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Old 18-09-2014, 09:12   #1
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Celestial Making Sense of Altitude Corrections

More guidance please.

I have been comparing altitude corrections for Sun, Stars & Moon.

Sun & Stars are similar. With an assumed Apparent Altitude of 16 degrees 10 mins the Sun is 3.15 min (winter) and 3.2 min (summer) Stars are 3.3 min.

However with same assumed app alt the moon is 62.7 min (lower) 32.7 min (Upper).

Can someone explain my misunderstanding?

I am using Celestial Nav for Yachtsmen Mary Blewitt.

Thanks

Mike
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Old 19-09-2014, 08:19   #2
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Re: Celestial Making sense of altitude corrections

100 odd views but no reply.

I suppose I should just be happy to learn to use the tables as prescribed but I also feel the need to understand. What is confusing me if I did not make it clear in my original post is I have read about and think I understand refraction. The fishing rod poked into a pond appears to bend (if this is a good analogy). The same happens when light enters the earths atmosphere. I am sure that light irrespective of its origin, (Sun, Moon,Planets or Stars) assuming it enters the earths atmosphere at the same angle (same apparent altitude) will bend about the same.

In the example above 16 deg 10 min.

I arrived at the Sun corrections by adding SD to lower limb and minus SD off upper limb in both cases the answer is about -3 min.

For the stars SD is not an issue and the correction of -3.3 min can be taken straight from the table.

The bit I am still confused about having looked again at it last night is why are corrections for the moon so different.

+ 62.7 min lower

+ 32.7 min upper

I am sure there is something I am missing as with the Sun SD in my previous thread.

Mike
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Old 19-09-2014, 09:09   #3
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Re: Celestial Making sense of altitude corrections

Pure refraction should be solely altitude dependent (roughly Refraction = 0.96/ Tan Altitude, or more precisely Ro = - 0.0167 / Tan[Ha + 7.31/(Ha+4.4)] degrees )

I believe you are using a correction that combines refraction and parallax. The parallax effect is proportional to the distance of the body. Thus the Horizontal Parallax for the Moon is about 1° but only 0’.15 for the Sun.

It has been a long time since I took a sight.
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Old 19-09-2014, 09:49   #4
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Re: Celestial Making sense of altitude corrections

Quote:
Originally Posted by Mike1956 View Post
100 odd views but no reply.

I suppose I should just be happy to learn to use the tables as prescribed but I also feel the need to understand. What is confusing me if I did not make it clear in my original post is I have read about and think I understand refraction. The fishing rod poked into a pond appears to bend (if this is a good analogy). The same happens when light enters the earths atmosphere. I am sure that light irrespective of its origin, (Sun, Moon,Planets or Stars) assuming it enters the earths atmosphere at the same angle (same apparent altitude) will bend about the same.

In the example above 16 deg 10 min.

I arrived at the Sun corrections by adding SD to lower limb and minus SD off upper limb in both cases the answer is about -3 min.

For the stars SD is not an issue and the correction of -3.3 min can be taken straight from the table.

The bit I am still confused about having looked again at it last night is why are corrections for the moon so different.

+ 62.7 min lower

+ 32.7 min upper

I am sure there is something I am missing as with the Sun SD in my previous thread.

Mike
I don't know the book of Mary Blewitt, but I guess it's based on the correction procedure as described in the Nautical Almanac.

The NA 1993 gives the moon correction in two parts:
  1. for Ha 16d 10' the first part is +62.7'
  2. the second part depends on the Horizontal Parallax and can be between +0.3' and +9.8'

Finally, only for upper limb, 30' should be subtracted. This is due to the fact that the tabulated values of the first part are based on lower limb altitudes.

The correction values for the moon in the NA include the effects of semi diameter (for lower limb), parallax, augmentation and refraction.

Note: Have a look at the OpenCPN website. The OpenCPN manual contains a part on a plugin for celestial navigation with a lot of information and hyperlinks.
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Old 19-09-2014, 13:03   #5
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Re: Celestial Making sense of altitude corrections

Quote:
Originally Posted by Mike1956 View Post
More guidance please.

I have been comparing altitude corrections for Sun, Stars & Moon.

Sun & Stars are similar. With an assumed Apparent Altitude of 16 degrees 10 mins the Sun is 3.15 min (winter) and 3.2 min (summer) Stars are 3.3 min.

However with same assumed app alt the moon is 62.7 min (lower) 32.7 min (Upper).
Ok, I just pulled out my HO229 tables (which I presume you are using), and looked at the altitude corrections.

