Star trails and the Earth's movemement

[hamischism]

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?

Thanks very much in advance...

 

[Drakkith]

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?

 

[hamischism]

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]

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]

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.

 

[hamischism]

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]

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.

 

[hamischism]

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?

 

[hamischism]

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]

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]

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.

 

[hamischism]

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.

 

[hamischism]

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]

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.

 

[hamischism]

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]

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 traveled 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.

 

[hamischism]

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 traveling 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.

 

[hamischism]

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]

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]

Look straight ahead. Turn your head. Do you see how everything is "moving"?
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]

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]

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]

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.

 

[russ_watters]

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.

Sorry, no - you're talking to astronomers, engineers, and physicists here. We know what we are talking about. And you aren't really even trying very hard to understand what we are saying, given that several of us have proposed some math to you and you haven't tried to do the math yourself, even when suggested.

 

[hamischism]

Look straight ahead. Turn your head. Do you see how everything is "moving"?
That is exactly what produces the star trails. The camera changes its orientation in space. This has nothing to do with motion.

This is not correct. https://en.wikipedia.org/wiki/Star_trail "Star trail photographs are possible because of the rotation of the Earth on its axis. The apparent motion of the stars is recorded as streaks on the film or detector."

It's an apparent motion because the motion of the Earth causes the trail.

Obviously this has everything to do with motion.

 

[hamischism]

Sorry, no - you're talking to astronomers, engineers, and physicists here. We know what we are talking about. And you aren't really even trying very hard to understand what we are saying, given that several of us have proposed some math to you and you haven't tried to do the math yourself, even when suggested.

I mean no disrespect. It's just that everything that has been said here is physically impossible.

If this were to be modeled in 3D software, none of the scenarios proposed would work because the Earth isn't rotating. It is spiraling. If you were to trace the path of the camera as a point in space, it is NOT going in a circle.

My question has always been: Why do we only see one of the motions that causes the spiral and not the other?

 

[russ_watters]

I mean no disrespect.

Fair enough, thank you. However:

It's just that everything that has been said here is physically impossible.

I'm sorry, but the problem here isn't that we aren't hearing you, it is that you aren't hearing us. We understand exactly what you are saying and why you are thinking what you are thinking. But you think what we are saying is physically impossible because you aren't really listening to us and you don't understand what we are saying. If you change your approach from "these guys don't know what they are talking about" to "maybe these guys are on to something, let me try to understand what they are saying", it will work out for you, I promise.

If this were to be modeled in 3D software, none of the scenarios proposed would work because the Earth isn't rotating. It is spiraling. If you were to trace the path of the camera as a point in space, it is NOT going in a circle.

We know. But it isn't the motion through space that causes the photo to have streaks, it is the changing direction the camera is facing that causes the photo to have streaks. The speed of the motion through space is reeeeeeeeallly slooooooooow.

My question has always been: Why do we only see one of the motions that causes the spiral and not the other?

And the answer to your question will be apparent to you when you do the math to calculate the impact of the rotational part of the motion. Or of you just recognize that the rotation changes the direction the camera is pointing, but the translation doesn't -- and you haven't factored that into your thought process.

 

[mfb]

This is not correct. https://en.wikipedia.org/wiki/Star_trail "Star trail photographs are possible because of the rotation of the Earth on its axis. The apparent motion of the stars is recorded as streaks on the film or detector."

It's an apparent motion because the motion of the Earth causes the trail.

No, it is an apparent motion because Earth rotates - and the camera rotates with it. Did you do the experiment I suggested? You get apparent motion without having to move at all.
You can also do it with a camera to get actual trails.

none of the scenarios proposed would work because the Earth isn't rotating

The Earth is rotating.

I mean no disrespect.

What you do here is very disrespectful. You dismiss explanations of others just because you don't understand them.

 

[Bandersnatch]

May these pictures be of some help (hopefully):

Situation A1 shows camera being stationary on the north pole. The planet is not moving through space w/r to other stars (not orbiting the Sun, not traveling through the Galaxy). In this idealised situation, the planet can only rotate (period: 24h), and there is just one star to look at.
Situation A2 is the same setup, but 6 hours later, with the planet having rotated by 90⁰. The camera has not moved (displacement = 0km). All it has done is change orientation. The resultant star trail is a fourth of a circle (90⁰ of arc). One again - despite there being no motion other than orientation changes, star trails still appear.

