Astro - navigation

[alant]

Alant, I'm happy to learn from you, and I know that your East/West formula has been long used, but I'm wondering if it is an added and unnecessary complication.

In astro navigation, there is no east or west longitude. All points are west of Greenwich. So if you are located on a map at 4 E. Then in actual fact you are at 356 W (in astro nav terms.) I believe that the E/W method that you mention is simply a method of turning map East into Astro West. Am I wrong here? I'm happy for your opinion.

Can't see why its an added complication, its the only straightforward way LHA can be found, as far as I know.


GHA, or even SHA, is always measured westward, from Greenwich in the case of GHA, in the case of SHA using 'the first point of aries, then adding the GHA of aries to give GHA of the star. Both derived from the exact time of the sight. However, your longitude is still measured as normal convention west & east from Greenwich.
Comparing GHA with longitude, gives LHA.

If your boat position is east of Greenwich & your heavenly body (Sun) is west of Greenwich, then the LHA is still the angle between the meridian the boat is on & the meridian the Sun is on, so (1) you have a measure of the angle from Greenwich to the Sun's position (GHA) (2) the angle from Greenwich to your boat (longitude east), which (3) are added together, to get the total angle (LHA).


LHA is the angular measurement of the distance between these 2 meridians & will be the same whether measured on the Earth, or on the Celestial Sphere. LHA doesn't have any west or east element.

 

[Uricanejack]

I have startend with Cunliffes Astro Navigation, unfortunatelly because of the rapid breakdown of the old grey matter I cannot get my head around LHA. I understand GHA, but LHA ???. If someone could explain to yet another Grandad, in terms of a previous Post ( spotlight over tennis court) would be very grateful.

I Part of your confusion may be time. Hour Angles = time. Hour Angles are time. Hour angles are also Longitude.

In order to explain LHA. I have explain HA Hour Angle, LHA Local Hour Angle and GHA Greenwich Hour Angle. This will be a bit long winded and hopefully does not confuse the issue.

Hour Angle, Longitude and Time are all just different ways of expressing the same thing.

Hour Angles are used to describe angles on the Celestial Sphere.
The Celestial sphere Is a big glass ball with stars stuck on it which surrounds the earth which of course is at the center of the Universe. The Sun is a fiery chariot pulled around this sphere every day by some ancient Greek Dude. The Planets wander about in circles on it and the Moon Does its own thing.

It all starts with Time. Particularly Noon.

High noon. When cowboys shoot each other. Has been the center of the day. The time from which time was measured for millennia. Is the basis of you Local Hour Angle. Or Local Time.

It can be demonstrated by a simple sun dial.

What is noon. Before modern clocks. Quite simply noon was when the sun reached its highest point in the sky. And was due south of your position.(unless you are on the Equator or in S Hemisphere)
This is when the sun crosses your Meridian.
Your Meridian is a line on the earth surface from the north to south pole passing through your position, the plane of which passes through the center of the earth. Your Celestial Meridian is the same line projected out onto the celestial sphere. Your Meridian and your celestial meridian are both Great Circles.

Any Line on the surface of the earth or on the celestial sphere the plane of which passes through the center of the earth is a Great Circle.

At noon the suns Local Hour Angle is 0.
The Earth Rotates once every 24 Hours. 360/12= 15 I hour = 15 Degrees. GHA increase. 15 Degrees Every Hour.
The Suns Local Hour Angle increase after Noon at a rate of 15 degrees per hour. Until after 24 Hours the sun has traveled 360 Degrees and is again at Noon on your meridian. This Local Hour Angle is also Local time.

LHA or Local hour Angle is one of the fundamentals principles of Astrology, Astronomy and Navigation. it has been used i some way or other from ancient times. Ancient observers noticed the star's remain fixed in the same place in the sky. Polaris stationary at In the North all the rest progress around the sky once every day.

The Local hour angle of each star would be 0 when it crosses your meridian.

The Planets progressed around the sky once a day but wandered slowly through the constellations.
The Moon moves through the constellations much faster and its local hour angle is O when on your Meridian.
In The time of Ptolemy. Astronomers knew the Sun also rose in the east at a different time each day, But was at its highest at the same time every day. It rose higher in the sky in the summer and lower in the winter. The Builders of Stone Henge, Callanish, ancient Greeks, Egyptians knew this. Sailors particularly navigators have known this, since the Phoenicians, Greeks, Vikings, Arabs, Chinese and Polynesians.

