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B Star trails and the Earth's movemement

  1. Jun 29, 2017 #1
    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...
     
  2. jcsd
  3. Jun 29, 2017 #2

    Drakkith

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    I'm sorry I don't understand your question. Could you elaborate?
     
  4. Jun 29, 2017 #3
    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.
     
  5. Jun 30, 2017 #4

    Drakkith

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    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.
     
  6. Jun 30, 2017 #5

    russ_watters

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    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.
     
  7. Jun 30, 2017 #6
    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.
     
  8. Jun 30, 2017 #7

    Drakkith

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    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.
     
  9. Jun 30, 2017 #8
    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.

    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?
     
  10. Jun 30, 2017 #9
    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?
     
  11. Jun 30, 2017 #10

    Drakkith

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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.

    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.
     
  12. Jun 30, 2017 #11

    Borg

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    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.
     
    Last edited: Jun 30, 2017
  13. Jun 30, 2017 #12
    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.
     
  14. Jun 30, 2017 #13
    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.
     
  15. Jun 30, 2017 #14

    Borg

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    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.
     
  16. Jun 30, 2017 #15
    Could you explain what you mean by the perceived motion of the star?
     
  17. Jun 30, 2017 #16

    Borg

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    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.
     
  18. Jun 30, 2017 #17

    Bandersnatch

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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 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.
     
    Last edited: Jun 30, 2017
  19. Jun 30, 2017 #18
    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?

    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.
     
  20. Jun 30, 2017 #19

    Bandersnatch

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    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.
    After being told by several people that you're wrong, perhaps it's time to reconsider who doesn't understand what.
     
  21. Jun 30, 2017 #20
    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.

    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.
     
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