Sent: Thu, 22 Nov 2007 13:00:44 +1100Dear all,
I have produced two animations (attached) that hopefully address some
of the questions raised during the last weeks time. This is a response to
several E-mails by several authors, raising the same kinds of questions.
Allen, that I do not reply explicitly to your E-mails, does not mean
that I am evading or ignoring your questions. Please take the time to
read this and see that I do address your questions.
I would rather have people read and understand and re-read this post,
rather than rush to write a quick (hurried) reply. If you do hurry your
reply, my time writing this post will most likely be wasted - and I hate
wasting time. And it did take some time...
General about the animations
They both show the Earth in orbit around the Sun. It is not to scale,
but the Earth's daily spin axis (dashed line) is shown at the correct
angle to the ecliptic plane (tilted 100 towards the viewer) and the
ecliptic axis (dotted line). I have shows latitudes for every 300 and
longitudes for every 450 (pink), to show the orientation of the Earth.
The pink straight line shows the direction to the Sun, and the dotted
part is inside the Earh, making it clearer where it enters the Earth.
Animation #1 - translational orbit
EarthOrb3_10.gif, please refer to this as Ani.1.
This shows the translational orbit of the Earth around the Sun.
This happens in the plane of the ecliptic, but involves no rotation.
The orientation of the Earth is the same throughout the year.
This is what you see if:
a) you do not include the daily spin around the celestial axis,
i.e., you isolate the translational part of Earth's motion during a year.
b) you include the spin and take a snapshot every period of that spin
i.e., the sidereal (stellar) day = 23h56m.
The result will be the exact same in either case.
Notice how the radial line to the Sun (the part inside the Earth, is dotted)
changes both latitude and longitude during the year.
Animation #2 - daily (Solar) snapshots
EarthOrb3_10_trop.gif, please refer to this as Ani.2.
We now add the daily rotation/spin of the Earth around the celestial axis,
and we take a snapshot every tropical (Solar) day.
Notice how the line to the Sun (pink) stays at the same longitude - that
is the definition of tropical (Solar) day. The latitude of that line,
however, changes during the year - going from +23.50 in the Northern
summer (right) to -23.50 in the Northern winter (left) - that's why we
Allen, Neville and others, have suggested that cameras mounted (fixed) on
Earth, would see a rotation around the ecliptic axis (dotted line) during
a year. I have therefore mounted a camera on the equator to look straight
up at zenith (radially out from the Earth). I have mounted my camera to
look towards the Sun at noon, instead of out at midnight, but I hope you
realize that this has no consequence for this discussion.
The green line shows the direction of view of that camera.
During the year it sweeps out the equatorial plane of Earth.
It rotates around the Earth's axis of daily rotation = celestial axis.
If you look at it from above, the projection will make it look like the
camera looks straight towards the Sun - This is what Allen's and Neville's
figures depicts (except they have their cameras face the opposite direction
towards the local meridian at midnight). It is however, a projection effect
- in three dimensions you realize that the camera (green line) only points
to the Sun twice a year - at the solstices.
It should also be clear that you can move the camera to any spot on Earth
and have it look in any direction - if it is kept fixed, it will only
see the daily rotation around the celestial axis (dashed line).
Taking snapshots every tropical (solar) day (24h00m), just means you are
taking pictures at an incrementing phase of the daily rotation whose real
period is 23h56m - the sidereal (stellar) day. For Each day, you let the
Earth rotate for 4 more minutes before taking a picture. A year of that
will complete a full ROTATION around the celestial axis. During the
same time you have completed a full TRANSLATION around the Sun.
Taking pictures every tropical (Solar) day does not depict a yearly motion,
just snapshots in different phases of the daily rotation.
Looking carefully at high-quality images taken every sidereal (stellar)
day (see Ani.1) you will see parallaxes for some of the closer stars
- this is the manifestation of the annual (translational) motion around
James, your drawing is beautiful and shows the same thing, as I show.
The only slightly misleading thing, is that you have drawn grid-lines on
Earth that are w.r.t. the ecliptic axis (green) - the grid should be tilted
to be aligned with the celestial (red) axis. I also agree with Neville and
Allen (I believe) that one of the blue "cameras" should be marked with a
different colour, to be able to follow the rotation.
Sorry for this post being so long, but there were many points to address.
I also try to keep misunderstandings to a minimum by rephrasing things.
P.S. The animations are animated gif-files. Please report if you have trouble
viewing them. I don't know whether they are trivial to Windows or Mac