Parallax by Day

On May 25, 1:07 pm, Anthony Ayiomamitis
wrote:
Ernie Wright wrote:
Anthony Ayiomamitis wrote:

http://www.perseus.gr/Astro-Lunar-Parallax.htm

The image scale of the resampled image is around 2.51"/pixel. ;-)

I get an estimate of 438,988 km for the distance of the moon from the
earth when, in fact, it was 395,520 km at the time of photography. In
other words, there is an error of approximately 10%.

I got an estimate of 443,368 km. This is assuming an image scale of
about 3.25"/pixel, which I got from the diameter of the Moon,

557 pixels using the ruler tool in Photoshop CS2
1812" according tohttp://aa.usno.navy.mil/data/docs/diskmap.html

The distance between the two images of Regulus is 337 pixels = 1096".

Moon distance = (Selsey Athens distance / 2) / tan(1096"/2)

I think the error comes from assuming that the Selsey-Athens base of the
triangle is at right angles to the Earth-Moon vector. In general it
won't be. If tilting that line up to make it perpendicular shortens it
to about 2100 km, we get a very accurate estimate.

Thanks for the feedback Ernie. My results vary slightly due to SkyMap
Pro which indicates the moon had an apparent diameter of 1839.34" and
the parallax angle which I estimated to be 1113.6". My estimate as to
the distance also ignored the image scale I specified in an earlier post
which for some reason is not correct and I must check as to the reason(s).

Anyway, a nice exercise. Just ask Oriel.

Anthony.





- Ernie http://home.comcast.net/~erniew- Hide quoted text -

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Here is the orbital motion of the Earth along with Jupiter -

http://antwrp.gsfc.nasa.gov/apod/ima...2000_tezel.gif

The common heliocentric orbit provides the basis for the recognition
of the anomalous motion of Io insofar as the stretching distance
between Earth and Jupiter accounts for the irregular occultation of Io
using finite light speed as conditioning factor.

Of course,you and you buddies refuse to acknowledge orbital
comparisons and use a hypothetical observer on the Sun to account for
the motion of Jupiter -

"For to the earth planetary motions appear sometimes direct,
sometimes stationary, nay, and sometimes retrograde. But from the sun
they are always seen direct, " Newton

As the Mora Luminis of Roemer can only be appreciated by people who
recognise the orbital motion of the Earth,any lesser view such as
parallax is going to highlight that you have no astronomical pedigree
and attaching yourself to Newton's views which exclude orbital
comparisons does just that.

The Roemerian refinement is a wonderful addition to the original
working principles provided by Copernicus and does not involve the
background stars but only the motion of the Earth and that of
Jupiter.If you want to continue to make yourself look foolish then so
be it,at least others are getting the benefit of an education by
exposing yourselves as dull and dour astrologers hellbent on ignoring
orbital motions or rather retaining celestial sphere geometry.

Some of the English who recognise an enormous astronomical version of
Piltdown man in the making can easily become familiar with the orbital
motion of the Earth for the first time and at least try to make the
effort of rectifying matters.As for you,continue taking those nice
pictures of the analemma,do you hear,those nice pictures where a 24
hour clock determines the postion of the Sun !!!!!!.

Ernie Wright wrote:
Anthony Ayiomamitis wrote:

[concerning http://www.perseus.gr/Astro-Lunar-Parallax.htm]

Thanks for the feedback Ernie.


Thanks to you and Pete for a fascinating collaborative exercise!

Ernie,

We thank you as well. I just hope you have generous bandwidth for your
website: http://www.lpod.org/?m=20070526

Anthony.

Le 25 mai 2007, Ernie Wright a écrit :
[concerning http://www.perseus.gr/Astro-Lunar-Parallax.htm]

The situation looks something like this:

. * Selsey
. \
. \ -------- to the Moon
. \
. * Athens

The base we should be using,

. * Selsey ....... |
. |
. | -------- to the Moon
. |
. * Athens ... |


When I did this, I got a length factor of 0.928. Multiplying this by the
chord length distance between Athens and Selsey (2356 km) gives a triangle
base of 2186 km. Using your (probably more careful than mine) estimate of
the parallax angle, 1113.6", yields a distance estimate of 404,897 km, for
an error of only a little more than 2%. That's pretty cool!

Well, actually, the 395,520 km Anthony gave is the geocentric distance
of the Moon, i.e. the distance from the center of the Earth to the
center of the Moon. In geocentric coordinates, the Moon is a little
closer. My ephemeris program tells me the real distance of the Moon from
Athens is 391,741 km, so that the error is around 3.4 %. That's still
cool, however ;-)

Anthony Ayiomamitis wrote:

Ernie,

We thank you as well. I just hope you have generous bandwidth for your
website: http://www.lpod.org/?m=20070526

Wow. Well, I guess I'll find out.

