# Star trails and the Earth's movemement

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## Main Question or Discussion Point

Greetings,

I wonder if someone could please kindly give a physics explanation for the phenomenon of circular star trails when earth is moving 67 times faster laterally than it is rotating?

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Drakkith
Staff Emeritus
I wonder if someone could please kindly give a physics explanation for the phenomenon of circular star trails when earth is moving 67 times faster laterally than it is rotating?
I'm sorry I don't understand your question. Could you elaborate?

I'm sorry I don't understand your question. Could you elaborate?
Certainly, and thanks for your attention.

If I take a time-lapse sequence of 10 hours one night, I will get a photo like this:

https://cdn-az.allevents.in/banners/022754a31051261f24faa84063560b86

During the night, here's how far the point of observation (the camera's lens) moved:

10 Hours x 1000 mph = 10,000 rotation miles - how far the camera moved in an arc as the earth rotated.
10 Hours x 67,000 mph = 670,000 lateral miles - how far the earth should have moved sideways (orbiting the sun)

10,000 rotation miles: As clearly seen in ever star-trail sequence, ever
670,000 lateral miles: Not seen in any star-trail sequence, ever.

Let me know if I can elaborate further.

Drakkith
Staff Emeritus
10,000 rotation miles: As clearly seen in ever star-trail sequence, ever
670,000 lateral miles: Not seen in any star-trail sequence, ever.
Neither of those matter for star trails. You could set up a camera at the north or south poles and you'd see the exact same kind of star trails. This is because it's not the distance traveled that matters, but the amount of rotation that matters. The stars are much too far away for the distance you and the Earth travel in a few hours or even an entire year to have a noticeable effect.

russ_watters
Mentor
1000 mph
That's how fast you appear to move if you are standing on the equator (roughly). Since the stars aren't sitting on the equator, it has very little to do with how fast the stars appear to move.

Try this:
Draw a triangle showing how far a point on the surface of the Earth moves in an hour. Then draw a similar triangle showing how far Alpha Centauri appears to move in an hour based on the same angular rotation rate.

This is because it's not the distance traveled that matters, but the amount of rotation that matters.
The camera is a point in space that has traveled in a path over 10 hours, and the star trails reveal that path. Why would you say the distance traveled and the rotation of the earth are separate factors? In this example, are they not the same?

If you forget the earth and just imagine the camera is a point in space. The star trails reveal the rotational path the camera has taken over 10 hours. During that time, though, the camera has traveled 67 times faster than that rotational motion, along a lateral (sideways) plane.

Why do star trails not reveal this motion? I hope I am explaining this properly.

Drakkith
Staff Emeritus
Why do star trails not reveal this motion?
Because the stars are so far away that the difference in position makes a minuscule difference. Not nearly enough to notice in a picture with a standard camera. If you move two feet to the left, your view of the inside wall of your home will change a great deal. However if you do the same thing outside, you can notice almost no difference for a building located a mile away.

That's how fast you appear to move if you are standing on the equator (roughly). Since the stars aren't sitting on the equator, it has very little to do with how fast the stars appear to move.
Yes I used the 1000 mph as the greatest possible speed - how it would be at the equator. In this example, it wouldn't make much difference if you were at a tighter latitude close to the north or south pole. The lateral speed of the earth still dwarfs any rotational movement that the camera is subject to.

Try this:
Draw a triangle showing how far a point on the surface of the Earth moves in an hour. Then draw a similar triangle showing how far Alpha Centauri appears to move in an hour based on the same angular rotation rate.
Yes, and I would expect these to match perfectly if we're just working with rotation. The point of this thread is that earth's orbit around the sun is 67,000 mph sideways which is not factored into star trails. Shouldn't all star trails look like crazy, wild streaks?

Because the stars are so far away that the difference in position makes a minuscule difference. Not nearly enough to notice in a picture with a standard camera. If you move two feet to the left, your view of the inside wall of your home will change a great deal. However if you do the same thing outside, you can notice almost no difference for a building located a mile away.
That's what I am asking. Why does distance not matter for rotational movement, but it does for lateral movement? If I look at a building a mile away, it will move the same relative amount whether I rotate my view or shift it sideways. There is no bias against sideways motion for objects at a distance, just as there is no bias against rotational motion. So why is space different?

Drakkith
Staff Emeritus
Yes, and I would expect these to match perfectly if we're just working with rotation. The point of this thread is that earth's orbit around the sun is 67,000 mph sideways which is not factored into star trails. Shouldn't all star trails look like crazy, wild streaks?
No, for the same reason that you can take a clear picture of a mountain in the distance while riding in a car, but the trees at the side of the road are blurred. They're so far away that you'd have to travel an immense distance to get even slight changes in perspective.

