How does a geostationary satellite remain over the same spot on Earth?
In: Planetary Science
Geostationary satellites orbit earth at the right distance so that one complete orbit takes 24 hours, the same amount of time for the earth to revolve. The ground and the satellite revolve around the center of the earth at the same rate. Geostationary satellites only really work directly above the equator, any inclined orbit will appear to drift north and south once per day.
For any given object, it can orbit another body at really any distance. Closer orbit means a higher speed is necessary to not fall down. The ISS is very close to the Earth, so it orbits very quickly (every 90 minutes, it completes an orbit). If it were further away, it would have to move slower as to not fly away. This means that there is some sweet spot where the ISS would take exactly 24 hours to orbit the Earth. If placed in orbit at this distance and speed, the Earth would turn underneath it exactly as fast as it travelled. It would remain over the exact same longitude line forever.
It is far away enough that their orbit matches the earth’s rotation. This only works for points on the equator. Wikipedia page for it has a very nice animation
In fact every “true” geostationary satellite shares same orbit, higher or lower or at a different angle and they would appear to move from an observer on the ground
for a fighter jet to fly a loop, it uses movement of the wings along with thrust from the jet engine to push against the air around it and fly the loop.
but the international space station(ISS) doesn’t have wings or thrust or air to push against. so, how does *it* fly in a giant loop? the answer is gravity.
gravity doesn’t stop at the edge of our atmosphere. so, even though the ISS is in space, the earth is pulling it the entire time. but because of how gravity works, it can only pull at a certain speed. the ISS was let loose at such a speed sideways to earth that by the time the ISS has fallen to where it would meet the surface of the earth, the ISS is really far to the side from where it would have landed.
and since the earth is round, the distance the ISS has fallen can actually curve *with* the earth so perfectly that the ISS is still the same distance from the surface and is now over a totally different area of the earth’s surface.
the ISS is roughly 250 miles above the earth’s surface, and it has to move sideways so fast to avoid falling into earth that it makes a full loop all the way around the earth about every 90 minutes.
because of how gravity works, the farther from the earth something is, the weaker the gravity, and the slower that object will fall to earth. as you go farther away from earth, the time it would take to complete a full loop around the planet reduces. far enough away at some point, it will take 100 minutes to complete a loop, at a farther distance it will take 120 minutes. and if you keep going, you will find a distance that will let you take 1460 minutes, or 24 hours, to complete a full loop.
what else take 24 hours? a day! and what is a day? it’s what we call a complete spin of the earth!
so, if the earth’s surface takes 24 hours to complete a spin and an object in space takes 24 hours to complete a loop, then that object is staying in motion above the same area of the earth’s surface. the surface and the object are “in sync”
Because this is ELI5, I’m going to use imprecise language that won’t *directly* translate to the underlying physics and math. I’m doing this so that we don’t actually need to use the formulas for centripetal force or get into “reference frames” and centrifugal force. The principles should be correct enough.
Being in orbit can be thought of as “continuously falling towards Earth, but always missing because you’re traveling too fast”. Basically, your “sideways” momentum, caused by moving in a direction *not* towards Earth, “cancels out” Earth’s gravity trying to pull you in.
To be in a stable orbit (i.e. not moving towards or away from Earth), these values need to *exactly* cancel out. The “force” of your momentum that prevents you falling towards Earth is dependent on your speed; if you’re moving faster, you’re more likely to break Earth’s gravity and go flying off. If you’re moving slower, Earth’s gravity will win out and you’ll fall to Earth.
The force of Earth’s gravity at a given distance away is fairly straightforward to calculate. When you combine all of this, you end up finding that, at every distance from Earth, there is one specific speed you need to maintain in order to stay in a stable orbit.
So, we want a “geostationary” satellite to always hover over the exact same spot on Earth. What this means is, we need that satellite’s (rotational) speed to exactly match that of the Earth’s rotation – it will complete 1 full orbit every 24 hours, which is when Earth completes 1 full rotation. You calculate that speed, and then, using our above approach, you figure out the distance from Earth at which that speed results in a stable orbit.
