But then it occured to me: we are looking at fixed sky objects here! The only (perceptible) movement they do, is because of earth rotation. And earth rotation is uniform! So when we calculate the angular separation between the two points an object is moving from and to (in fixed intervals like every second or every minute), it will always be the same! because earth rotation is also the same in this time interval!.....................................................
O.K. follow me if you will here. I was thinking you may have seen something I didn't and could explain it to me, but let me share my musing of yesterday.
Firstly let me clarify an important distinction because I can see where this may confuse the issue beyond its current complexity.
And I think you start in this post with the term "apparent motion" as it is used in astronomy to differentiate between the real/proper motion of stars in 3-D space. I think you are not using it precisely now.
I read your first post to mean "apparent motion" depended on where different objects are located, not that the same object would change its apparent motion.
I think you are intending to mean this:
The link Howie posted that you also referred to in your first post and Hiten's found graph already take into account field rotation effects of a tracking alt/az mount, yes?
[at this point my mind is mush and don't necessarily want to consider how this complexity fits in at the moment]
I interpreted your "apparent motion" to mean just not field rotation but apparent motion and the graph to be only the first stage in this calculus.
with the labeling, looks like:
given a time on x-axis,
y-axis plots at a given point:
- the apparent angular distance change,
- in relation to time (per second)....
- of an object,
- describing its movement across
- a fixed framed image (not tracked),
- since Alt/AZ coordinates are relative to fixed points describing[raise scope(alt) and rotate it(az)]
the observer at a given location.
My real-world go-to for grasping alt/az is Geostationary satellites that stay in a fixed alt/az position in the sky relative to observer and location because they fly the same rotational speed as the Earth's rotation and are thus fixed above a specific location on Earth at the Equator....
Given that EAA use is to track stars,
but Alt/Az and "angular distance" normally firstly describes the change from a fixed referent (a camera on a photo tripod),
before considering the interference of the "rotational effect" when tracked by a robotic alt/az mount....
My first interest,
is the answer to this question:
If one sets up a camera/scope fixed,
pointed in the direction,
so that a particular celestial object goes from one side of the frame to the other,
(and therefore pre=planned and rotated the fixed orientation of the camera so the movement is just on x-axis for ease of calculations),
Say in a time of one minute,
From a given same location,
will that same object go across the same amount of pixels (rotated fixed ahead of time so only x-axis movement),
at a faster or slower rate depending on where the SAME object is located in the sky over-the-horizon?????
Start with a simple scenario:
observing at the Poles.
Clearly the answer is NO change here. The circular speed of the Earth's rotation is constant, so the rate of change for an object of a particular Right Ascension would not change its rate across the same camera's FOV no matter where it is.........................
Now offset the RA/Dec grid and Alt/AZ by changing observation location.....
Let's get wild and go to Equator to see if this shakes things up. edit[best example of offset between RA/Dec and Alt/AZ]
If you've used a GEM mount you know the RA clockdrive of a perfectly polar-aligned mount will track a celestial object at the same rate across the sky. It doesn't speed up or slow down....
edit:but I didn't take into account the translation needed when Alt/Az and RA/Dec grids are offset......
And as you realized, your chart of apparent motion then should be flat lines.....edit[@ Poles]
Sorry to distract you on this. As I get you are aiming to calculate the field rotation issue that is affected by where the same target is depending on where it is in the sky.
And as said including the imaging spatial resolution to determine the sensitivity of a system(camera/optics) to notice the field rotation will be a key add.....
Here's my additional musing on conceptualizing positioning of objects:
Consider the benefit of the Coordinate systems of astronomy,
measured logically by angles because otherwise how far away do you place the grid to describe 2-D points to refer to sky objects?
--Consider an ancient looking out a window and putting a grid on the window to describe the stars' positions.....
This would be a useless non-stand way to describe positions....
Also the difficulty of the translation to the 3-D world, not dependent on waiting for the objects to pass by that particular window.
additionally the observer is located standing on an approximate sphere (if you believe NASA ,just kidding)....
So this also adds to the benefit of a concept of an "outer-sphere" to map celestial objects to [hence measuring distance between coordinates people imagine require spherical trig calculations]...
Additionally the Earth rotates, so it is also helpful that the coordinates describe 'fixed' celestial sky objects with a spherical concept.....
However from my musings,
the Spherical concept for coordinates (which are really in themselves descriptions of angles edit[not RA) is first and foremost based on the utility of the observer's perspective....IE a coordinate
RA/Dec or Alt/Az are measured angles from a given reference point....
The outer sphere diagram that many illustrations map to describe the astronomical coordinates is helpful when we talk about closer objects that do orbit the Earth.
Consider an ideal example: an artificial satellite in a circular orbit around the Earth, maintaining the same [height altitude in reference to ground (NADIR-point directly below)].
Here the simple trig math can describe its positional change across the sky because it remains "on/in" an artificial illustrated sphere around the Earth.
But stars/galaxies are in a matter of scale of infinite distance (like "infinity" focus) and fixed in space.
They aren't stuck all in one thin illustrated sphere surrounding the Earth..... There are in more of a cubic 3-d coordinate system out there.....
[for illustrate let's discount real motion of everything speeding through space and the real motion of the celestial objects]....
Consider if the stars are fixed in a cubic system,
the rotation of the Earth creates from the observer's perspective that they maintain a constant altitude above the Earth (at Nadir) in 'their orbit' since a globe is rotating under them and the momentary Nadir position on Earth does really stay the same distance from a fixed position star...
And although an orbiting satellite in an illustrated thin sphere shell above the Earth is 'close' and the spherical distances cause noticeable changes in perceptible distances over time (slow at horizon, speeds overhead),
stars in a conceptual sphere would be relatively at an infinite distance away so this perceptual change would not be noticeable.
Atmospheric refraction I believe would have more of a perceptible effect.....
edit:still processing all this...
Edited by t_image, 19 June 2019 - 12:16 PM.