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Main
Date: 14 Aug 2006 09:07:39
From: Dave Blake
Subject: Mixed Coordinate conversion - ra from long and dec
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Can any one help me with a bit of math.
I would like to get right ascension given the celestial longitude and
declination of an object. Yes, that's right I do mean mixed co-ordinate
systems. I know the equations that convert ecliptical to equatorial
co-ordinates e.g. celestial long and lat to ra and dec (and vica versa)
but I'm darned if I can get the trig re-arranged to give ra as a
function of celestial longitude and declination. Not so worried about
celestial lat, but it could be part of it.
It might sound odd, but I really do need to solve this. Hope this is
right place to try.
Dave
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Date: 14 Aug 2006 10:34:37
From: canopus56
Subject: Re: Mixed Coordinate conversion - ra from long and dec
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"Dave Blake" <Barnswood@hotmail.com > wrote in message
news:1155571659.407592.290880@m79g2000cwm.googlegroups.com...
> Can any one help me with a bit of math.
> I would like to get right ascension given the celestial longitude and
> declination of an object. <snip>
To clarify,, do you mean to convert from ecliptic long and lat to equatorial
(celestial) r.a. and dec?
- Canopus56
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Date: 14 Aug 2006 15:57:54
From: Ernie Wright
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Dave Blake wrote:
> Can any one help me with a bit of math.
> I would like to get right ascension given the celestial longitude and
> declination of an object. Yes, that's right I do mean mixed co-ordinate
> systems.
I think this is easier to do in Cartesian coordinates.
The solution is the intersection of two circles. One is a great circle
of constant longitude. The latitude changes as you move along this
circle. The other is a (non-great) circle of declination. The right
ascension changes as you move along that one.
Each circle is embedded in a plane. The intersection of the circles is
on the line which is the intersection of the planes. You should be able
to find this as the vector cross-product of the plane normals, which are
also the pole vectors of the two circles.
I don't have time to work out what this would look like, but to give you
a start: you need to define both circles in the same coordinate system.
Choose the Cartesian system with its axes aligned with the plane and
pole of the equatorial (ra and dec) system. In this system, Z points to
the north celestial pole, and X and Y form the plane of the equator.
The center of the longitude circle is just (0, 0, 0). The center of the
declination circle is (0, 0, sin dec). The radius of the dec circle is
cos( dec ), and the radius of the longitude circle is 1.
The normal of the dec circle is (0, 0, 1). The normal of the longitude
circle is a vector pointing toward (lon + 90, 0). Convert that to ra
and dec in the usual way, then convert the result to a vector using
nx = cos( dec ) * sin( ra )
ny = cos( dec ) * cos( ra )
nz = sin( dec )
to get the components of the longitude circle's normal.
Now you have the two planes in point-normal form.
dec: P = (0, 0, sin dec) N = (0, 0, 1)
lon: P = (0, 0, 0) N = (nx, ny, nz)
Googling will reveal how to find the line representing the intersection
of these two planes. Then you just need to find the two points on this
line that intersect the dec circle.
All those 0's and 1's probably mean that this simplifies a great deal
once you work through it. Unfortunately the margins of my newsreader
are too small to contain the proof.
- Ernie http://home.comcast.net/~erniew
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Date: 14 Aug 2006 19:43:37
From: Paul Schlyter
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
In article <1155571659.407592.290880@m79g2000cwm.googlegroups.com >,
Dave Blake <Barnswood@hotmail.com > wrote:
> Can any one help me with a bit of math.
> I would like to get right ascension given the celestial longitude and
> declination of an object. Yes, that's right I do mean mixed co-ordinate
> systems. I know the equations that convert ecliptical to equatorial
> co-ordinates e.g. celestial long and lat to ra and dec (and vica versa)
> but I'm darned if I can get the trig re-arranged to give ra as a
> function of celestial longitude and declination. Not so worried about
> celestial lat, but it could be part of it.
>
> It might sound odd, but I really do need to solve this. Hope this is
> right place to try.
> Dave
Use an astronomical ephemeris rather than an astrological ephemeris - then
you don't have to bother with this problem...... :-)
The relevant conversion equations can otherwise be found here:
http://en.wikipedia.org/wiki/Ecliptic_coordinates
So what you'll have to do is to find the solution of a system of equations,
where you know lambda, delta and epsilon, and you want to solve for alfa
and perhaps also for beta.
Good luck!
--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/
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Date: 14 Aug 2006 12:35:18
From: oriel36
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Here is an exercise for you and be sure to take your time.
If the Ra\Dec system works using 3 years of 365 days and 1 year of 366
days,actually requires those values to work,can you guess what it means
as an accurate reflection of the Earth's orbital motion when you force
the stellar background into heliocentric reasoning.
http://www.dur.ac.uk/john.lucey/users/sidereal_day.gif
http://www.bedford.k12.ny.us/flhs/science/geoscience/images/siderealdaysm.jpg
A few years ago ,many would happily play along with your simpleminded
celestial sphere system couched in non geometric language but that is
then and this is now.When you base the Earth's orbital motion on the
calendrical system you get pure junk couched in wonderful math
Bill Owen wrote:
> Dave Blake wrote:
> > Can any one help me with a bit of math.