Your Meridian, Local Noon, Local Time, Local Hour Angle are easily defined as real phenomena based on where you are.
The Local Hour Angle and Local Time are the simplest concept's in defining where the Sun is in the sky. These concepts were the basis for how we defined time the universe and everything. For a couple of Thousand years.

Greenwich Hour Angle and Longitude are a bit more complex. They are abstract, Every location on the surface of the earth has its own unique meridian, Local time and local hour angle. Astronomers knew the concept of longitude but could not measure it or define it.

The Royal Society and The Royal observatory at Greenwich is where it started.

If you are at Greenwich and the sun is on your meridian the local hour angle of the sun is 0. The Local Hour Angle of the Sun will increase as the sun moves west by 15 degrees every hour until after it sets rises again in the east and the hour angle increases to 360 and crosses your meridian again at noon.
Obviously. If you are on the Greenwich Meridian, Your Local Hour Angle, is The Greenwich Hour Angle and Your Local Time, is Greenwich Time.

The Greenwich Hour Angle is The Local Hour Angle at the Greenwich Meridian. Greenwich Time is Local Time at Greenwich.
If you travel west from Greenwich. Your Local Noon will Occur after Noon at Greenwich. Astronomers realised if you know the local time at Greenwich when the sun was on Your Meridian. You would be able to figure out how many degrees from Greenwich you were.

This was just a nice theory until Harrison created the Chronometer. Along with Astronomers publishing an annual Almanac, giving the Greenwich Hour Angle of the Sun, The Planets, The Moon and The first Point Of Aries.
What is the Longitude?. Quite simply Longitude is. The difference in Hour Angle, or time between your Meridian and the Greenwich meridian.

For some strange reason unknown to me. Although, Hour Angle and Longitude are basically the same thing. Longitude is named and measured East or West Of Greenwich. Greenwich is 0 Degrees Longitude and it is measured and identified as East or West Longitude up to a maximum of 180 degrees.
Hour Angles of any objects on the Celestial Sphere are measured from Greenwich but only in one direction going west all the way back round to Greenwich from 0 to 360. They are Known as Greenwich Hour Angles or GHA.

The LHA or Local Hour Angle. Is the Angle between Your Longitude and The Longitude or Hour Angle Of the Celestial Body

Hour Angles are always positive.
East Longitudes are positive.
West Longitudes are negative.

I have not mentioned mean time or apparent time in order to leave it simple. Mean time and apparent time are not the same. What I have described is apparent time. Or time as it appears. Even the time i described at Greenwich was apparent time.

You don't really need to worry much about the difference if you just want to look up and crunch the numbers. If anyone wants to know I will try and give a reasonable explanation. The Almanac gives Greenwich Mean Time rather than apparent time at Greenwich.

To Figure Out GHA of the Sun. Look up the GHA for the Greenwich Mean Time or GMT. In The Annual Nautical Almanac. It is listed for every hour and there is an increment table at the back for the minutes and seconds.
GHA of Sun GHA for the Hour +Increments for The Minutes.
To Find The Local Hour Angle of the Sun
LHA= GHA + East Longitude
LHA= GHA - West Longitude
Or LHA = GHA + Longitude.
LHA = GHA + East+ Longitude. ++=+
LHA= GHA + West-Longitude.+-=-

Local Hour Angles of the Sun after it rises until Noon will be between 180 and 360
Local Hour Angles Of The Sun from Noon Until it sets will be between 000 and 180.
LHA is one the required known angles in the spherical triangle from which you can calculate the altitude of the celestial object.
Hope this helped rather than confused.

 

[Skylark]

What a great thread, this and the other one running a similar subject, speaks volumes about the gentlemanly conduct of those practising and/or interested in the fine art of celestial navigation. Such a wealth of information shared so freely.

This is how I eventually figured it out.

Don’t think of the AP3270 vol 2 and 3 as Navigation Tables, think of them more along the lines of a set Log Tables as used when you were a school boy. The tables refer to spherical trigonometry, nothing more.

