude of around 280 kilometers – beneath the orbit of the international

space station – and satellites there could only see 2% of the earth's surface at one

time – not very useful for communications!

On the other hand, if a planet is spinning too slowly, geosynchronous orbits will be

super far away.

Sure, a satellite might see nearly half of the planet's surface from there, but it would

be much harder to put satellites into that orbit, you'd need super powerful antennas

to send signals back and forth, and there would be a long delay while you wait for the

signal to get there and back.

For example, satellites in a geosynchronous orbit around Venus - I mean, a venusynchronous

orbit - would be 4 times farther from Venus than the distance from the earth to the moon,

so all communications signals would have a 10-second round-trip delay: Satellite TV wouldn't

work on Venus.

And a geosynchronous orbit around the sun - I mean, a helio-synchronous orbit - would

be half way to the planet Mercury with a nearly 3 minute round-trip signal delay!

[note: a day on the sun is not well defined since different parts of it rotate at different

speeds].

So as weird as geosynchronous orbits are, it's perhaps even weirder that we happen to

live on a planet that's not just in the goldilocks zone for life, but also in the goldilocks

zone for satellite TV.

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