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Converting RA/Dec to earth centered coordinates?



 
 
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  #1  
Old May 2nd 11, 10:28 PM posted to sci.astro
Steve Willner
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Posts: 1,172
Default Converting RA/Dec to earth centered coordinates?

In article ,
"W. eWatson" writes:
My xy plane is in the plane of the equator, and its projection into the
sky represents the celestial equator. Declination is measured +/- from
the celestial equator to each pole along great circle lines that pass
through each pole.

Somewhere on the celestial equator is point from where RA is measured.


To go from RA/Dec to an x,y,z unit vector is just simple trignometry:

x = cos(dec)*cos(RA)
y = cos(dec)*sin(RA)
z = sin (dec)

Make sure to convert RA/dec to degrees or radians (whatever units
your calculator or program uses). It's easy to forget to multiply
hours by 15 to get degrees.

The zero point of RA is the place where the ecliptic and celestial
equator intersect with the equinox heading north. Both this zero
point and the location of the celestial poles changes with respect to
the stars because of precession. If you want a _current_ x,y,z unit
vector, you need to start from current RA/Dec coordinates rather than
coordinates at a standard "ecliptic and equinox" (B1950 or J2000).
The Meeus book will tell you how to do that calculation.

Ah, the obliquity of the ecliptic (e) is what I need.


Don't see why you need that. Did you mean ecliptic coordinates
rather than celestial?

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  #2  
Old May 3rd 11, 02:48 AM posted to sci.astro
W. eWatson[_2_]
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Posts: 465
Default Converting RA/Dec to earth centered coordinates? (Correction)

On 5/2/2011 2:28 PM, Steve Willner wrote:
In ,
"W. writes:
My xy plane is in the plane of the equator, and its projection into the
sky represents the celestial equator. Declination is measured +/- from
the celestial equator to each pole along great circle lines that pass
through each pole.

Somewhere on the celestial equator is point from where RA is measured.


To go from RA/Dec to an x,y,z unit vector is just simple trignometry:

x = cos(dec)*cos(RA)
y = cos(dec)*sin(RA)
z = sin (dec)

Make sure to convert RA/dec to degrees or radians (whatever units
your calculator or program uses). It's easy to forget to multiply
hours by 15 to get degrees.

The zero point of RA is the place where the ecliptic and celestial
equator intersect with the equinox heading north. Both this zero
point and the location of the celestial poles changes with respect to
the stars because of precession. If you want a _current_ x,y,z unit
vector, you need to start from current RA/Dec coordinates rather than
coordinates at a standard "ecliptic and equinox" (B1950 or J2000).
The Meeus book will tell you how to do that calculation.

Ah, the obliquity of the ecliptic (e) is what I need.


Don't see why you need that. Did you mean ecliptic coordinates
rather than celestial?

Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec. In a unit sphere I think
of z as pointing through the north pole, x pointing south through 1,0,0,
and y pointing east through 0,1,0.

In my case, precession does not enter into matters. I'm constructing a
simulation that is mostly grounded in az/el and lat/lng. I wrote a
program that produces the path of a fake meteor moving in a straight
line. Time is not yet useful as a consideration yet.

The direction of the line points to the radiant point in the sky.
Meteors lie on a great circle, hence pass their plane passes through the
earth's center (spherical earth). My program has not yet needed ra/dec,
which is usually the measure of the radiant point in the sky and is
given in ra/dec. However,I have the data from a similar program, and
they provide the radiant as ra/dec. internally, my program seems sound
when I sort of run it backwards. I get agreeable results. I want to see
if the independent source and I agree.
  #3  
Old May 5th 11, 10:43 PM posted to sci.astro
Steve Willner
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Posts: 1,172
Default Converting RA/Dec to earth centered coordinates? (Correction)

In article ,
"W. eWatson" writes:
Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec.


So just invert the equations I gave you.
Dec = arcsin(z)
RA = atan2(x,y)
You might have to use (y,x) in the second one, depending on your
atan2 function. Don't forget to convert to degrees/hours from
whatever units your calculator or program uses.

In a unit sphere I think
of z as pointing through the north pole, x pointing south through 1,0,0,
and y pointing east through 0,1,0.


Something is confused here. If +z is north, south will be -z, not x.
Anyway, check a few cases that you know the answer for and make sure
there's no sign inversion or 90-degree error.

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Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
  #4  
Old May 6th 11, 12:34 AM posted to sci.astro
Bill Owen
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Posts: 154
Default Converting RA/Dec to earth centered coordinates? (Correction)

Steve Willner wrote:
In article ,
"W. eWatson" writes:
Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec.


So just invert the equations I gave you.
Dec = arcsin(z)


Better: Dec = atan2 (z, sqrt(x^2 + y^2)), which will work for all
vectors (not just unit vectors) and will give accurate results near the
poles.

RA = atan2(x,y)
You might have to use (y,x) in the second one, depending on your
atan2 function. Don't forget to convert to degrees/hours from
whatever units your calculator or program uses.


It's universally atan2(y,x) as far as I know. You do have to make sure
you put the y coordinate in the numerator.