> > I would like to get right ascension given the celestial longitude and
> > declination of an object. Yes, that's right I do mean mixed co-ordinate
> > systems. I know the equations that convert ecliptical to equatorial
> > co-ordinates e.g. celestial long and lat to ra and dec (and vica versa)
> > but I'm darned if I can get the trig re-arranged to give ra as a
> > function of celestial longitude and declination. Not so worried about
> > celestial lat, but it could be part of it.
> >
> > It might sound odd, but I really do need to solve this. Hope this is
> > right place to try.
>
> Yup. In what follows, I'll use (a,d) for (RA,Dec) and (l,b) for
> ecliptic (lon,lat) and e for the obliquity, just to save keystrokes.
> (Note that l and b are really lambda and beta, NOT galactic coordinates!)
>
> Use rectangular coordinates. The conversion from (RA,Dec) to (lon,lat):
>
> cos l cos b = cos a cos d
> sin l cos b = cos e sin a cos d + sin e sin d
> sin b = -sin e sin a cos d + cos e sin d
>
> Divide the second equation by the first:
>
> sin l cos e sin a cos d + sin e sin d
> ----- = -------------------------------
> cos l cos a cos d
>
> This equation contains RA, longitude, declination, and obliquity -- the
> latitude has been removed. We need to solve it for RA in terms of the
> others. Cross multiply and gather everything on one side:
>
> sin a (cos e cos d cos l) - cos a (cos d sin l) + sin e sin d cos l = 0
>
> Now -- here's the tricky part -- make the substitution
>
> cos e cos d cos l = m cos M
> cos d sin l = m sin M
> sin e sin d cos l = C
>
> so the previous equation reduces to
>
> sin a (m cos M) - cos a (m sin M) + C = 0
>
> or
>
> m sin (a-M) = -C
>
> whose solution is
>
> a = M + arcsin (C/m)
>
> where
>
> M = atan2 (sin l, cos e cos l)
> m = cos d sqrt (sin^2 l +cos^2 e cos^2 l)
>
> Use the principal value for arcsin (C/m) and the 4-quadrant arctan
> to get M.
>
> As one would expect, this blows up at the poles. :-)
>
> I'll leave it as an exercise for the reader to prove that
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Date: 14 Aug 2006 23:29:04
From: David G. Fitzgerald
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
oriel36 wrote:
> Here is an exercise for you and be sure to take your time.
>
> If the Ra\Dec system works using 3 years of 365 days and 1 year of 366
> days,actually requires those values to work,can you guess what it means
> as an accurate reflection of the Earth's orbital motion when you force
> the stellar background into heliocentric reasoning.
>
> http://www.dur.ac.uk/john.lucey/users/sidereal_day.gif
>
> http://www.bedford.k12.ny.us/flhs/science/geoscience/images/siderealdaysm.jpg
>
> A few years ago ,many would happily play along with your simpleminded
> celestial sphere system couched in non geometric language but that is
> then and this is now.When you base the Earth's orbital motion on the
> calendrical system you get pure junk couched in wonderful math
>
>
>
>
Are you on Haldol? I am, and I still can't thiunk like that,yet.
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Date: 14 Aug 2006 11:51:53
From: Bill Owen
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Dave Blake wrote:
> Can any one help me with a bit of math.
> I would like to get right ascension given the celestial longitude and
> declination of an object. Yes, that's right I do mean mixed co-ordinate
> systems. I know the equations that convert ecliptical to equatorial
> co-ordinates e.g. celestial long and lat to ra and dec (and vica versa)
> but I'm darned if I can get the trig re-arranged to give ra as a
> function of celestial longitude and declination. Not so worried about
> celestial lat, but it could be part of it.
>
> It might sound odd, but I really do need to solve this. Hope this is
> right place to try.
Yup. In what follows, I'll use (a,d) for (RA,Dec) and (l,b) for
ecliptic (lon,lat) and e for the obliquity, just to save keystrokes.
(Note that l and b are really lambda and beta, NOT galactic coordinates!)
