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### Author Topic: Why is there only one geostationary orbit altitude?  (Read 1085 times)

#### svenrufus

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##### Why is there only one geostationary orbit altitude?
« on: 26/05/2016 20:01:40 »
I've been trying to get my head round the idea that all geostationary orbits have to be at the one possible altitude (~35000 km).

I would have thought that if the satellite gets stuck up a bit higher, and thus travels faster to maintain position, this would allow it to still be geostationary. I'd assumed that the height of the orbit would be determined by the mass of the satellite, but apparently the geostationary orbit height is independent of mass.

Can someone explain this to me in words - the equations that I've been looking at online are leaving me with a headache.

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#### chiralSPO

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #1 on: 26/05/2016 20:22:12 »
First, let's address the mass independence:

If we ignore the effects of drag from the air (which don't apply in space, and don't really apply to reasonably dense objects near the ground) all object fall to the ground at the same rate. A marble and a bowling ball, when dropped from the same height should reach the ground at nearly identical times. This is because the Earth's gravity exerts more force on more massive objects, and it take more force to make a more massive object move (and these two trends cancel out exactly!). The same is true for orbital velocities (orbiting is a special case of falling.)

Now let's address the speeds of different orbits:

The force that the Earth's gravitational field has on an object decreases as that object gets farther and farther away. It turns out that the force decreases with distance squared (so an object three times as far from the center of the Earth feels only 1/9 the force). So a bowling ball will take slightly longer to fall 10 meters when dropped from a very high weather balloon that it would from 10 meters above the ground (and significantly longer if dropped from as far away as the moon is).

If we assume that an orbit follows a circular path (a reasonable assumption for this discussion), then the length of the orbit is the circumference of the circle, and the radius of the circle is the distance from the object to the center of the Earth. If the distance of the object is increased by a factor of three, the path of the orbit also increases by a factor of three (because the circumference of a circle is equal to the radius times 2π).

So, if moving an object three times farther from the Earth decreases the force by a factor of nine, and increases the path it needs to take by a factor of three, it will obviously take much longer for the object to make one full orbit. Essentially, the farther away from the Earth the orbit is, the longer it will take.

An example: The International space station is only about 250 miles above the ground (~4250 miles from the center of the Earth), and orbits every 90 minutes. A Geostationary orbit is about 22000 miles above the ground (~26000 miles from the center of the Earth), and orbits every 24 hours. The moon orbits at about 240000 miles, and completes an orbit every 27 days.

Therefore for an object in geostationary orbit, if it begins to move away from the Earth, it will take longer than 24 hours to orbit, and if it moves closer to the Earth, it will take less than 24 hours to orbit, no matter how massive that object is (as long as the Earth is much, much more massive)

Hope this helps!

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#### chris

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #2 on: 26/05/2016 22:13:48 »
So what you're saying is that because objects "fall" to Earth at the same rate regardless of their mass, and the farther something is from Earth the slower it accelerates (falls) downwards because the gravity field is weaker, there's only a single altitude at which things are "falling" towards Earth at the right rate that equates to the speed at which the Earth is turning. As a result, as they fall, relative to the Earth's surface they stay in the same place?

#### evan_au

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #3 on: 26/05/2016 22:34:24 »
Quote from: svenrufus
I would have thought that if the satellite gets stuck up a bit higher, and thus travels faster to maintain position, this would allow it to still be geostationary.
It is theoretically possible to have a satellite higher than "Geostationary orbit" still take 24 hours to orbit the Earth - but it needs to travel faster than the natural orbital period to make it around the Earth in 24 hours. And it takes an additional force to keep it in orbit (more than the force that is provided "for free" by gravity). Such a space probe would need to be firing its engines continually, 365 days per year. A practical satellite would run out of fuel in hours.

This is why satellites use Geostationary orbit. They can sit there for 15 years, and just use a small amount of fuel for "station-keeping", ie cancelling out the smaller gravitational tugs of the Moon and the Sun. Communications satellites carry enough fuel for 15 years of station-keeping, plus a reserve to move them into a "Parking orbit" when their useful lie is over.

The recent "SkyMuster" satellite uses an ion drive for station-keeping, which means it needs even less fuel mass.

Quote
the geostationary orbit height

This "magic" height was highlighted by Arthur C. Clarke (perhaps better known for his science fiction story 2001 - A Space Odyssey). This allows a satellite to sit at a fixed position in the sky, relative to the Earth, and carry communications.

But this height is not "fixed" - it depends on the rotation speed of the Earth. This speed is slowly decreasing over time, as the tides wash backwards and forwards every day. So Geosynchronous orbit is slowly getting higher - but its not going to get close to the Moon any time soon.

Some other orbits are also used for communications - from Russia, Geostationary orbits are inconveniently near the horizon, so they use an elliptical orbit which spends considerable time in high latitudes. But it requires steerable antennae.

See: https://en.wikipedia.org/wiki/Geostationary_orbit

#### jeffreyH

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #4 on: 27/05/2016 00:11:10 »
The strangest thing about orbit or freefall is that differing mass density has no effect on gravitational acceleration. Within what could be considered a normal range of densities. So this would naturally exclude black holes and very sparse gas clouds. This is why geometry seems to be an apt description of spacetime within a gravitational field. This does not seem to fit well with a smooth flux of force carriers through a surface. How can this not be affected by density?