Using the tables is quite straightforward. You know the declination of the body (from the Almanac) and you know your latitude (in whole numbers from your DR position). The “same or contrary” malarkey is simply to work out the angle between you and the body in that plane. Then you need to know your position east or west, a sort of celestial longitude known as LHA.

Entering these arguments in the trig tables gives you two pieces of information. One is altitude, or the angle between the horizon and the body, the other is its azimuth or bearing relative to north.

Compare tabulated altitude with that measured by your trusty sextant. Remember that degrees can equally mean angle, time or distance in navigation. The difference is marked along the azimuth from your assumed position of lat and celestial long. The position line is really a radius from the body to the surface of the earth, that’s why we draw a straight line perpendicular to the azimuth at the point of intersection. Voila.

 

[lw395]

...Hope this helped rather than confused.

Yes it helps!
I think I'll read that through again with some diagrams in front of me!
I find it very easy to confuse the definitions of a lot of angles which are nearly the same thing.
Ta!

 

[AntarcticPilot]

Not so, that rule is only good if your longitude is west of Greenwich.
If your longitude is east of Greenwich, you add this to the GHA to obtain LHA.
Basically, it is the angular distance between your longitude meridian and the meridian upon which the geographic position of the observed heavenly body sits.

Rules for calculating LHA:

Long East, LHA = GHA + LONG (- 360o as necessary)​

Long West, LHA = GHA – LONG (+ 360o as necessary)


​

Alant, I'm happy to learn from you, and I know that your East/West formula has been long used, but I'm wondering if it is an added and unnecessary complication.

In astro navigation, there is no east or west longitude. All points are west of Greenwich. So if you are located on a map at 4 E. Then in actual fact you are at 356 W (in astro nav terms.) I believe that the E/W method that you mention is simply a method of turning map East into Astro West. Am I wrong here? I'm happy for your opinion.

As long as you apply the correct sign convention (East +ve, West -ve), the rule GHA + Long always works; adding a negative number is subtracting!

 

[Foolish Muse]

If your boat position is east of Greenwich & your heavenly body (Sun) is west of Greenwich, then the LHA is still the angle between the meridian the boat is on & the meridian the Sun is on,

I think you've confused the situation a bit. In astro navigation, LHA is the difference in longitude between the sun and your AP (assumed position), not between the sun and your boat.

The “same or contrary” malarkey is simply to work out the angle between you and the body in that plane.

I think we can make this really simple: "Same Name" is used during your Spring and Summer. "Contrary Name" is used during your Autumn and Winter.

Uricanejack: I think that your discussion about local hour angle has more to do with taking a noon shot, right? One of the problems I had with learning the sextant was the different uses of similar terms like LHA. I only want one definition that I can use all the time.

All the other stuff above is exactly why I wrote the users guide. I had read 5 books and I was more confused than ever. I wrote it so that I could understand it. Using a sextant is actually very easy. If it takes you more than 1 hour to learn, then you are doing it wrong.

 

[alant]

]I think you've confused the situation a bit. In astro navigation, LHA is the difference in longitude between the sun and your AP (assumed position), not between the sun and your boat. [/B]


I think we can make this really simple: "Same Name" is used during your Spring and Summer. "Contrary Name" is used during your Autumn and Winter.

Uricanejack: I think that your discussion about local hour angle has more to do with taking a noon shot, right? One of the problems I had with learning the sextant was the different uses of similar terms like LHA. I only want one definition that I can use all the time.

All the other stuff above is exactly why I wrote the users guide. I had read 5 books and I was more confused than ever. I wrote it so that I could understand it. Using a sextant is actually very easy. If it takes you more than 1 hour to learn, then you are doing it wrong.

Not so, you, are confusing it with the LHA specifically used to derive Hc (calculated altitude).
Only then, is it taken from an assumed position (which isn't actually where you are & is only an arbitary position, which is selected, usually with a latitude which is a whole degree to make it easier to enter the tables, with longitude selected to be within 30 minutes of your estimated position & such that an LHA in degrees only, is derived again for easier use of tables).