Use rectangular coordinates. The conversion from (RA,Dec) to (lon,lat):
cos l cos b = cos a cos d
sin l cos b = cos e sin a cos d + sin e sin d
sin b = -sin e sin a cos d + cos e sin d
Divide the second equation by the first:
sin l cos e sin a cos d + sin e sin d
----- = -------------------------------
cos l cos a cos d
This equation contains RA, longitude, declination, and obliquity -- the
latitude has been removed. We need to solve it for RA in terms of the
others. Cross multiply and gather everything on one side:
sin a (cos e cos d cos l) - cos a (cos d sin l) + sin e sin d cos l = 0
Now -- here's the tricky part -- make the substitution
cos e cos d cos l = m cos M
cos d sin l = m sin M
sin e sin d cos l = C
so the previous equation reduces to
sin a (m cos M) - cos a (m sin M) + C = 0
or
m sin (a-M) = -C
whose solution is
a = M + arcsin (C/m)
where
M = atan2 (sin l, cos e cos l)
m = cos d sqrt (sin^2 l +cos^2 e cos^2 l)
Use the principal value for arcsin (C/m) and the 4-quadrant arctan
to get M.
As one would expect, this blows up at the poles. :-)
I'll leave it as an exercise for the reader to prove that
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Date: 14 Aug 2006 12:19:45
From: William Hamblen
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
On 2006-08-14, Dave Blake <Barnswood@hotmail.com > wrote:
> I would like to get right ascension given the celestial longitude and
> declination of an object. Yes, that's right I do mean mixed co-ordinate
> systems. I know the equations that convert ecliptical to equatorial
> co-ordinates e.g. celestial long and lat to ra and dec (and vica versa)
> but I'm darned if I can get the trig re-arranged to give ra as a
> function of celestial longitude and declination. Not so worried about
> celestial lat, but it could be part of it.
Jean Meeus's books (http://www.willbell.com) tells all.
Wikipedia (of all things) gives the Reader's Digest condensed
version:
http://en.wikipedia.org/wiki/Ecliptic_coordinate_system
It's the condensed version because it doesn't go into things
like changing epochs or changes in the inclination of the
earth's axis. Meeus has all the nasty little details.
Bud
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Date: 15 Aug 2006 09:43:56
From: John Carruthers
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
oriel36 wrote:
> Here is an exercise for you and be sure to take your time.
......
Please ignore OT botcheck.
SUN TZU ON THE ART OF WAR
THE OLDEST MILITARY TREATISE IN THE WORLD
Translated from the Chinese
By LIONEL GILES, M.A. (1910)
I. LAYING PLANS
1. Sun Tzu said: The art of war is of vital importance
to the State.
Kepler.
2. It is a matter of life and death, a road either
to safety or to ruin. Hence it is a subject of inquiry
which can on no account be neglected.
heliocentricity.
3. The art of war, then, is governed by five constant
factors, to be taken into account in one's deliberations,
when seeking to determine the conditions obtaining in the field.
4. These are: (1) The Moral Law; (2) Heaven; (3) Earth;
(4) The Commander; (5) Method and discipline.
5,6. The Moral Law causes the people to be in complete
accord with their ruler, so that they will follow him
regardless of their lives, undismayed by any danger.
7. Heaven signifies night and day, cold and heat,
times and seasons.
8. Earth comprises distances, great and small;
danger and security; open ground and narrow passes;
the chances of life and death.
9. The Commander stands for the virtues of wisdom,
sincerely, benevolence, courage and strictness.
10. By method and discipline are to be understood
the marshaling of the army in its proper subdivisions,
the graduations of rank among the officers, the maintenance
of roads by which supplies may reach the army, and the
control of military expenditure.
11. These five heads should be familiar to every general:
he who knows them will be victorious; he who knows them
not will fail.
12. Therefore, in your deliberations, when seeking
to determine the military conditions, let them be made
the basis of a comparison, in this wise:--
13. (1) Which of the two sovereigns is imbued
with the Moral law?
(2) Which of the two generals has most ability?
(3) With whom lie the advantages derived from Heaven
and Earth?
(4) On which side is discipline most rigorously enforced?
(5) Which army is stronger?
(6) On which side are officers and men more highly trained?
(7) In which army is there the greater constancy
both in reward and punishment?
14. By means of these seven considerations I can
forecast victory or defeat.
15. The general that hearkens to my counsel and acts
upon it, will conquer: let such a one be retained in command!
The general that hearkens not to my counsel nor acts upon it,
will suffer defeat:--let such a one be dismissed!
16. While heading the profit of my counsel,
avail yourself also of any helpful circumstances
over and beyond the ordinary rules.
17. According as circumstances are favorable,
one should modify one's plans.
18. All warfare is based on deception.
Oriel36.
19. Hence, when able to attack, we must seem unable;
when using our forces, we must seem inactive; when we
are near, we must make the enemy believe we are far away;
when far away, we must make him believe we are near.
20. Hold out baits to entice the enemy. Feign disorder,
and crush him.
21. If he is secure at all points, be prepared for him.
If he is in superior strength, evade him.
22. If your opponent is of choleric temper, seek to
irritate him. Pretend to be weak, that he may grow arrogant.
23. If he is taking his ease, give him no rest.
If his forces are united, separate them.
24. Attack him where he is unprepared, appear where
you are not expected.
25. These military devices, leading to victory,
must not be divulged beforehand.
26. Now the general who wins a battle makes many
calculations in his temple ere the battle is fought.
