42a

How the velador works

Since the velador is composed of a laser at a fixed bar and a CCD it measures motion in only two directions.  The two directions are related to the CCD.  A x and y axis.  The direction that lies in the direction of the laser light cannot be measured without turning the velador.  This is due to the geometry of the situation.  The spot of light that hits the CCD occurs opposite to the direction of motion.  A principle that is an agreement with stellar aberration.

Consider a rotational motion having a component on the x axis and on the y axis.  Consider the velador set up so that the CCD is either in the South or the North position.  The other various positions can be figured out from this example.

Try to use the concept of absolute space in this problem.  This should become clearer as we progress.

Consider a rotational vector moving the CCD clockwise when the CCD is in the south.  That is the top of the CCD moves to the west or in other words to your right.  The right side of the CCD moves down with this clockwise rotation.  The bottom moves east or to your left.  So say in the southern position of the CCD laser spot hits the x-axis at a low value.  And hits the y axis at a low value.  The CCD measures from the top left corner going to your right as the x-axis increasing.  It measures from the top left going down as the y axis and as you go down the value increases.  Look at the diagram below for a reference.

Consider just the x-values for now.  As we have said the x-values are low and the y values are low at a particularly arbitrary spot that we have chosen the laser to hit the CCD on.  Now we are going to swing the velador to the north.  As the basic rotation remains the same that is the top has to rotate to the west because we have changed its position it now is rotating counterclockwise.  This reveals a major problem with using clockwise and counterclockwise for rotations.  Anyway now the top of the CCD is moving to the west which is our left.  Thus the motion will carry the spot impact to our right which is a higher value for the x-axis.  In the first example when the CCD was in the South the x was a low value. Now because we have basically changed the left and right of the CCD the motion carries the spot in an opposite direction to that that existed in the South compared to the now north position.  If there were no motion at all the impact spot would be midway between these two values but say the first value was zero and the value in the north was 10 then the x-value would be five, midway.

Now consider the y-values.  In the south say the why motion is down at the west or to your right edge of the CCD the spot will be hitting the y at a low value in this example. The other side of the CCD that is east and to your left will be rotating up but we should just consider the right side. Now go to the north position where the motion  is counterclockwise and your right side is going up and the left is down. The  motion appears reversed from the South direction.  Now the y is measured opposite.  but say if no motion existed the y would be at five.  From the diagram notice that the left is going down and the right side is going up, opposite yo what we found in the southern position.

This is why the x and the y axis reverse values when we go from one direction to the opposite direction. the green spot is where the light woyuld hit if there were no motion.