In a unit sphere I think
of z as pointing through the north pole, x pointing south through 1,0,0,
and y pointing east through 0,1,0.


Something is confused here. If +z is north, south will be -z, not x.
Anyway, check a few cases that you know the answer for and make sure
there's no sign inversion or 90-degree error.

  #5  
Old May 6th 11, 04:59 AM posted to sci.astro,sci.astro.amateur
oriel36[_2_]
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Posts: 8,478
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 6, 1:34*am, Bill Owen wrote:
Steve Willner wrote:
In article ,
*"W. eWatson" writes:
Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec.


So just invert the equations I gave you.
Dec = arcsin(z)


Better: Dec = atan2 (z, sqrt(x^2 + y^2)), which will work for all
vectors (not just unit vectors) and will give accurate results near the
poles.

RA = atan2(x,y)
You might have to use (y,x) in the second one, depending on your
atan2 function. *Don't forget to convert to degrees/hours from
whatever units your calculator or program uses.


It's universally atan2(y,x) as far as I know. *You do have to make sure
you put the y coordinate in the numerator.







In a unit sphere I think
of z as pointing through the north pole, x pointing south through 1,0,0,
and y pointing east through 0,1,0.


Something is confused here. *If +z is north, south will be -z, not x.
Anyway, check a few cases that you know the answer for and make sure
there's no sign inversion or 90-degree error.


All the doctorates here with not enough sense to look at a telescope
tracking a circumpolar star at all times during a year where the
turning telescope creates its own axis rather than following the
attributes of planetary geometry,in short,you are not dealing with the
convenience of calendar based geocentric coordinates but pure
homocentricity.

Let me spell it out for you and for the people who pay your salary,Ra/
Dec is not a geocentric system hence it does not translate into
planetary dynamics directly even though you and your colleagues have
this idea that the daily and orbital motion of the Earth can be
squeezed into right ascension.This requires something even more plain
for the reader,when you assume there is an imbalance between the
amount of daylight/darkness cycles over a 4 year orbital period,and
this is what Ra/Dec applied to the Earth's planetary dynamics does,you
are in trouble with the most basic cause and effect of all - the
correspondence between one 24 hour rotation and one day/night cycle.

Don't know how any of you can do it,no matter how hard you try to skip
over or ignore what is a fundamental astronomical cause and effect or
treat it like trivia,the more your empirical agenda looks
inconsequential and while the calendar based Ra/Dec is a convenience
it seems you just don't have the ability to interpret that any
telescope turning on its mount gives a homocentric picture and not a
geocentric one.









  #6  
Old May 6th 11, 05:52 AM posted to sci.astro,sci.astro.amateur
palsing[_2_]
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Posts: 3,068
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 5, 8:59*pm, oriel36 wrote:

All the doctorates here with not enough sense to look at a telescope
tracking a circumpolar star at all times during a year where the
turning telescope creates its own axis...


...it seems you just don't have the ability to interpret that any
telescope turning on its mount gives a homocentric picture and not a
geocentric one.


Set that telescope on a star tonight, any star at all, and turn the
drive off, no tracking needed. About 23:56:04 will pass before the
same star is centered up again in the telescope, and it will continue
to do so, every night, night after night, in the exact same time
frame. What could this mean? Clearly, with respect to that star,
rotation takes about 23:56:04... what other possible conclusion could
a rational person come to?

Where does your own superior ability to interpret lead you, given this
incontrovertible, easily observable fact?



  #7  
Old May 6th 11, 07:50 AM posted to sci.astro
Quadibloc
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Posts: 7,018
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 5, 3:43*pm, (Steve Willner) wrote:
In article ,
*"W. eWatson" writes:

Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec.


So just invert the equations I gave you.
Dec = arcsin(z)
RA = atan2(x,y)
You might have to use (y,x) in the second one, depending on your
atan2 function. *Don't forget to convert to degrees/hours from
whatever units your calculator or program uses.


If you have the ATAN2 function, that would mean you are using FORTRAN,
which uses radians as its units... I would have thought. However, in
C, math.h also includes an atan2 function.

The C atan2 function is described as being atan2(y,x) and returning
the arctangent of y/x, set in the appropriate quadrant.

Thus, given the signs of y and x, the result is in the range:

y - positive, x - positive: [0, pi/2]
y - positive, x - negative: [pi/2, pi]
y - negative, x - positive: [-pi/2, 0]
y - negative, x - negative: [-pi, -pi/2]

Thus, positive angles are measured counterclockwise from the positive
x-axis where x is the second argument.

This is the same convention as FORTRAN used.

John Savard
  #8  
Old May 6th 11, 03:23 PM posted to sci.astro,sci.astro.amateur
oriel36[_2_]
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Posts: 8,478
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 6, 6:52*am, palsing wrote:
On May 5, 8:59*pm, oriel36 wrote:

All the doctorates here with not enough sense to look at a telescope
tracking a circumpolar star at all times during a year where the
turning telescope creates its own axis...
...it seems you just don't have the ability to interpret that any
telescope turning on its mount gives a homocentric picture and not a
geocentric one.