The general who loses a battle makes but few
calculations beforehand. Thus do many calculations
lead to victory, and few calculations to defeat:
how much more no calculation at all! It is by attention
to this point that I can foresee who is likely to win or lose.
|
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Date: 15 Aug 2006 00:50:17
From: Dave Blake
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Many thanks Bill, that was just what I needed.
The mcosM substitution was the key, I didn't spot that one. Instead I
went off with tan half angles and quadratic roots - ending in a mess
that I never found my way out of!
Ernie was also correct, in that it is about finding the solution to the
interesction of two circles, but the cartesian approach was just too
scary.
Dave Blake
|
| | |
Date: 16 Aug 2006 00:32:45
From: Ernie Wright
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Dave Blake wrote:
> Ernie was also correct, in that it is about finding the solution to the
> interesction of two circles, but the cartesian approach was just too
> scary.
I lean toward Cartesian approaches because they usually mesh better with
common computer graphics techniques. But in this case I really wish I'd
given the answer Bill gave. :)
- Ernie http://home.comcast.net/~erniew
|
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Date: 15 Aug 2006 12:01:21
From: Linux Utilisateur
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
oriel36 wrote:
> Here is an exercise for you and be sure to take your time.
[remainder of missive deleted for brevity]
are you on medication?
|
| |
Date: 15 Aug 2006 11:16:18
From: Linux Utilisateur
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Your writing reminds me of some mental patients who used to smoke lot
of Ecstasy, and they think everything they said was utterly amazing.
Incidentally, didn't you say that the Venus de Milo is an evidence that
Aphrodite exists!
oriel36 wrote:
> What you see in the other postings is simply the convenience of
> spotting objects on a celestial sphere based on the calendrical
> system,the people are almost ghosts,they see nothing other than what
> moves on a sphere tied to terrestial lomgitudes and care not to think
> otherwise.
>
> No disrespect to mr tzu but this is an attempt to raise men above
> mediocrity of celestial sphere geometry and into the realm of
> Copernican heliocentricity and its later refinements.It matters a great
> deal that those who graduate from astrophotography to astronomy proper
> to not justify the convenience of the 1461 day calendrical cycle,cut
> the motions of the planets loose from the stellar background and work
> on the properties and utilities of axial and orbital motion in
> isolation.
>
> Turn up the volume on coordinate systems and I cut these guys to
> pieces,they end up saying nothing and they are highlighted as having
> said nothing astronomically worthwhile.
>
> Did you learn the lesson why it is not a good idea to justify the
> orbital motion of the Earth through the Ra\Dec system of 3 years of
> 365 days and 1 year of 366 days .
>
>
>
> John Carruthers wrote:
> > oriel36 wrote:
> > > Here is an exercise for you and be sure to take your time.
> > ......
> >
> > Please ignore OT botcheck.
> >
> >
> >
> > SUN TZU ON THE ART OF WAR
> > THE OLDEST MILITARY TREATISE IN THE WORLD
> >
> > Translated from the Chinese
> > By LIONEL GILES, M.A. (1910)
> >
> >
> >
> > I. LAYING PLANS
> >
> >
> > 1. Sun Tzu said: The art of war is of vital importance
> > to the State.
> > Kepler.
> >
> > 2. It is a matter of life and death, a road either
> > to safety or to ruin. Hence it is a subject of inquiry
> > which can on no account be neglected.
> > heliocentricity.
> > 3. The art of war, then, is governed by five constant
> > factors, to be taken into account in one's deliberations,
> > when seeking to determine the conditions obtaining in the field.
> >
> > 4. These are: (1) The Moral Law; (2) Heaven; (3) Earth;
> > (4) The Commander; (5) Method and discipline.
> >
> > 5,6. The Moral Law causes the people to be in complete
> > accord with their ruler, so that they will follow him
> > regardless of their lives, undismayed by any danger.
> >
> > 7. Heaven signifies night and day, cold and heat,
> > times and seasons.
> >
> > 8. Earth comprises distances, great and small;
> > danger and security; open ground and narrow passes;
> > the chances of life and death.
> >
> > 9. The Commander stands for the virtues of wisdom,
> > sincerely, benevolence, courage and strictness.
> >
> > 10. By method and discipline are to be understood
> > the marshaling of the army in its proper subdivisions,
> > the graduations of rank among the officers, the maintenance
> > of roads by which supplies may reach the army, and the
> > control of military expenditure.
> >
> > 11. These five heads should be familiar to every general:
> > he who knows them will be victorious; he who knows them
> > not will fail.
> >
> > 12. Therefore, in your deliberations, when seeking
> > to determine the military conditions, let them be made
> > the basis of a comparison, in this wise:--
> >
> > 13. (1) Which of the two sovereigns is imbued
> > with the Moral law?
> > (2) Which of the two generals has most ability?
> > (3) With whom lie the advantages derived from Heaven
> > and Earth?
