An absolutely incorrect and unfounded assertion. Where is your evidence in support of that assertion?The big problem with all of your reasoning is that you flip backwards and forwards between seeing it as a three-dimensional movement and a two-dimensional movement.
Sure, but then the object would also be diminishing is size and there is no such diminishing across the period between 6:17 and 7:03 (while notably after this period there definitely is…).In order for the object to appear to slow down it doesn't have to be curving away from us or actually slowing down, instead it could start off close to us and get further away, i.e. travelling in a straight line at an angle away from us.
Actually, strictly speaking, “proper motion” is the apparent motion of an object travelling across our field of view with respect to background objects (such as the stars). In the video the object seems to tangentially cross our field of view while slowing down.The result would be that its apparent speed across our line of sight would get lower as it gets further away. This is called proper motion, and is inversely related to actual speed across the line of sight.
However, I have absolutely no idea how you get to relate that “proper” motion as being inversely proportional to its actual (or true) motion. An assessment of the object’s true speed would require knowledge of the angle it is travelling away from us on (and perhaps even the distance the object is away from us would help). That is, the shallower the angle, the closer to proper motion will be to the true motion; and the greater angle, the greater the deviation.
Now interestingly (and having already demonstrated your conceptual error above – but to diagrammatically represent it to make it crystal clear), imagine an object travelling away from us at a constant speed at a specific angle in a straight line. We can apply basic trigonometry to show that the proper motion is precisely and directly proportional to the true motion (no inverse rules required at all).
You will note that an object travelling away from us at constant velocity (true motion) when divided into equal distances, causes corresponding equal distances along the line of proper motion – meaning of course that the “proper” velocity is directly proportional to the true velocity and critically does not change as the object ravels away from us. That is, it does not appear to slow down at all. Only a curving trajectory will do that (as per the diagram in my previous post).
If we know x (proper velocity), and we know angle a, then we can work out (using trigonometry) the true velocity. Thus the following statement from you is absolutely in error.
This scenario only occurs if the true motion is curved.If you double the distance you halve the proper motion, provided the tangential speed remains constant. This would lead to an apparent steady slowing of the object's motion from right to left.
Actually, I think you may find the stars are moving substantially more than the closer object – but of course you seem now to be flipping between true motion and proper motion in your statements. This is as confusing for the reader as I am sure it is for you.The fact that MIR remains in roughly the same place in the video merely indicates that any object relatively nearby will also move less than the very distant stars.
“On average”? Actually between 6:17 and 7:03, the object actually maintains a constant brightness and size. It is only after 7:03 (when the trajectory undergoes a number of changes) that the object both diminishes in size and gets fainter.This idea would be supported by the fact that the object also gets continually fainter (on average).
Oh I see… it is a satellite. But the trajectory changes are rather abrupt for that hypothesis don’t you think?As for where the Earth is in respect to our POV, it's incredibly important, because I think the Earth is down and slightly to the left, in which case what we're seeing is a satellite in a lower orbit overtaking us, and then following its orbit around the Earth. It moves off into the distance, apparently slowing down due to its increasing distance (see above), and as it does so it starts to curve downwards, slowly at first, and then more quickly, getting fainter all the time until it gets too faint to see.
It is clear now that you have not watched the correct video (or are not observing the correct object). Please do so here ((http://www.youtube.com/watch?v=sZ7EgRiU5Zo&feature=related). The object in question appears at 6:17 ( I downloaded a copy and play it in VLC Player so the timing might not be exact) at the lower right bottom of frame some small distance in from the right corner. It then continues at an angle upward and to the left in a straight line until 7:03, where it changes trajectory to travel (still to the left) parallel to the bottom of frame. It changes direction two more times (the next is a change to head it down toward the bottom left corner and the next is a change to head it directly down, parallel to the left edge of frame) and it even comes to a complete halt after the last direction change, maintaining position until it moves off downward again to disappear.Not once in all of the time it's on frame does it make a sudden course change, nor does it change the sense of its course change. It is always changing from left and up to roughly straight down.
Not really, I have done them above.If I had the time I could do some more precise positional measurements, but I'm afraid it would be very tricky…
No… the shuttle's motion can be determined from the background stars (as the camera is fixed) in conjunction with our perspective on MIR.…as I'd have to take account of the fact that the shuttle's motions would be projected onto the object (proper motion and parallax, assuming it's a nearby satellite)…
However, I will admit that parallax is a tricky concept here. As we have no objective indication of actual object distance, we cannot accurately determine the affect of parallax at all. Nevertheless, given that the object maintains size and brightness over the period under direct discussion (from 6:17 to 7:03), it seems unlikely that parallax would significantly affect the calculations (and certainly in any event not to affect an apparent five fold velocity decrease in proper motion). However, after the trajectory changes it may have a minor role to play…
For your sake then I sincerely hope your calculations in that paper do not contain such mathematical and conceptual errors as I have demonstrated in your workings above.…and I'm currently far too busy writing a paper on stellar motions and distances.