- Ernie http://home.comcast.net/~erniew

Khanh-Dang wrote:

Le 25 mai 2007, Ernie Wright a écrit :

yields a distance estimate of 404,897 km, for an error of only a
little more than 2%. That's pretty cool!

Well, actually, the 395,520 km Anthony gave is the geocentric distance
of the Moon, i.e. the distance from the center of the Earth to the
center of the Moon. In geocentric coordinates, the Moon is a little
closer. My ephemeris program tells me the real distance of the Moon from
Athens is 391,741 km, so that the error is around 3.4 %.

You're right, of course. And as it turns out, my first calculation,
which I did by hand, had an error in it (I switched sine and cosine in
the declination term of the coordinate conversions; I described this the
right way in my post but did it backwards). I've written a program to
run the calculation more rigorously and it finds a distance about 3%
*less* than the topocentric distance.

That's still cool, however ;-)

Doing this calculation gives one a renewed appreciation for what
Hipparchus was able to accomplish before trigonometry was invented.

- Ernie http://home.comcast.net/~erniew

Ernie Wright wrote:
Doing this calculation gives one a renewed appreciation for what
Hipparchus was able to accomplish before trigonometry was invented.

Modern trigonometry, yes, but they had similar and basically sufficient
mathematical tools.

Your point stands, though: Very impressive. Then again, of course, he
was Hipparchus, not some doof.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html

oriel36 wrote:
The motion of the visble stars of our galaxy around a central axis
will change their orientation to the external galaxies,as you
creatures have the visible stars stuck on an astrological framework
there is no possibility of appreciating this great cycle,even in
principle.
..
No. This is not the case.

Of course we can recognize that the "fixed" stars in the Milky Way
galaxy really do move, slowly.

Just as we realize that precession of the equinoxes is a real
phenomenon.

We still use the position of the equinoxes, or the "fixed stars", as a
background, as a reference frame, because they move so slowly that
they serve as *reasonably* fixed landmarks, but, naturally, a closer
approximation to an inertial frame *is* possible through using distant
galaxies as a reference.

Even the galaxies, though, are in motion.

But we are talking, as I noted in a previous post, about a matter of a
hundredth of a second per day, even with the largest correction, the
one for precession. The precession cycle takes about 24,000 years.
Compare that with the *one year* cycle that causes the difference
between the 24 hour synodic day and the 23 hour and 56 minute sidereal
day.

If you advocate adopting the system of Tycho Brahe because you are
annoyed that we sometimes ignore the small precession effect, you are
straining out a gnat yet swallowing a camel. If that is not what you
are doing, then your point is still a mystery to me.

John Savard

On May 28, 1:50 pm, Quadibloc wrote:
oriel36 wrote:
The motion of the visble stars of our galaxy around a central axis
will change their orientation to the external galaxies,as you
creatures have the visible stars stuck on an astrological framework
there is no possibility of appreciating this great cycle,even in
principle.

.
No. This is not the case.


It is an absolute geometric certainty that you base you concepts on a
astrological/celestial sphere framework -

"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun.

This proportion, first observed by Kepler, is now received by all
astronomers; for the periodic times are the same, and the dimensions
of the orbits are the same, whether the sun revolves about the earth,
or the earth about the sun." Newton

When you are faced with silly quasi-geocentric statements like this
from Newton and especially when he invokes Kepler,you turn to what
Kepler actually said and especially as regards the 'periodic
times'.The periodic times argument is based on orbital comparisons and
it is a fully heliocentric argument in replacing the pre-Copernican
arrangement of the Sun between Venus and Mars with the Earth's orbital
motion.

It goes like this -

Epitome Of Copernican Astronomy by Johannes Kepler


Finally by what arguments do you prove that the centre of the Sun
which is at the midpoint of the planetary spheres and bears their
whole system - does not revolve in some annual movement,as Brahe
wishes,but in accordance with Copernicus sticks immobile in one
place,while the centre of the Earth revolves in an annual movement.


Argument 10


" The 10th argument,taken from the periodic times, is as follows; the
apparent movement of the Sun has 365 days which is the mean measure
between Venus' period of 225 days and Mars' period of 687
days.Therefore does not the nature of things shout out loud that the
circuits in which those 365 days are taken up has a mean position
between the circuits of Mars and Venus around the Sun and thus this is
not the circuit of the Sun around the Earth -for none of the primary
planets has its orbit arranged around the Earth,as Brahe admits,but
the circuit of the Earth around the resting Sun,just as the other
planets,namely Mars and Venus,complete their own periods by running
around the Sun." Johannes Kepler

I would not wish to use the wonderful argument of Kepler in support of
heliocentricity to be used to counter Newton's twisting of the
periodic times argument for a heliocentric/geocentric orbital
equivalency but at least people can see how the original 'periodic
times ' argument looks.