For 16 degrees 10 minutes:

Sun lower limb: 12.7' (from page altitude correction tables 10-90 sun, stars, planets)
Plus if you want to get picky there should be an additional .1' correction for 'non-standard conditions' which is the relatively low altitude (this comes from the page Altitude correction tables - additional correction)
So an Ho = 16 6.8' (assuming zero dip and IC)

Moon lower limb: 62.7' (from altitude correction tables 0-35 moon)
Plus the same additional picky .1' correction
Plus additional parallax .6' (from the bottom table on altitude correction tables 0 35 moon)
So an Ho = 16 58.7

Star: -3.3' (from altitude correction tables 10-90 sun stars planets)
plus the picky .1' as above
So an Ho 16 6.8

As mentioned in the posts above . . . . These Ho229 'main corrections' include multiple factors, not just refraction, with parallax being the big factor for the moon.
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Old 19-09-2014, 13:31   #6
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Re: Celestial Making sense of altitude corrections

Estarzinger has nailed the reason.
The moon is much closer to the earth than the sun and other stars.
When you correct the sextant altitude, the end result is the angle at the centre of the Earth, and NOT your position. As the object you are taking a sight of gets further away, the correction becomes smaller.
Try sketching it out, should make sense then.
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Old 19-09-2014, 14:05   #7
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Re: Celestial Making Sense of Altitude Corrections

There are two external corrections for stars: altitude correction for refraction and height of eye.

For the sun you also correct for semi diameter which varies thru the year.

For the moon semi-diameter varies thru the lunar month plus you need to correct for parallax which is altitude dependent same as refraction and is also slightly dependent on the point in the lunar month.

It seems like she is conflating two or more corrections for the moon. Without having the tables at hand I can't determine which ones.

For all bodies there is separate table for redaction when shooting very low in the sky, 10-15 degrees, that takes into account air temp & pressure.


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Old 19-09-2014, 14:43   #8
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Re: Celestial Making Sense of Altitude Corrections

Mike,

I hope this helps. Have attached some PDF files.
One is from the daily pages of the Admiralty Nautical Almanac showing the hourly values for GHA, Declination, and Horizontal Parallax.
Second is the Total Correction for moon. Enter with arguments of apparent alt and HP, and finally a page from the almanac with a comparison of the various corrections for moon, sun stars.

Good luck
Attached Files
File Type: pdf Daily Page.pdf (87.9 KB, 54 views)
File Type: pdf Moon Corrn.pdf (80.2 KB, 59 views)
File Type: pdf Corrections.pdf (134.7 KB, 71 views)
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Old 19-09-2014, 16:11   #9
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Re: Celestial Making Sense of Altitude Corrections

I wrote this about 20 years ago.....

'The first of them, the moon, is probably the most infrequently used of all. The reason for this is that , although the actual reduction of a lunar sight is no different to reducing a sun or planet sight and utilises either Volume 2 or 3 of the Sight Reduction Tables for Air Navigation, the preliminary work involved in correcting the altitude and establishing the LHA and declination of the moon is more complex and is prone to error if sufficient care is not taken.

The ability to take lunar sights may, however, come in handy for the very same reasons Venus is useful in daylight hours. There may come a time when we are able to get a good fix on our position by taking simultaneous sun and moon sights when approaching a low lying and dangerous coast. At other times the moon may be all that is visible at twilight through a thin veil of cloud.

The reason why lunar sights are more complex is due, in the main, to the moon‟s relative proximity to the earth. Now this closeness to the earth, combined with the fact that the moon‟s orbit is an ellipse, means that the hourly rate of change of the moon‟s GHA varies considerably over the lunar month, as does its declination. So, while it is a simple matter to lift the GHA and declination from the almanac for a whole hour, you invariably have to apply large „v‟ and „d‟ corrections for increments of an hour.

The application of these corrections is not new to us – we have already seen how to apply them when working with the planets- but with the moon they are of far greater magnitude and a simple mistake in applying them can result in an error in our position of more than 30 miles.

Completely new to us, however, are the corrections we have to apply to the moon‟s observed altitude – after we have corrected the sextant altitude for index error and our height of eye – to obtain a true altitude. Because it is so close to the earth the amount of parallax associated with the moon is considerable. You may recall that with the sun parallax has a maximum value of 0.15 ́ at 0 ̊ altitude decreasing to zero at 90 ̊ altitude. With the moon, its parallax at 0 ̊ altitude (known as its horizontal parallax or HP) is a whopping 50 ́ and this amount varies on a daily basis as the moon‟s distance from earth either increases or decreases.

This HP is listed for every hour on the daily pages of the almanac along with an hourly „v‟ and „d‟ correction and the moon actually has two full pages of corrections given over to it in the back of the almanac for the correction of its altitude. These corrections are total corrections and are applied to the apparent altitude i.e. the sextant altitude which has already been corrected for index error and dip. The method of using this table is fully described in the almanac but we shall run over it here anyway.