> > (4) On which side is discipline most rigorously enforced?
> > (5) Which army is stronger?
> > (6) On which side are officers and men more highly trained?
> > (7) In which army is there the greater constancy
> > both in reward and punishment?
> >
> > 14. By means of these seven considerations I can
> > forecast victory or defeat.
> >
> > 15. The general that hearkens to my counsel and acts
> > upon it, will conquer: let such a one be retained in command!
> > The general that hearkens not to my counsel nor acts upon it,
> > will suffer defeat:--let such a one be dismissed!
> >
> > 16. While heading the profit of my counsel,
> > avail yourself also of any helpful circumstances
> > over and beyond the ordinary rules.
> >
> > 17. According as circumstances are favorable,
> > one should modify one's plans.
> >
> > 18. All warfare is based on deception.
> > Oriel36.
> >
> > 19. Hence, when able to attack, we must seem unable;
> > when using our forces, we must seem inactive; when we
> > are near, we must make the enemy believe we are far away;
> > when far away, we must make him believe we are near.
> >
> > 20. Hold out baits to entice the enemy. Feign disorder,
> > and crush him.
> >
> > 21. If he is secure at all points, be prepared for him.
> > If he is in superior strength, evade him.
> >
> > 22. If your opponent is of choleric temper, seek to
> > irritate him. Pretend to be weak, that he may grow arrogant.
> >
> > 23. If he is taking his ease, give him no rest.
> > If his forces are united, separate them.
> >
> > 24. Attack him where he is unprepared, appear where
> > you are not expected.
> >
> > 25. These military devices, leading to victory,
> > must not be divulged beforehand.
> >
> > 26. Now the general who wins a battle makes many
> > calculations in his temple ere the battle is fought.
> > The general who loses a battle makes but few
> > calculations beforehand. Thus do many calculations
> > lead to victory, and few calculations to defeat:
> > how much more no calculation at all! It is by attention
> > to this point that I can foresee who is likely to win or lose.
|
| |
Date: 15 Aug 2006 10:14:27
From: oriel36
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
What you see in the other postings is simply the convenience of
spotting objects on a celestial sphere based on the calendrical
system,the people are almost ghosts,they see nothing other than what
moves on a sphere tied to terrestial lomgitudes and care not to think
otherwise.
No disrespect to mr tzu but this is an attempt to raise men above
mediocrity of celestial sphere geometry and into the realm of
Copernican heliocentricity and its later refinements.It matters a great
deal that those who graduate from astrophotography to astronomy proper
to not justify the convenience of the 1461 day calendrical cycle,cut
the motions of the planets loose from the stellar background and work
on the properties and utilities of axial and orbital motion in
isolation.
Turn up the volume on coordinate systems and I cut these guys to
pieces,they end up saying nothing and they are highlighted as having
said nothing astronomically worthwhile.
Did you learn the lesson why it is not a good idea to justify the
orbital motion of the Earth through the Ra\Dec system of 3 years of
365 days and 1 year of 366 days .
John Carruthers wrote:
> oriel36 wrote:
> > Here is an exercise for you and be sure to take your time.
> ......
>
> Please ignore OT botcheck.
>
>
>
> SUN TZU ON THE ART OF WAR
> THE OLDEST MILITARY TREATISE IN THE WORLD
>
> Translated from the Chinese
> By LIONEL GILES, M.A. (1910)
>
>
>
> I. LAYING PLANS
>
>
> 1. Sun Tzu said: The art of war is of vital importance
> to the State.
> Kepler.
>
> 2. It is a matter of life and death, a road either
> to safety or to ruin. Hence it is a subject of inquiry
> which can on no account be neglected.
> heliocentricity.
> 3. The art of war, then, is governed by five constant
> factors, to be taken into account in one's deliberations,
> when seeking to determine the conditions obtaining in the field.
>
> 4. These are: (1) The Moral Law; (2) Heaven; (3) Earth;
> (4) The Commander; (5) Method and discipline.
>
> 5,6. The Moral Law causes the people to be in complete
> accord with their ruler, so that they will follow him
> regardless of their lives, undismayed by any danger.
>
> 7. Heaven signifies night and day, cold and heat,
> times and seasons.
>
> 8. Earth comprises distances, great and small;
> danger and security; open ground and narrow passes;
> the chances of life and death.
>
> 9. The Commander stands for the virtues of wisdom,
> sincerely, benevolence, courage and strictness.
>
> 10. By method and discipline are to be understood
> the marshaling of the army in its proper subdivisions,
> the graduations of rank among the officers, the maintenance
> of roads by which supplies may reach the army, and the
> control of military expenditure.
>
> 11. These five heads should be familiar to every general:
> he who knows them will be victorious; he who knows them
> not will fail.
>
> 12. Therefore, in your deliberations, when seeking
> to determine the military conditions, let them be made
> the basis of a comparison, in this wise:--
>
> 13. (1) Which of the two sovereigns is imbued
> with the Moral law?
