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Thread: Angular Sizing with Reference Objects in Image

  1. #1

    Angular Sizing with Reference Objects in Image

    This question is a bit complicated, or at least from my end, but I've spent quite a while trying to solve it on my own without luck. I feel like I should have the information I need, but I can't figure out how to reference the variables together to make them work.


    This is the basic premise, take the image I've got here.

    QHelper1.jpg


    Since it doesn't really have depth, I'll explain it. Basically, we have a person falling through a tunnel, so the person is flat parallel to the top of the ground, let's say and falling directly down. The tunnel (which is a cylinder) is the brown section, the outer circle being the entrance and inner circle being the exit of said tunnel. The person is currently above the entrance of the tunnel. Finally, the earth-like circle in the back is a very large sphere a long distance away.

    QHelper2.jpg


    Here, I've crudely drawn what this should look like from above the perspective given in the original image. Now, I have the angular diameter of every single circle shown, and I also have the real diameters as well as distance to the person falling and the far away sphere. We also know that the tunnel is a cylinder, and therefore the real diameter of the two inner circles are equal. However, we don't know their real diameters or their distance away from us or each other. Can we find their real diameters or distance away with the information we currently have? If so, how? Thanks!

  2. #2
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    You've got me running in circles...

    One question for now: why d'heck is it
    a "person" that's falling?
    I'm just an imagination of your figment !

  3. #3
    Quote Originally Posted by Denis View Post
    You've got me running in circles...

    One question for now: why d'heck is it
    a "person" that's falling?
    If you prefer you can just think of it as a circle-shaped object at the same distance, and the falling is irrelevant too, I was just trying to give context so the picture could be easier to understand due to the fact it has no depth which makes it difficult to visualize what you're looking at without context.

    Basically, ignore the person, imagine a non-falling circular disk is there, we have it's real diameter, angular diameter, & distance from our point of view, and the same with the "Earth" way in the background.

    We only have the angular diameter, but neither the distance to or real diameter of the circular openings of the tunnel, which are in between the other two as shown in the image.

  4. #4
    Elite Member mmm4444bot's Avatar
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    I don't think you have enough information.

    The angular diameter isn't really useful, unless you have either the distance or the real diameter.

    Let's say the angular diameter of a planet is one millimeter.

    It could be a huge planet very far away, or it could be a small planet much closer.

    Just to confirm, in addition to not knowing the length of the tunnel, you also do not know the distance from the observer to the person falling, correct?
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  5. #5
    Quote Originally Posted by mmm4444bot View Post
    I don't think you have enough information.

    The angular diameter isn't really useful, unless you have either the distance or the real diameter.

    Let's say the angular diameter of a planet is one millimeter.

    It could be a huge planet very far away, or it could be a small planet much closer.

    Just to confirm, in addition to not knowing the length of the tunnel, you also do not know the distance from the observer to the person falling, correct?
    We do have the distance to the person, and we do have the distance to the little Earth way in the background. Which means we also have the actual size of both of those.

    What we don't have is the distance to the tunnel opening or its diameter, but we have both for the objects on either side of it. We also know that these objects have same actual diameter, we just don't know what it is.

    So, if you want I can define the variables as best I can here and what they are, and whether we have them:

    Dp = Distance to person
    Dn = Distance to near entrance of tunnel
    Df = Distance to far entrance of tunnel
    De = Distance to “earth”

    Sp = Size of person
    Sn = Size of near entrance of tunnel
    Sf = Size of far entrance of tunnel
    Se = Size of “earth”

    δp = Angular diameter of person
    δn = Angular diameter of near entrance of tunnel
    δf = Angular diameter of far entrance of tunnel
    δe = Angular diameter of “earth”

    Here’s what we know
    Dp | De | Sp | Se | δp | δn | δf | δe

    Here’s what we need any one of the following (which would allow us to calculate the rest easily)
    Dn | Df | Sn | Sf

    We also know
    Sn = Sf
    2.28Dn = Df

    I’ll be trying to work on this further, but I’m thinking you might be right. Elaborating on what you stated, it would appear likely that there is a large set of possible answers and no way to narrow it down with the information we have. Basically any distances past the person would result in a possible answer so long as they match the ratio of distance between them. The distance to or the size of for either of them seems to be a potential pre-requisite.

    I know I set the focus on angular diameter to begin with, but if there is another solution regarding some other sort of method that's fine too, but the more dead ends I run into stemming from the same reason (we need a distance), the more I'm thinking it's unlikely.

  6. #6
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    Quote Originally Posted by DS_Blizzard View Post
    This question is a bit complicated, or at least from my end, but I've spent quite a while trying to solve it on my own without luck. I feel like I should have the information I need, but I can't figure out how to reference the variables together to make them work.


    This is the basic premise, take the image I've got here.

    QHelper1.jpg


    Since it doesn't really have depth, I'll explain it. Basically, we have a person falling through a tunnel, so the person is flat parallel to the top of the ground, let's say and falling directly down. The tunnel (which is a cylinder) is the brown section, the outer circle being the entrance and inner circle being the exit of said tunnel. The person is currently above the entrance of the tunnel. Finally, the earth-like circle in the back is a very large sphere a long distance away.

    QHelper2.jpg


    Here, I've crudely drawn what this should look like from above the perspective given in the original image. Now, I have the angular diameter of every single circle shown, and I also have the real diameters as well as distance to the person falling and the far away sphere. We also know that the tunnel is a cylinder, and therefore the real diameter of the two inner circles are equal. However, we don't know their real diameters or their distance away from us or each other. Can we find their real diameters or distance away with the information we currently have? If so, how? Thanks!
    What Math or Physics class asked you to solve this problem? What was the topic?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  7. #7
    Yeah, I just spent another couple hours trying to move all sorts of variables around and I'm basically convinced at this point that every single use of angular diameter is going to just be proportional depending on distance, so even though we can find, for example, how far away they are from each other or even some other ratios that I found (such as how large the person or the "earth" would be at the distance of the tunnel), those ratios are true at every distance and therefore without the distance we can't know the size.

    I hadn't haven't had a math refresher since my junior year in high school about 9 years ago, and that was AP calc so it's been a minute since I've dealt with any sort of geometrical situations or equations, so i was just trying to get a more seasoned look since I can only re-learn so much in a day or so. So I do appreciate the time you guys took to respond, thanks!!

  8. #8
    Quote Originally Posted by Subhotosh Khan View Post
    What Math or Physics class asked you to solve this problem? What was the topic?
    It's a personal project, if that's not what this forum is for I do apologize. I read the rules before posting but there's only an implication of tutoring for topics so I didn't see that as being explicitly exclusionary for other math questions, but if that is the case then I am sorry.

  9. #9
    Elite Member mmm4444bot's Avatar
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    That's not the case, so there's no need to apologize.

    Subhotosh asked for context because there are not only different approaches available for a single exercise but also different interpretations. Knowing whether you're studying a particular topic helps tutors to plan a course of action.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  10. #10
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by DS_Blizzard View Post
    We do have the distance to the person, and we do have the distance to the little Earth way in the background. Which means we also have the actual size of both of those.
    Yes, I see that in your post now. Thanks.

    I'll probably ponder your question again, tomorrow. Gotta go root for the Huskies.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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