The result looks [like this.](https://i.stack.imgur.com/nxIh2.jpg). The satellites close to Earth in that image are all moving much faster than Earth’s rotation – you can occasionally see them moving across the night sky like airplanes or shooting stars. The ones in those “rings” *way* out there are geosynchronous/geostationary. They need to be moving much slower, so they have to be placed way out where Earth’s gravity is weaker (and the radius of their orbit is bigger).
In practice, nearly all satellites have stabilizers that will fire off to make tiny adjustments to keep the satellite on its orbit, because we’ll never get everything *perfectly* right (and there are too many variables to make it worthwhile over these simple adjustments every so often).
Imagine skateboarding east down a straight street at 10mph with a 10mph tailwind (so there is no wind resistance). If you throw a tennis ball straight up, it will already be traveling 10mph east like you so even though you threw it straight up, it will arc and land in your hand again further down the road. Now imagine that the road isn’t straight, but a sphere. There is a height and speed the ball can travel where the tennis ball falls at the same arc as the curvature and will appear to hover above you as you skateboard around the sphere at 10mph. That’s orbit.
FYI when rockets launch payload to orbit, very little energy is spent getting the rocket to move straight up. Most of the energy is to get the rocket moving horizontal to the surface (often east) to find this orbital path.
If you throw a ball, it falls to the ground pretty quickly, right?
If you throw it faster, it stays up longer before falling.
If you throw it from higher up, it also stays up longer before hitting the ground, even if you throw it slower.
For something to orbit, we have to throw it fast enough that it misses the ground when it falls.
Turns out, the higher you go, the slower you have to throw it for it to miss the ground.
At a certain height, the speed that it has to go is exactly the same as the speed at which the earth rotates.
That’s the altitude that geostationary satellites orbit at.
And as someone else said, this only works of the satellite is on the equatorial plane. If it’s at an angle to the plane, it will appear to move north and south, making a figure 8.
Everything in orbit needs to go a certain speed to stay there, otherwise it will end up coming back inward towards the earth. The closer you are to the surface, the faster you need to go. The further you are, the slower you need to go.
At the very other extreme, if something isn’t moving sideways at all, it just falls straight down. That’s just… dropping.
Now, this has completely nothing to do with the rotation of the earth. Orbital speed and earth’s rotation are two completely separate things.
So in low earth orbit things need to go about mach 23 to stay there. The ISS completes an orbit in about 90 minutes, much faster than the 24 hours the earth itself takes to rotate.
But as mentioned, you need less speed the further away you are. At some point, which is about 35 thousand kilometres up, one orbit takes exactly as much time as it takes the earth itself to rotate. From earth’s surface, that satellite seems… Stationary.
Geostationary.
That of course assumes that this orbit actually rotates roughly around the same axis as the earth, and in the same direction. That doesn’t need to be true. As already said, orbits and earth’s rotation are unrelated. You can absolutely have a satellite orbiting at 90 degrees, overflying the poles. But then it obviously wouldn’t have the property of just hanging over a specific spot on the surface.
If you are close to the earth, like the space station (ISS), then it takes about 90 minutes to go around the earth. If you are very far from the earth, like the moon, it could take weeks to go around the earth. The further you are, the longer it takes to go around the planet.
If you do the math, there is an exact distance from the earth where the time to go around the earth happens to match the time it takes for the earth to rotate. This distance is about 22,300 miles.
Such an orbit it is called geosynchronous. If that orbit is perfectly along the equator, it’s called geostationary and the object will appear to sit motionless in the sky. It’s actually orbiting the earth, but the Earth happens to be turning under it at the same speed.
Lets imagine an instant in time, without gravity. The satellite is above some special point on the earth, and is moving quite fast. Of course, the Earth is turning. If the Earth were flat, then this would be like it moving in the same direction as the satellite, at the same speed. Since it isn’t flat, though, the special point is actually “falling away” from the satellite.
Now let’s add gravity. Gravity causes the satellite to fall towards the earth. Geosynchronous orbit happens when the Earth is falling away from the satellite at the same speed that the satellite is falling towards the Earth.
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