Of course we can recognize that the "fixed" stars in the Milky Way
galaxy really do move, slowly.

Just as we realize that precession of the equinoxes is a real
phenomenon.

We still use the position of the equinoxes, or the "fixed stars", as a
background, as a reference frame, because they move so slowly that
they serve as *reasonably* fixed landmarks, but, naturally, a closer
approximation to an inertial frame *is* possible through using distant
galaxies as a reference.

Even the galaxies, though, are in motion.


At the core of the Newtonian concepions for orbital motions beats an
astological heart created by Flamsteed.Linking axial rotation directly
to the stellar background is bad enough,the correlation is an
incredible leap by any stretch of the imagination,what encloses it in
a celestial sphere is the fact that a star return in 23 hours 56
minutes 04 seconds of a 24 hour day only in the calendar system where
4 annual orbits are recknoed in a system of 3 years of 365 days and 1
year of 366 days.

In short,while Newtonj talked a system of 365.25 days he used
Flamsteed's calendrical framework which in turn amounts to an
astrological framework -

http://members.tripod.com/~gravitee/phaenomena.htm

You have no reason to be hostile,I have had to go through these
difficult arguments that you can simply skip at will and whatever I
may say about Newton,one thing is certain,the way he reworked
astronomical things to suit his agenda he is consistent and makes it
possible to untangle what is correct from what is not.







But we are talking, as I noted in a previous post, about a matter of a
hundredth of a second per day, even with the largest correction, the
one for precession. The precession cycle takes about 24,000 years.
Compare that with the *one year* cycle that causes the difference
between the 24 hour synodic day and the 23 hour and 56 minute sidereal
day.

If you advocate adopting the system of Tycho Brahe because you are
annoyed that we sometimes ignore the small precession effect, you are
straining out a gnat yet swallowing a camel. If that is not what you
are doing, then your point is still a mystery to me.

John Savard

The preccessional motion of the Earth is always,always,always the
most used to muddy the waters while the most immediate axial and
orbital motions are ignored,it is like an indoctrinated thumbsucking
tactic to call on preccession and for the most part it works.I can
simply compare the faster orbital motion of the Earth against the
slower motion of the outer planets to remove 3 centuries worth of
Newtonian rubbish but apparently nobody is interested -

http://antwrp.gsfc.nasa.gov/apod/ima...2000_tezel.gif

Without appreciating what is occuring from a moving Earth you cannot
admire the Keplerian refinement which uses the orbital motion of the
Earth against that of Mars or the Romerian insight on finite light
distance which uses the orbital motion of the Earth against Jupiter.

You can bluff and bluster for 3 centuries,indeed you can do it for
another 3 centuries but ultimately it is not worth it.I have to find a
group who actually likes astronomy,its methids and its insights in
order to make the neccessary modifications.I cannot do in in an
empirical/astrological forum and that is that.

Brian Tung wrote:

Ernie Wright wrote:

Doing this calculation gives one a renewed appreciation for what
Hipparchus was able to accomplish before trigonometry was invented.

Modern trigonometry, yes, but they had similar and basically sufficient
mathematical tools.

Indeed. There's no mathematically important difference between using
sines and using chords.

Your point stands, though: Very impressive. Then again, of course, he
was Hipparchus, not some doof.

That's pretty much what I was trying to say. He didn't need *any* of
the tools I perhaps doofily relied on. And unlike us, he couldn't peek
at the answers in the back of the book.

As Brian already knows, almost none of Hipparchus's original writing has
survived. We have to rely mainly on the bits and pieces conveyed to us
by Ptolemy in the Almagest. Ptolemy's description of lunar parallax
calculations is in book V part 17. The diagram (Fig. 5.13 in Toomer's
translation) shows the situation pretty clearly.

- Ernie http://home.comcast.net/~erniew

Re http://www.lpod.org/?m=20070526

I had a chance this weekend to do a few 3D renders showing the geometry
of the Earth-Moon system at the time of the images. They include a
stereo pair of the views from Athens and Selsey.

http://home.comcast.net/~erniew/astro/moonpar.html

I'll probably add some details to the text at the end of the page in the
next couple of days.

- Ernie http://home.comcast.net/~erniew