> (2) Which of the two generals has most ability?
> (3) With whom lie the advantages derived from Heaven
> and Earth?
> (4) On which side is discipline most rigorously enforced?
> (5) Which army is stronger?
> (6) On which side are officers and men more highly trained?
> (7) In which army is there the greater constancy
> both in reward and punishment?
>
> 14. By means of these seven considerations I can
> forecast victory or defeat.
>
> 15. The general that hearkens to my counsel and acts
> upon it, will conquer: let such a one be retained in command!
> The general that hearkens not to my counsel nor acts upon it,
> will suffer defeat:--let such a one be dismissed!
>
> 16. While heading the profit of my counsel,
> avail yourself also of any helpful circumstances
> over and beyond the ordinary rules.
>
> 17. According as circumstances are favorable,
> one should modify one's plans.
>
> 18. All warfare is based on deception.
> Oriel36.
>
> 19. Hence, when able to attack, we must seem unable;
> when using our forces, we must seem inactive; when we
> are near, we must make the enemy believe we are far away;
> when far away, we must make him believe we are near.
>
> 20. Hold out baits to entice the enemy. Feign disorder,
> and crush him.
>
> 21. If he is secure at all points, be prepared for him.
> If he is in superior strength, evade him.
>
> 22. If your opponent is of choleric temper, seek to
> irritate him. Pretend to be weak, that he may grow arrogant.
>
> 23. If he is taking his ease, give him no rest.
> If his forces are united, separate them.
>
> 24. Attack him where he is unprepared, appear where
> you are not expected.
>
> 25. These military devices, leading to victory,
> must not be divulged beforehand.
>
> 26. Now the general who wins a battle makes many
> calculations in his temple ere the battle is fought.
> The general who loses a battle makes but few
> calculations beforehand. Thus do many calculations
> lead to victory, and few calculations to defeat:
> how much more no calculation at all! It is by attention
> to this point that I can foresee who is likely to win or lose.
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Date: 16 Aug 2006 07:50:31
From: Dave Blake
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Ernie Wright wrote:
> I lean toward Cartesian approaches because they usually mesh better with
> common computer graphics techniques. But in this case I really wish I'd
> given the answer Bill gave. :)
>
You are right again, but they are still scary :)
But I'll note for posterity that there was a tiny typo in Bill's
elegant solution: it should read " a = M + arcsin (-C/m) " note the
minus sign.
However, having implemented it I am having problems (Bill I hope that
you are listening). I am getting wrong answers for ra for all values of
long where dec >= 90-obliquity. Frustratingly I still can't see any
errors in Bill's trig or my code.
I have coded it in Delphi, but that is pretty readable. Anyone care to
spot (and fix) the problem?
function RAFromLongDec(Long, de, e: Double):Double;
var
ce, se, sl, cl, sd, cd, A, B, C: double: Double;
begin
se := Dsin(e);
ce := Dcos(e);
sl := dsin(long);
cl := dcos(long);
sd := dsin(de);
cd := dcos(de);
A := cd*sqrt(sqr(sl) + sqr(ce*cl));
if ce*cl < > 0 then
B := Dinvtan2(sl, ce*cl)
else
B := 90*sgn(sl);
C := se*sd*cl;
Result := B + dinvsin(-C/A);
end;
Wrong values of ra returned when de >= 90-e or near -90. So near and
yet so far....
Thanks
--Dave Blake
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Date: 16 Aug 2006 10:18:05
From: Bill Owen
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Dave Blake wrote:
> Ernie Wright wrote:
>> I lean toward Cartesian approaches because they usually mesh better with
>> common computer graphics techniques. But in this case I really wish I'd
>> given the answer Bill gave. :)
And I wish I'd caught that minus sign *before* I posted it. Thanks for
the kind words nevertheless.
> You are right again, but they are still scary :)
> But I'll note for posterity that there was a tiny typo in Bill's
> elegant solution: it should read " a = M + arcsin (-C/m) " note the
> minus sign.
Correct. One could equally write "a = M - arcsin (C/m)".
> However, having implemented it I am having problems (Bill I hope that
> you are listening). I am getting wrong answers for ra for all values of
> long where dec >= 90-obliquity. Frustratingly I still can't see any
> errors in Bill's trig or my code.
If it makes you feel any better, I can duplicate your problem in
Fortran.
It turns out that you can't just take the principal value of the arcsin
for these cases near the pole. For instance, I started with RA 210 deg
(14h if you prefer), Dec +80, which is longitude 115.728678, latitude
69.731592. Note that RA is in the third quadrant but Lon is in the 2nd
quadrant. Then I ran RA and Lat through the formula and got
M = 113.851181
arcsin (C/m) = -83.851181 (principal value)
Subtract the two and the *wrong* result is RA = 197.702363. But if
I use the other value for the arcsin, 180 - (-83.851181) = 263.851181,
then 113.851181 - 263.851181 = -150, and when you add 360 it comes out
correct.