(t=elapsed time; ε=angular displacement; d=linear displacement)

In situation B1 we place the camera on the equator. The planet is still not moving. The camera is made to rotate in the opposite direction to the planet's rotation, so as to compensate (analogous to the setup in the video linked to by mfb in post #22).
In B2, the planet has rotated by 90⁰, but its rotation was compensated by the camera, for net rotation =0⁰. This eliminated most of the apparent motion of the star (the regular star trails). However, since the camera is no longer on one of the poles, rotation of the planet has carried it away from the initial position, so that after 6 hours it is displaced by the planet's radius - as counted in the plane of the planetary cross-section (i.e., as seen from the star; I don't want to get into detail why like this, and not e.g. 1/4th equatorial circumference; it has to do with small angle approximation).
The displacement causes parallax to appear.
To reiterate - this situation shows that motion across the planet surface does not cause star trails to appear, providing you compensate for orientation changes.

Situations C1 and C2 show combination of the rotational star trails with parallactic displacement. As in all pictures, parallax is exaggerated.

Situations D1 and D2 additionally include the motion of the planet, traveling with some velocity V to the right, which causes additional parallax to appear.

In all these pictures, parallax is negligibly tiny as compared to the apparent motion due to rotation (changes in orientation). In other words, motion through space, be it rectilinear or spiral-like, has very little bearing on star trails, and is not their primary cause.

Lastly, look at this snapshot from the Vsauce video you linked to earlier, to which I added some arrows:

It illustrates components of motion causing parallax
- 1, displacement due to motion of the Sun through the galaxy
- 2, displacement due to orbital motion
- 3, displacement due to being carried by Earth's surface during a day - with magnitude depending on latitude, with 0 at the poles and maximum at the equator

Blue arrows illustrate changing orientation of the camera/observer during approx 6 hours (90 degrees of arc), and arrow 4 shows rotational component of motion, which approximates the star trail visible as a result.
It cannot be stressed enough, only component no.4 causes star trails - the other components cause parallax.

If this were to be modeled in 3D software

Try one of the interactive planetarium software available (for free) on the Net. E.g. Celestia. You can fly to any modeled object, land at any spot, look in any direction, advance time as you see fit, or even mod an artificial solar system with the parameters you desire (e.g. a planet with no rotation, just the orbital motion - see if you'll find any star trails there).

 

[hamischism]

No, it is an apparent motion because Earth rotates - and the camera rotates with it.

Yes, the camera rotates as it moves laterally with the earth. This combined motion makes a spiral. Yet only we only see circles.

 

[hamischism]

We know. But it isn't the motion through space that causes the photo to have streaks, it is the changing direction the camera is facing that causes the photo to have streaks. The speed of the motion through space is reeeeeeeeallly slooooooooow.

Relatively speaking, the motion through space (orbiting the sun) compared with the rotation is really fast. 67 times faster.

I should see star streaks that curl over into a spiral at a ratio of 1:67 ie really long spirals.

 

[hamischism]

May these pictures be of some help (hopefully)

I agree with all those diagrams and calculations, but they have nothing to do with what I am talking about. I already asked you not to further complicate this discussion.

We're talking about a very simple scenario here. The camera is a point in space. For example, the camera is looking directly at Polaris from the north pole. Now forget about the earth, and describe the path the camera takes, as a point of observation in space.

It is:

a) Rotating, which is revealed in circular star trail streaks.
b) Moving sideways at 67 times this rotational speed.

So it's not JUST a rotating point of observation. It is a spiraling point of observation.

If you were to look at each star trail, you'd be able to relate the length of the trail to the distance that the point of observation has traveled over 10 hours. If it were 5 hour period, the streaks would be half the length.

The arcing motion of the camera's path is revealed in the star trails, but the path the camera took was not an arc. It moved in a spiral motion - not a rotational motion.

If I had to recreate this scenario in Autocad, how would I possibly end up with what we see in real life star-trails? It would be an impossible model. If the Earth spins on the spot, looking at distant objects, I will get circles. If the Earth spins and moves laterally, spiraling streaks. You can't have it both ways.

 

[Bandersnatch]

a) Rotating, which is revealed in circular star trail streaks.
b) Moving sideways at 67 times this rotational speed.

How do you calculate this? Show your work.
Seriously, this is the crux of the problem. Don't forget units.