Directions...

I was wondering if someone could help answer the question of how close
(from a solid angle) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination

east-west direction with Leo on the horizon...


0°
^
-
' | '
' | '
|
' | '
|
' | '
----|----
' --- | --- '
'- | -'
'-------------+-------------'
- CL -
--- ---
--------

In other words, if one takes one of these as a line point as a zero
line, what is the conic solid angle of the others???

I'd appreciate any help in this, thanks...

Paul Stowe

Dear Paul Stowe:

"Paul Stowe" wrote in message
...
I was wondering if someone could help answer the question of how close
(from a solid angle) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination

Declination defined:
URL:http://www.site.uottawa.ca:4321/astr...ml#declination

Ascention defined:
URLhttp://www.site.uottawa.ca:4321/astronomy/index.html#declination

I'd go for:
(17-11) / 24 * 360 = 90 degrees "east west" (theta)
and
(68- (-7)) = 75 degrees "north south" (phi)

Then to figure the included angle, I'd go for:
cos( angle) = (u.v) / (|u| * |v|)

where the "." is the dot product...

Anybody have a simpler formula that his?

David A. Smith

On Wed, 19 Nov 2003 19:44:33 -0700, \(formerly\)" dlzc1.cox@net
wrote:

Dear Paul Stowe:

"Paul Stowe" wrote in message
.. .
I was wondering if someone could help answer the question of how close
(from a solid angle) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination

Declination defined:
URL:http://www.site.uottawa.ca:4321/astr...ml#declination

Ascention defined:
URLhttp://www.site.uottawa.ca:4321/astronomy/index.html#declination

I'd go for:
(17-11) / 24 * 360 = 90 degrees "east west" (theta)
and
(68- (-7)) = 75 degrees "north south" (phi)

Then to figure the included angle, I'd go for:
cos( angle) = (u.v) / (|u| * |v|)

where the "." is the dot product...

Anybody have a simpler formula that his?

Thanks David, I guess this means



0°
^
-
' | '
' | '
^ |
' \| | '
-o-75° x 90°
' | | '
-\\-|----
' --- \ | --- '
'- \| -'
'-------------+-------------'
- C\ -
--- \ ---
-------\


???

Paul Stowe

In article ,
Paul Stowe writes:
I was wondering if someone could help answer the question of how close
(from a solid angle) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination

It's an ordinary two-dimensional angle, not a solid angle.

What you want is one of the spherical triangle formulas:

cos A = sin(d1)*sin(d2) + cos(d1)*cos(d2)*cos(a1-a2)

where a1,d1 are the ra and dec of one direction, a2,d2 the other
direction. When calculating, be sure to convert to the proper units
for your trig functions, probably radians or degrees. (My calculator
gives a choice of degrees or radians; Excel insists on radians. I
won't tell you how often that last has caught me.)

In this case, cos A = -.0113 + 0 , A = 96.5 degrees (approximately).

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

On 21 Nov 2003 17:24:52 -0400, (Steve Willner) wrote:

In article ,
Paul Stowe writes:
I was wondering if someone could help answer the question of how close
(from a solid angle) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination

It's an ordinary two-dimensional angle, not a solid angle.

What you want is one of the spherical triangle formulas:

cos A = sin(d1)*sin(d2) + cos(d1)*cos(d2)*cos(a1-a2)

where a1,d1 are the ra and dec of one direction, a2,d2 the other
direction. When calculating, be sure to convert to the proper units
for your trig functions, probably radians or degrees. (My calculator
gives a choice of degrees or radians; Excel insists on radians. I
won't tell you how often that last has caught me.)

Thank (and you too David) for taking the time to respond & help out. I
am not an astronomer and these give me a headache. But something's wrong
then with the claimed directions since one is suppose to point to Virgo
and the other Leo... These are ~ 15° apart, NOT 96°...

So a followup question is, where do these reported direction point?

Paul Stowe

In this case, cos A = -.0113 + 0 , A = 96.5 degrees (approximately).

"PS" == Paul Stowe writes:

PS On 21 Nov 2003 17:24:52 -0400, (Steve
PS Willner) wrote:
In article , Paul Stowe
writes:
I was wondering if someone could help answer the question of how
close (...) are the following celestrial lines in space.

11 hrs right ascension, -7 degrees declimation
17 hrs right ascension, +68 degrees declination
It's an ordinary two-dimensional angle, not a solid angle.

What you want is one of the spherical triangle formulas:

cos A = sin(d1)*sin(d2) + cos(d1)*cos(d2)*cos(a1-a2)
[...]

PS But something's wrong then with the claimed directions since one
PS is suppose to point to Virgo and the other Leo... These are ~ 15°
PS apart, NOT 96°...

Yep, something's wrong. You can tell from the declinations alone that
these two directions differ by at least 75 degrees (68 - -7).

Virgo is somewhere around 12--14 h right ascension, 0 deg. declination
while Leo is somewhere around 10--12 h right ascension, 15 deg. declination.

PS So a followup question is, where do these reported direction
PS point?

The first is in the constellation Crater.

The second is in the constellation Draco.

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