LHA is the angle BNU on the Earth’s surface which corresponds to the angle ZPX in the Celestial sphere. In other words, it is the angle between the meridian of the observer and the meridian of the geographical position of the celestial body (GP).

 

[Foolish Muse]

Not so, you, are confusing it with the LHA specifically used to derive Hc (calculated altitude).

Yes, I'm only talking about the LHA used to derive Hc because I only care about that. The point of determining LHA is because it tells us what page to look at in the sight reduction tables. Is there another reason for some other LHA that I'm not considering?

I also eliminated any discussion of celestial sphere because I really can't see a purpose for it. The latitude and longitude of the sun in the celestial sphere is the same as the latitude and longitude of the very tall flag pole on Earth directly beneath it. The almanac tells us the exact position of the base of that flag pole for every second of the year. That is all we care about. We determine our position as a circle around the base of that flag pole.

Can I ask that you take a look at the sextant users guide and go through the steps that I outlined. I'd be really appreciative if you found something wrong with my approach. I've tried to simplify something that was previously very complex.

 

[Uricanejack]

Hi. Yes and No.

My goal was to explain Local Hour Angle.

I used the sun as an example.

I might not have explained it very well. It's kind of difficult to draw a picture with words. when you are used to demonstrating something.
It depends how much you want to know?

 

[AntarcticPilot]

Hi. Yes and No.

My goal was to explain Local Hour Angle.

I used the sun as an example.

I might not have explained it very well. It's kind of difficult to draw a picture with words. when you are used to demonstrating something.
It depends how much you want to know?

From years of working professionally with this type of spherical trigonometry, I can confidently state that there is one absolutely reliable universal approach to getting the maths right, that works in all the "edge" cases. It is simply this - rigorously apply the correct sign convention to latitudes and longitudes . N and E are positive, S and W are negative. This will ALWAYS give the correct answer, if you apply it rigorously. If you look at the examples people have given, they all boil down to the same expression:

LHA = GHA + LONG

GHA and LONG may both be either East or West; putting the correct sign on them will always result in the right answer.

Note that this approach works throughout the spherical trigonometry of navigation and map projections. Of course, you sometimes need to know how the trigonometric functions of angles change sign with the sign of the angle (it isn't quite straightforward - who else uses the mnemonic "All Silly Tom Cats"?)

Later addition: For those who don't know it, the mnemonic gives the sign of trigonometric functions for angles in different quadrants. ALL trig. functions are positive in the first quadrant (0-90), only SINE is positive in the second quadrant (90-180), TANGENT in the third quadrant (-180 to -90, or 180 to 270) and COSINE in the last quadrant (-90 to 0, or 270 - 360). You don't need it is you have the correct sign convention and use a computer or spreadsheet, but you do need it if using tables.

 

[Skylark]

I think we can make this really simple: "Same Name" is used during your Spring and Summer. "Contrary Name" is used during your Autumn and Winter.

I still think this is a great thread with so much interesting and informative information (so I'm trying to be constructive).

Taking your approach doesn't lead to an understanding of "why". As I've posted previously, I can't get on with many of the templates kicking around because I don't follow the authors logic. I can't simply reduce a sight "parrot fashion", I need to understand what I'm doing.

As others have said, this is easier to draw a diagram than to put into words. Bearing in mind that the process is to resolve spherical trigonometry, simply drawing a diagram to show declination and your latitude makes it crystal clear, in my view anyhow, that doing so defines one of the points of the triangle.

Albeit most people only use the sun, having that understanding makes the progression to using other heavenly bodies quite straightforward.

 

[alant]

From years of working professionally with this type of spherical trigonometry, I can confidently state that there is one absolutely reliable universal approach to getting the maths right, that works in all the "edge" cases. It is simply this - rigorously apply the correct sign convention to latitudes and longitudes . N and E are positive, S and W are negative. This will ALWAYS give the correct answer, if you apply it rigorously. If you look at the examples people have given, they all boil down to the same expression:

LHA = GHA + LONG

GHA and LONG may both be either East or West; putting the correct sign on them will always result in the right answer.

Note that this approach works throughout the spherical trigonometry of navigation and map projections. Of course, you sometimes need to know how the trigonometric functions of angles change sign with the sign of the angle (it isn't quite straightforward - who else uses the mnemonic "All Silly Tom Cats"?)