#### Alan McDougall

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #5 on: 27/05/2016 01:21:06 »
I've been trying to get my head round the idea that all geostationary orbits have to be at the one possible altitude (~35000 km).

I would have thought that if the satellite gets stuck up a bit higher, and thus travels faster to maintain position, this would allow it to still be geostationary. I'd assumed that the height of the orbit would be determined by the mass of the satellite, but apparently the geostationary orbit height is independent of mass.

Can someone explain this to me in words - the equations that I've been looking at online are leaving me with a headache.

What about the Lagrange points between the moon and earth, if an object were placed there it would be far more stable situation, than any geocentric orbit?

#### evan_au

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #6 on: 27/05/2016 12:11:55 »
Quote from: Alan McDougall
What about the Lagrange points between the moon and earth?
These Lagrangian points are fixed in the Earth-Moon system, ie they rotate once around the Earth every time the Moon rotates around the Earth, ie once every 27.3 days.
• This also means that the satellite is invisible half of the time, from any given point on Earth.
• And when you can see it, you need a tracking dish to track it across the sky, which is more expensive and more likely to malfunction.
• It is about 10 times farther away from the Earth than geosynchronous orbit (nearer the Moon at 380,000km, compared to geosynchronous orbit at 35,000km)
• This means that transmitters have to be about 100 times more powerful (due to the inverse square law)
• Communication delays are about 10 times greater; interactive voice communications becomes impossible (it takes a bit of effort even via geosynchronous satellite).
• Internet browsing is already slow from geosynchronous orbit; it would be 10 times worse at Lunar Lagrange points.
• There are 5 Lagrangian points, of which one is on the other side of the Moon. This gives 4 satellite locations visible from Earth, compared to the 180 satellite slots at 2 degrees separation for geosynchronous satellites sharing the same frequency bands.

For effective communications, a 24-hour orbit is very much preferred, compared to a Lunar Lagrangian point, since the geosynchronous satellite sits in a fixed position in the sky, as seen from Earth's surface.

Quote
if an object were placed there it would be far more stable situation, than any geocentric orbit
Of the 5 Lagrangian points, only 2 are stable (ie at L4 and L5, a satellite will stay there, provided the cyclic gravitational tugs of the Sun and Jupiter don't build up an oscillation that gets too large).

For the other Lagrangian points, if the satellite drifts away from the precise point, it will accelerate away from that point. However, a number of satellites have been positioned at (or orbiting around) various Lagrangian points - they just need to use fuel for station-keeping, to keep them in the right location. Not so different from satellites in geosynchronous orbit.

See:
https://en.wikipedia.org/wiki/Lagrangian_point
https://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_points
https://en.wikipedia.org/wiki/List_of_satellites_in_geosynchronous_orbit[/list]

#### chris

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #7 on: 27/05/2016 13:56:10 »
compared to the 180 satellite slots at 2 degrees separation

And how "full" is the geosynchronous orbit at the moment? Are all 180 slots occupied, or or we operating at densities other than 2 degrees at the moment?

#### evan_au

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #8 on: 27/05/2016 23:53:26 »
Quote from: chris
And how "full" is the geosynchronous orbit at the moment?

I understand that there are over 400 satellites in geosynchronous orbit at present. Some of these are spares, and some are dead (and there was even a "zombie" satellite prowling around for 8 months in 2010, trying to kill neighbouring satellites!).

Managing the geosynchronous orbit is a difficult area of international negotiations.
Whoever first lays claim to an orbital slot has rights to it forever, even if their satellite program has no funding.

As you can imagine, slots over USA and Europe are hotly contested, leaving few slots available for countries in Africa and South America.  Slots over the middle of the Pacific Ocean are less congested.

There are ways to share slots, by agreeing to use different frequency bands than the other satellites (but the "original" operator may want to later upgrade their existing satellite with one that uses these bands too).

Or you can use directional antennas on the satellite so it doesn't interfere with broadcasts from the other satellite.

But it is a multi-year process to negotiate an orbital slot for a new satellite.

At one time, equatorial nations declared that they owned all geosynchronous orbital slots over their territory (so they would have the right to charge rent, or to auction off a 10-year lease to the highest bidder). But the countries with the satellites have basically ignored them.
« Last Edit: 28/05/2016 13:24:56 by evan_au »

#### evan_au

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #9 on: 28/05/2016 13:44:16 »
Quote from: Alan McDougall
What about the Lagrange points between the moon and earth?
There is an additional problem with the L1 Lagrange Point directly between Earth and Moon: The Moon sits right behind it.

Satellite dishes point at communications satellites seen against the blackness of space, with a typical temperature of around 2.7K (the Cosmic Microwave Background Radiation). This gives them a good signal-to-noise ratio, and high capacity.

However, the surface of the Moon reaches temperatures of around 400K every Full Moon, degrading the signal integrity. A New Moon is not so bad, with a temperature of only around 100K - but it is still noisier than staring at a point in empty space.

Note that individual users of geosynchronous satellites are disabled for a few minutes every 6 months, as the Sun passes behind the satellite from the viewpoint of their individual ground station. The 5500K temperature of the Sun produces microwave noise that overpowers any signal transmitted by the satellite. Lunar L1 would have a small advantage here - the Moon would shield the satellite signal from the intense radio noise of the Sun.

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##### Re: Why is there only one geostationary orbit altitude?
« Reply #9 on: 28/05/2016 13:44:16 »