Then I repeated the calculations for RA 197.702363, Dec +80. This time
the latitude is 67.6001035, *but the longitude is again 115.728678*.
And sure enough, M - arcsin(C/m) gives 197.702363.
*** There are two different points on the celestial sphere with the same
declination and ecliptic longitude *** for declination > 90 - obliquity
or declination < -90 + obliquity. If you draw a small circle, centered
on the NCP, with radius < obliquity, you can then draw a great
semicircle passing through the NEP (constant longitude) which will
intersect the small circle in two points. Each of those points is a
valid solution to your problem.
(If the radius of the small circle > obliquity, the great *semicircle*
can intersect it no more than once as the NEP lies inside the small
circle.)
The only thing you can do is to check whether the declination is
either > 90 - obliquity or < -90 + obliquity; and if so, compute both
values of RA.
Sorry for the confusion ... but I've learned something too along the
way.
-- Bill Owen
> I have coded it in Delphi, but that is pretty readable. Anyone care to
> spot (and fix) the problem?
>
> function RAFromLongDec(Long, de, e: Double):Double;
> var
> ce, se, sl, cl, sd, cd, A, B, C: double: Double;
> begin
> se := Dsin(e);
> ce := Dcos(e);
> sl := dsin(long);
> cl := dcos(long);
> sd := dsin(de);
> cd := dcos(de);
> A := cd*sqrt(sqr(sl) + sqr(ce*cl));
> if ce*cl <> 0 then
> B := Dinvtan2(sl, ce*cl)
> else
> B := 90*sgn(sl);
> C := se*sd*cl;
> Result := B + dinvsin(-C/A);
> end;
>
> Wrong values of ra returned when de >= 90-e or near -90. So near and
> yet so far....
>
> Thanks
> --Dave Blake
>
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Date: 16 Aug 2006 12:37:17
From: oriel36
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Linux Utilisateur wrote:
> oriel36 wrote:
> > Here is an exercise for you and be sure to take your time.
>
> [remainder of missive deleted for brevity]
>
> are you on medication?
Alas,there is no medication thjat can save you from stupidity and
especially the Ra\Dec celestial geometrical system that justifies
axial rotation through 360 degrees in 23 hours 56 min 04 sec.
Keep up with the coordinate system you assign to your observations,I
will even provide the geometry to which you fix all celestial motions
-
http://astrosun2.astro.cornell.edu/academics/courses//astro201/images/sidereal_day.gif
http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/celestial_sphere_anim.gif
No doubt you are entirely happy with constellational astrology and I
am only too happy to point out exactly what your mathematical
treatments amount to.May as well turn your telescopes in baseball
bats,at least there would be less damage done to the fabric of the once
great astronomical tradition.
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Date: 18 Aug 2006 14:44:37
From: oriel36
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
I hope you learned that it is not a good idea to base the orbital
motion of the Earth on a system which uses 3 years of 365 days and 1
year of 366 days.
Your celestial sphere geometry relies on the return of a star in 23
hours 56 min 04 sec and it requires a leap day correction to work for
in your system.
There is no moral when stupidity exists at the bottom of your
principles and all because John Flamsteed needed to tie terrestial
longitudes to the return of a star to a meridian.Ultimately the whole
system looks exactly like your warped space ideas,maybe somebody will
be good enough to add rotation to constellational astrophotography and
you will close the awful loop that begins and ends with Newton -
http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/celestial_sphere_anim.gif
Are you positive that a star returning to a meridian denotes axial
rotation through 360 degrees ?.
Dave Blake wrote:
> Bill Owen wrote:
> > *** There are two different points on the celestial sphere with the same
> > declination and ecliptic longitude *** for declination > 90 - obliquity
> > or declination < -90 + obliquity.
>
> Doh! Thanks Bill, of course there are. The moral of the tale for me is
> never blindly implement trig solutuons for which you have not
> visualised the problem properly!
>
> For a given dec, some ecliptic longitudes never cut it, others cut it
> once (cosl = cosd/sine marks the boudary) and for dec near the poles it
> can be cut twice.
>
> > Sorry for the confusion ... but I've learned something too along the
> > way.
>
> I have learned lots too. Thanks
> --Dave Blake
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Date: 18 Aug 2006 10:16:36
From: Dave Blake
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
Bill Owen wrote:
> *** There are two different points on the celestial sphere with the same
> declination and ecliptic longitude *** for declination > 90 - obliquity
> or declination < -90 + obliquity.
Doh! Thanks Bill, of course there are. The moral of the tale for me is
never blindly implement trig solutuons for which you have not
visualised the problem properly!
For a given dec, some ecliptic longitudes never cut it, others cut it
once (cosl = cosd/sine marks the boudary) and for dec near the poles it
can be cut twice.