Set that telescope on a star tonight, any star at all, and turn the
drive off, no tracking needed. About 23:56:04 will pass before the
same star is centered up again in the telescope, and it will continue
to do so, every night, night after night, in the exact same time
frame. What could this mean? Clearly, with respect to that star,
rotation takes about 23:56:04... what other possible conclusion could
a rational person come to?


Any person here who concludes there are 366 1/4 rotations in a year
through this late 17 the century junk is either a complete fraud or
criminally incompetent,it is not an accusation,it is not an opinion
but something which far more dangerous than any act of terrorism as
it undermines the actual correspondence between what the body
experiences and the mind accepts as valid.You have these guys from
NASA and Harvard with an ideology that sinks below a standard that the
world hasn't seen before and while you may try to reason your way to
justify stellar circumpolar motion using the Earth's planetary
dynamics,it cannot be done .

Never.never has the world had to deal with these creatures who
willingly try to avoid a open debate and even when it is pointed out
that their Ra/Dec reckoning is homocentric,not geocentric,they still
continue to push for something which is contrary to all known
astronomical principles ,either geocentric or the astronomy of
planetary dynamics.

A telescope tracking a star creates its own axis of rotation ,a sane
person interpreting that individual rotation will ultimately conclude
that Ra/Dec is based on the calendar system,no more or less.What a
horrible bunch of people that go out of their way to propose a system
which does not tally with cause and effect of the daylight/darkness
cycle and can call themselves astronomers despite the inability to
comprehend the proportion of rotations to orbital cycles as 1461 to 4
or 365 1/4 rotations to 1 orbital cycle.

You think you are better than a flat Earther or a creationist by
arguing against the rotation of the planet once in 24 hours and 365
1/4 times in an orbital year but you are far,far below what those
people accept as fact,the difference is that the toxic strain of
empiricism which ran with Ra/Dec reasoning is a dominant force in the
education system via the 'scientific method'.

You have moved on,let the other readers who stuck their necks out
continue.










Where does your own superior ability to interpret lead you, given this
incontrovertible, easily observable fact?


  #9  
Old May 6th 11, 04:13 PM posted to sci.astro,sci.astro.amateur
palsing[_2_]
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Posts: 3,068
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 6, 7:23*am, oriel36 wrote:

You think you are better than a flat Earther or a creationist by
arguing against the rotation of the planet once in 24 hours and 365
1/4 times in an orbital year...


I'm not arguing against anything here, in fact, I agree with you, with
respect to the sun, and so does everyone else.

I'm only asking for your own interpretation of the fact that an
undriven telescope centered on any star of your choice will have that
same star momentarily centered in the field of view every 23:56:04...
an undeniable fact that is readily observable by anyone, anytime,
anywhere. It doesn't have a thing to do with any calendar, but it does
mean something, and I'm just asking you for your interpretation.
Simple.
  #10  
Old May 6th 11, 05:42 PM posted to sci.astro,sci.astro.amateur
oriel36[_2_]
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Posts: 8,478
Default Converting RA/Dec to earth centered coordinates? (Correction)

On May 6, 5:13*pm, palsing wrote:
On May 6, 7:23*am, oriel36 wrote:

You think you are better than a flat Earther or a creationist by
arguing against the rotation of the planet once in 24 hours and 365
1/4 times in an orbital year...


I'm not arguing against anything here, in fact, I agree with you, with
respect to the sun, and so does everyone else.


Empiricists,a spectacularly intellectually impotent bunch,are arguing
for 366 1/4 rotations in an orbital year hence the attempt to create
an imbalance between rotations and the daylight/darkness cycles so
this is an issue of cause and effect experienced by the body,assign
any other value than 1461 rotations and day/nights cycles across the
calendar,and this is what criminally incompetent individuals try to do
and the things descends to a level worse than any the world has ever
known as ultimately all it requires is the ability to count.

Go teach the NASA,Harvard guys,people who can't distinguish geocentric
from homocentric by interpreting the tracking of a stellar circumpolar
star using a GoTo telescope deserve the same ridicule as any group
that tries to make something out of nothing.Go ahead and explain why
Feb 29th as a 24 hour rotation and day/night cycle is required to
complete the proportion of 1461 rotations to 4 orbital circuits.It is
not the these intellectual freaks are repentant,much like the old Nazi
were,it is the lack of support for the rotation of the Earth once in
24 hours and 365 1/4 times in an orbital year.

Fundamentalists have nothing on empiricists,that much is for certain
and while some like yourself can be excused as nuisances, the worst
behavior has always been self-serving silence.



The simple fact that the 1461 rotations spanning 4 orbital circuits
accounts for the day/night cycle of Feb 29th would simply transfer to
the basic proportions of 365 1/4 rotations per circuit so yes,you are
arguing against something so fundamental to human understanding that





I'm only asking for your own interpretation of the fact that an
undriven telescope centered on any star of your choice will have that
same star momentarily centered in the field of view every 23:56:04...
an undeniable fact that is readily observable by anyone, anytime,
anywhere. It doesn't have a thing to do with any calendar, but it does
mean something, and I'm just asking you for your interpretation.
Simple.


 




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