That's what I am asking. Why does distance not matter for rotational movement, but it does for lateral movement? If I look at a building a mile away, it will move the same relative amount whether I rotate my view or shift it sideways. There is no bias against sideways motion for objects at a distance, just as there is no bias against rotational motion. So why is space different?
If I want to move around a building to see the other side, I may only need to move a few dozen feet if I'm standing next to the building. But if I'm 100 yards away (and I maintain that distance) I have to move much further to get around so I can see the other side. Moving a few dozen feet changes my view of the building only imperceptibly. Now increase that distance from 100 yards to dozens or hundreds of light years. Even though the Earth is traveling at great speed, it is not nearly enough to compensate for the unimaginable increase in distance.

In addition, the rotation of the camera involves another factor. If you rotate your camera 180 degrees along its optical axis (so you keep the lens pointed towards the object as you rotate the camera) the incoming light rays now strike the sensor on opposite sides as they did before. Those rays that used to strike the sensor on the top now strike on bottom and so forth. This is just an orientation change and it is the predominant factor for star trails because the other effects are so minuscule. Since light rays are constantly falling on your camera's sensor as the Earth (and the camera) rotates, they gradually build up streaks over time.

Borg
Gold Member
Try looking at the numbers. A star that is 10 light years away will appear to 'travel' in a circle that is 2 * pi * r or approx. 60 light years in 24 hours. In an hour, it will seem to have traveled 2.6 light years. Now compare that with the distance that the earth actually moves around the sun (29.78 km / sec). So, while the earth moves about 100,000 km around the sun in an hour, the star appears to move 2.6 light years due to the earth's rotation. Guess which one is more noticeable to an observer on earth.

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No, for the same reason that you can take a clear picture of a mountain in the distance while riding in a car, but the trees at the side of the road are blurred. They're so far away that you'd have to travel an immense distance to get even slight changes in perspective.
The stars in star trail sequences clearly reveal the motion of the camera as earth rotates. I don't understand how you can see one motion without the other.

Try looking at the numbers. A star that is 10 light years away will appear to 'travel' in a circle that is 2 * pi * r or approx. 60 light years in 24 hours. In an hour, it will seem to have traveled 2.6 light years. Now compare that with the distance that the earth actually moves around the sun (29.78 km / sec). So, while the earth moves about 100,000 km around the sun in an hour, the star appears to move 2.6 light years due to the earth's rotation. Guess which one is more noticeable to an observer on earth.
I don't know why the rotation is more observable, when you consider the physicality of this scenario. It makes no sense.

If the stars are too far away, then why do we see any motion from our fixed point at all? And because we see motion, why is it only the rotation and not the much faster lateral orbit motion?

Please consider the physicality of what I am discussing here. Nobody has grasped the point of my original question, which is disappointing.

Borg
Gold Member
If the stars are too far away, then why do we see any motion from our fixed point at all? And because we see motion, why is it only the rotation and not the much faster lateral orbit motion?
The lateral motion is not faster than the perceived motion of the star due to the earth's rotation. It is significantly smaller. If you can't grasp this, I doubt that anyone can help you to understand the answer to your question.

The lateral motion is not faster than the perceived motion of the star due to the earth's rotation. It is significantly smaller. If you can't grasp this, I doubt that anyone can help you to understand the answer to your question.
Could you explain what you mean by the perceived motion of the star?

Borg
Gold Member
Could you explain what you mean by the perceived motion of the star?
I did in post #11. The earth's actual motion around the sun is approx. 4 billionths of the perceived motion of the star due to the earth's rotation. This is like looking at a building a mile away and comparing how much it seems to move when you take a deep breath vs. turning your entire body. You're expecting it to look like it moves more when you take a deep breath.

Bandersnatch
You're confusing linear and angular displacement. These are two separate quantities, which produce their separate effects.

Star trails are due to angular displacement as Earth rotates with some angular velocity. It's what you get when you turn your head around, or stand on a turntable, or at the poles. The dimension of this physical quantity is degrees of angle (or degrees/second for angular velocity).

This has nothing to do with linear displacement caused by linear velocity, such as 'riding' on the Earth's surface or in its orbit around the Sun (but it can be combined with the aforementioned rotational effect - see below).

Linear displacement causes apparent parallactic motion. This is what you see when riding on a train and looking at closer and father objects passing your visual field at different angular velocities (your visual field is a section of a sphere, centred on you). The magnitude of the parallactic motion is dependent on the distance to the object, and on linear displacement - the closer the object, and the farther you move, the greater the observable parallax.

When you stand on Earth anywhere other than the poles, you are being both rotated and displaced. In a single 12h night (i.e. at equinox) you rotate by 180 degrees and you're displaced by the length of Earth's diameter. Additionally, as you ride the planet in its orbit, you are furthermore and independent from the above displaced by some 1.3 million km, which is obviously more than the Earth's diameter.

So, you've got three observable effects acting at the same time, in the order of their decreasing magnitude:
- angular displacement of the stars due to Earth's rotation making you look in different directions,
- angular displacement due to the parallax caused by being linearly displaced by Earth's orbit,
- angular displacement due to the parallax caused by being linearly displaced by Earth's surface.