> Sorry for the confusion ... but I've learned something too along the
> way.
I have learned lots too. Thanks
--Dave Blake
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Date: 19 Aug 2006 09:33:53
From: John Carruthers
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
oriel36 wrote:
> I hope you learned that it is not a good idea to base the orbital
> motion of the Earth on a system which uses 3 years of 365 days and 1
> year of 366 days.
>
> Your celestial sphere geometry relies on the return of a star in 23
> hours 56 min 04 sec and it requires a leap day correction to work for
> in your system.
>
While you dream tonight of Kepler my 'scope will be tracking the
heavens accurately. Be assured they will turn without your supervision.
Any coordinate system we aply is purely arbitrary, use the most
convenient for your purpose. If we stood on the sun a heliocentric
system would undoubtedly work. We do not. We are on earth (not sure
about you though) and geocentric co-ordinates work just fine. They get
our probes to their targets and our 'scopes stay centred. We are all in
step exept you.....
jc
|
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Date: 19 Aug 2006 13:28:02
From: oriel36
Subject: Re: Mixed Coordinate conversion - ra from long and dec
|
John Carruthers wrote:
> oriel36 wrote:
> > I hope you learned that it is not a good idea to base the orbital
> > motion of the Earth on a system which uses 3 years of 365 days and 1
> > year of 366 days.
> >
> > Your celestial sphere geometry relies on the return of a star in 23
> > hours 56 min 04 sec and it requires a leap day correction to work for
> > in your system.
> >
> While you dream tonight of Kepler my 'scope will be tracking the
> heavens accurately.
http://mitpress.mit.edu/journals/pdf/POSC_13_1_74_0.pdf
Kepler's representation known as the Panis Quadragesimalis (Page 86) is
just one of those exquisite astronomical jewels that most intelligent
people would enjoy with a little effort or familiarity.
The two dates of 1580 and 1596 represent the 18 orbital cycles of Earth
in comparison to the orbital cycles of Mars where retrogrades are
plotted against the stellar background.Using these comparisons,Kepler
would use the periodic time comparisons to argue for heliocentricity in
terms of the motion of the Earth between Venus and Mars *.
No telescope is required to enjoy what Kepler did and how he reasoned
as an extension of the original Copernican insight but it will be there
for all to see.
Be assured they will turn without your supervision.
> Any coordinate system we aply is purely arbitrary, use the most
> convenient for your purpose.
Pseudo-authority is fine and indeed I marvel at the casual and carefree
manner in which 'arbitrary' is assigned to celestial phenomena.My turn.
The 24 hour clock system and its calendrical extension are almost two
seperate system's but the core principle is based strictly on the
pre-Copernican return of the Sun to noon where the Equation of
correction is applied to facilitate the seamless transition from one 24
hour day to the next.The exquisite adaption by the heliocentric
astronomers was to apply the Equation of Time correction to the idea
that the Earth's axial rotation is an independent motion,something the
pre-Copernican astronomers knew nothing about.
The calendrical extension has no astronomical basis save that it is a
convenience based on celestial sphere averaging,roughly 1461 days.Its
basic format of a star returning to a meridian in 23 hours 56 min is
conditioned by the 1461 calendrical cycle of 3 years of 365 days and 1
year of 366 days.
If we stood on the sun a heliocentric
> system would undoubtedly work. We do not. We are on earth (not sure
> about you though) and geocentric co-ordinates work just fine.
Everyone deserves a chance,you can turn to page 86 and affirm that
Kepler is making orbital comparisons between Mars and Earth using the
stellar background as a reference for Mars and taking the Earth's
orbital cycle in years as a gauge .The working language of Kepler,as it
is for all heliocentric astronomers is an orbitally moving Earth in
accounting for observed planetary motion.It is all made very easy today
with images of the position of the planets against a fixed background
and rendered into time lapse footage,like so
http://antwrp.gsfc.nasa.gov/apod/image/0112/jupsatloop_tezel.jpg
http://antwrp.gsfc.nasa.gov/apod/image/0112/JuSa2000_tezel.gif
They get
> our probes to their targets and our 'scopes stay centred. We are all in
> step exept you.....
> jc
Indeed you are all in step,that is abundantly clear.I do however
require at least a few to gauge correctly that Newton is not in step
with the original reasoning of Copernicus and Kepler,not even with the
Ptolemaic astronomers -
" 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
The correct answer is,of course,that planetary heliocentric motion is
seen directly from Earth -
http://antwrp.gsfc.nasa.gov/apod/image/0112/JuSa2000_tezel.gif
Climate and geological concerns are far more important than keeping you
telescopes in sync with celestial sphere geometry,as long as nobody
tries to justify the celestial sphere they can happily carry on with
astrophotography.But,and there is a but,astrophotography is just a
minor facet of astronomy and presently a feebleminded and destructive
facet having allied itself with empirical theorists.
-----------------------------------------------------------------------------------------------------------------------------
*
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
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