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• Geosynchronous orbits are weird.

• 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 kilometersbeneath the orbit of the international

• space stationand satellites there could only see 2% of the earth's surface at one

• timenot 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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Geosynchronous orbits are weird.

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# Geosynchronous Orbits are WEIRD

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Summer posted on 2022/10/24
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