I find 'any' mnemonics difficult to remember.

 

[Uricanejack]

I find 'any' mnemonics difficult to remember.

Try rude ones they stick in the mind more readily

 

[Uricanejack]

From years of working professionally with this type of spherical trigonometry, I can confidently state that there is one absolutely reliable universal approach to getting the maths right, that works in all the "edge" cases. It is simply this - rigorously apply the correct sign convention to latitudes and longitudes . N and E are positive, S and W are negative. This will ALWAYS give the correct answer, if you apply it rigorously. If you look at the examples people have given, they all boil down to the same expression:

LHA = GHA + LONG

GHA and LONG may both be either East or West; putting the correct sign on them will always result in the right answer.

Note that this approach works throughout the spherical trigonometry of navigation and map projections. Of course, you sometimes need to know how the trigonometric functions of angles change sign with the sign of the angle (it isn't quite straightforward - who else uses the mnemonic "All Silly Tom Cats"?)

+1 on the use of the arithmetic sign.

 

[Serin]

Taking your approach doesn't lead to an understanding of "why". As I've posted previously, I can't get on with many of the templates kicking around because I don't follow the authors logic. I can't simply reduce a sight "parrot fashion", I need to understand what I'm doing.
.

http://www.imray.com/Publications/Bookshop/Navigation/RB0302/

Clearest and best textbook of nautical astronomy I have ever come across. I recommend it to anyone who wants to delve deeper into this subject than the basic "how to do it" texts ever do. Fascinating, even if you don't plan to become a practical astro navigator.

 

[Skylark]

http://www.imray.com/Publications/Bookshop/Navigation/RB0302/

Clearest and best textbook of nautical astronomy I have ever come across. I recommend it to anyone who wants to delve deeper into this subject than the basic "how to do it" texts ever do. Fascinating, even if you don't plan to become a practical astro navigator.

https://wordery.com/american-practi...JGWFNjNFE9PQ&gclid=CLyz2eGMlcsCFUgq0wod6aMFrw

A number of year ago through this forum I was introduced to Bowditch. I'm a big fan of text books and this one sits in pride of place on my shelves.

 

[alant]

L

Try rude ones they stick in the mind more readily

I then can't remember which problem to apply them too.

 

[Neil]

I really got into astro, but just for the pleasure of knowing how to to do it. I bought a Astra IIIb when they were less than £300 (why have they gone up so much?), went through Cunnliffe's book (OK, but his chapter on position lines wasn't really clear) and have regularly managed to do the sun, moon (it's not that much more difficult) the planets and stars. But only in the back garden using the reflection in a saucer of oil!

The greatest advance for me was producing my own pro forma sheets - I know it's only adding and subtracting, but mistakes can still be made!

Navsoft used to have the current year's almanac in standard format for download, but no longer, it seems. I haven't gone back to astro it for a while, as consequence.

I always promised myself that 'one day' I'd learn how do do everything from first principles and work it out on a slide rule......maybe when I retire

 

[snowleopard]

The greatest advance for me was producing my own pro forma sheets - I know it's only adding and subtracting, but mistakes can still be made!

Navsoft used to have the current year's almanac in standard format for download, but no longer, it seems. I haven't gone back to astro it for a while, as consequence.

I had a DOS program that printed off pages of the Nautical Almanac which I bought at the boat show years ago. I think it ran up to about 2010. Since then a forumite distributed copies of a spreadsheet that did the same job but I seem to have lost it in one of the many PC upgrades since then.

I used to print off my own pro-formas. As all my ocean sailing at that time was done in summer in the North Atlantic it was considerably simpler than the generic ones you find in text books. Only N latitudes and declinations always of Same Name.

 

[GHA]

By

I had a DOS program that printed off pages of the Nautical Almanac which I bought at the boat show years ago. I think it ran up to about 2010. Since then a forumite distributed copies of a spreadsheet that did the same job but I seem to have lost it in one of the many PC upgrades since then.

Almanac for 2016 available here...
http://www.nauticalalmanac.it/en/navigation-astronomy/the-nautical-almanac.html