Since the latter two depend on the proportion between the distance travelled and the distance to the star (so, are different in magnitude for each star), and this proportion is a very small number even for the closest stars, you won't notice them unless using very precise equipment.

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You're confusing linear and angular displacement. These are two separate quantities, which produce their separate effects.
Star trails are due to angular displacement as earth rotates with some angular velocity. It's what you get when you turn your head around, or stand on a turntable, or on the poles. The dimension of this physical quantity is degrees of angle (or degrees/second for angular velocity).
This has nothing to do with linear displacement caused by linear velocity, such as 'riding' on the Earth's surface or in its orbit around the Sun (but it can be combined with the aforementioned rotational effect - see below).
In the scenario of the camera travelling on a spiraling path, how could you possibly separate the two? Isn't it clear that we're really describing the physical journey of the camera?

The camera rotates, but it is also moving sideways 67 times faster. We should be seeing spirals, not concentric circles/arcs.

This animation reveals the spiral path of the camera. Shouldn't we be seeing spirograph star-trails?

Linear displacement causes apparent parallactic motion. This is what you see when riding on a train and looking at closer and father objects passing your visual field ad different angular velocities (your visual field is a section of a sphere, centred on you). The magnitude of the parallactic motion is dependent on the distance to the object, and on linear displacement - the closer the object, and the farther you move, the greater the observable parallax.
Not sure why you're talking about parallax here. This is not a question of distance or parallax, as we can clearly see the path that the camera travels on by looking at the star trails. Do you understand?

Please refrain from further complicating this simple scenario with unrelated phenomena.

Bandersnatch
The camera rotates, but it is also moving sideways 67 times faster.
No, you're still confused. Rotation and linear velocity ('moving sideways') are different quantities. It doesn't make sense to compare the two. If you disagree, then ask yourself, which is larger: 1 rad/s or 100 km/s?

Please refrain from further complicating this simple scenario with unrelated phenomena.
It's not unrelated. The spiralling motion gives you parallactic displacement.
After being told by several people that you're wrong, perhaps it's time to reconsider who doesn't understand what.

No, you're still confused. Rotation and linear velocity ('moving sideways') are different quantities. It doesn't make sense to compare the two. If you disagree, then ask yourself, which is larger: 1 rad/s or 100 km/s?

It's not unrelated. The spiralling motion gives you parallactic displacement.
It is unrelated. Can you imagine if there was only one star in the sky, and we tracked it's path with a star trail sequence? Would it not move in an arc, and therefor reveal the path the camera has taken? Why do you need to talk about some stars being closer and some stars being further? You are adding a further complication, and I am trying to narrow in on the nature of the scenario which has escaped everybody who has replied to this thread so far.

After being told by several people that you're wrong, perhaps it's time to reconsider who doesn't understand what.
What does the truth have to do with consensus? The replies in this thread are incorrect, because the authors aren't thinking correctly. Nothing that has been proposed here is physically possible. If you tried modelling this scenario in auto-cad, you'll have spiraling star-circles every time.

Borg
Gold Member
The replies in this thread are incorrect, because the authors aren't thinking correctly.
So all of us who have actually studied the topic for years are wrong but, the person who had the original question asking us to explain his misunderstanding of the science isn't wrong? That's an interesting conclusion.

mfb
Mentor
That is exactly what produces the star trails. The camera changes its orientation in space. This has nothing to do with motion.

If you stabilize the camera orientation in space, it looks like this. The Earth rotates.
If you would speed up this video a few million times more, you would also see some motion of stars.

phinds
Gold Member
2019 Award
If you would speed up this video a few million times more, you would also see some motion of stars.
Since speeding up the video would just make it happen in the blink of an eye, I think what is intended here is "if you were to take this time lapse over millions of hours instead of just a small number of hours, you would see some movement of the stars." @mfb, do I have that right?

mfb
Mentor
Well, sure, you would need a longer video. A few hundred years should be sufficient. A single year will work if the camera is mounted to a telescope.

russ_watters
Mentor
Yes, and I would expect these to match perfectly if we're just working with rotation. The point of this thread is that earth's orbit around the sun is 67,000 mph sideways which is not factored into star trails. Shouldn't all star trails look like crazy, wild streaks?
If you do the calculation I suggested (or look at the result already given to you...), you will see that the 67,000 mph speed is insignificantly small compared to the apparent rotational speed. It takes years to notice its effect.

Again: your 1,000 mph speed on the Earth's surface is the speed of that point relative to a stationary (non-rotating point) at the same distance from the center of the Earth. It has nothing to do with the apparent speed of a distant star with respect to your rotation. As @mfb pointed out, your "rotational speed" (the linear speed you have due to your rotation) is zero if you spin in place, but the apparent speed of everything around you is much faster even than with Earth's rotation.

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