Having taken a sight and applied index error and dip to the sextant altitude the next task is to extract the HP for the hour (GMT) at which you have taken the sight. You then go to the table of corrections and - entering the table with apparent altitude as an argument - lift out the main part of the correction that is then added to the apparent altitude. Then, still working in the same column and using HP as an argument lift out the secondary correction: you also add this to your apparent altitude. Make sure that you take it from either the upper (U) or lower (L) limb column as required. If you happen to be using the upper limb, which is not uncommon with moon sights, you now have to subtract 30 ́ from the altitude so found.

As you will have noticed while inspecting the table quite a bit of interpolation is required in this operation and you could have knocked over half a dozen stars in the time taken to reduce one moon sight. This is one of the reasons moon sights are given a wide berth by most navigators.'

I have 172 pages of this stuff I can email to you if you like.....
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Old 19-09-2014, 16:27   #10
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Re: Celestial Making Sense of Altitude Corrections

Just following up on Nigel's post:

To find/calculate all the corrections in my above post . . . here are all the specific tables with the specific cells used in yellow for the 16 degree 10 minute case

For the sun:

Main correction (lower limb): Click image for larger version

Name:	IMG_0835.jpg
Views:	621
Size:	331.6 KB
ID:	88470

Picky additional refraction correction: Click image for larger version

Name:	IMG_0836.jpg
Views:	264
Size:	272.6 KB
ID:	88471
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Old 19-09-2014, 16:27   #11
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Re: Celestial Making Sense of Altitude Corrections

For star: Click image for larger version

Name:	IMG_0840.jpg
Views:	197
Size:	342.1 KB
ID:	88472

(same page as above but using the 'stars' column)
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Old 19-09-2014, 16:30   #12
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Re: Celestial Making Sense of Altitude Corrections

For moon:

Main correction Click image for larger version

Name:	IMG_0837.jpg
Views:	289
Size:	349.3 KB
ID:	88473

HP needed for next correction Click image for larger version

Name:	IMG_0839.jpg
Views:	359
Size:	394.9 KB
ID:	88474

moon additional parallax correction Click image for larger version

Name:	IMG_0838.jpg
Views:	781
Size:	349.1 KB
ID:	88475 (Same page as first one above but using the the lower table)
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Old 20-09-2014, 02:55   #13
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Re: Celestial Making Sense of Altitude Corrections

Using the direct calculation method (formula's for each required individual correction) as described in the Nautical Almanac on pages 277 to 281, I find the results as shown in the Word attachment. This document is an exported and translated page from my celestial spreadsheet.

Remarks
1. Hs is calculated backwards from given Ha = 16° 10' by applying dip.
2. Ephemeris data is not obtained from the NA, but from truncated versions of VSOP87 and ELP2000/82 (as described by Meeus in Astronomical Algorithms and as applied in the spreadsheets from Navigation Spreadsheets).
3. All required, individual corrections are shown, as well as two intermediate values.
4. My spreadsheet is still under development, so no guarantee that is without errors (if you notice a strange value, please let me know).
Attached Files
File Type: doc Observation constants.doc (99.5 KB, 60 views)
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Old 20-09-2014, 04:47   #14
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Re: Celestial Making sense of altitude corrections

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Originally Posted by estarzinger View Post
.... correction for 'non-standard conditions' which is the relatively low altitude (this comes from the page Altitude correction tables - additional correction)
The non-standard conditions refer to air temperatures10 °C and air pressure≠1010 hPa. These meteorological values make that the given standard corrections for refraction (based on temperature=10 °C and pressure =1010) hPa are not sufficiently correct. Differences are relatively large at low altitudes of bodies.

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Old 20-09-2014, 04:58   #15
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Re: Celestial Making sense of altitude corrections

Quote:
Originally Posted by estarzinger View Post
For 16 degrees 10 minutes:

Sun lower limb: 12.7' (from page altitude correction tables 10-90 sun, stars, planets)
Plus if you want to get picky there should be an additional .1' correction for 'non-standard conditions' which is the relatively low altitude (this comes from the page Altitude correction tables - additional correction)
So an Ho = 16 6.8' (assuming zero dip and IC)

Moon lower limb: 62.7' (from altitude correction tables 0-35 moon)
Plus the same additional picky .1' correction
Plus additional parallax .6' (from the bottom table on altitude correction tables 0 35 moon)
So an Ho = 16 58.7
Perhaps I'm wrong, but both Ho values calculated above seem not correct to me.
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