Converting RA & Dec into Normal Earth Surface Latitude & Longitude

[Gannet]

Good Day Everyone,

Been searching this site and the internet for over a week and have not found the answer to my questions.

What I want to do, is take the sun's and moon's RA and Dec and convert them to their normal Earth surface coodinate (latitude & longitude).

Also, should I be using Astrometric or Apparent RA & Dec?

My goal is to be able to compare Tidal Potential to actual tide data

Thanks in Advance

 

[Gannet]

Good Day Everyone,

Maybe it would be better asking for validation on my assumptions:

1. That RA & Dec are Geocentric and therefore should be normal to the mean Earth surface
2. That the angle of declination from the celestial equator is equal to the latitude on earth
3. If 1 & 2 are correct, then all I would need is the longitude on Earth of the vernal equinox

From http://aa.usno.navy.mil/data/docs/geocentric.php"

Has the following definitions for apparent & astrometric position

Apparent position: A calculated apparent position corresponds most closely to the observed position of an object on the celestial sphere. The aberration of light (due to the velocity of the observer) and the relativistic bending of light (due to the Sun's gravitational field) are taken into account. For solar system objects, light propagation time is also included.

Astrometric position: An astrometric position is formed simply by a vector difference of the instantaneous positions of the object and the observer, as obtained from catalog data or the planetary ephemeris. It is comparable to the positions of stars that are published in catalogs and is therefore useful in plotting the positions of solar system objects on star charts. For solar system objects, light propagation time is also included. (Light-time computations are never done for stars; it is assumed that the catalog positions and proper motions of stars implicitly include light-time and its derivative.)

After reading numerous times, I am still not sure which one I should be using

Thanks

 

[D H]

Good Day Everyone,

Maybe it would be better asking for validation on my assumptions:

1. That RA & Dec are Geocentric and therefore should be normal to the mean Earth surface
2. That the angle of declination from the celestial equator is equal to the latitude on earth
3. If 1 & 2 are correct, then all I would need is the longitude on Earth of the vernal equinox

1 is incorrect. The Earth's surface is more or less ellipsoidal. The difference between geocentric and geodetic coordinates makes a significant difference when it comes to astronomical observations.

2 depends on the coordinate system being used for right ascension and declination. The website to which you linked uses the True Equator and Equinox of Date system, aka True of Date. Declination here is comparable to geocentric (not geodetic) latitude but projected onto the celestial sphere. Other reference frame choices include mean of date, ICRF, GCRF, J2000, and mean of 1950.

 

[Gannet]

Thank you DH for your comments
I am not trying to do astronomical observations. I am trying to use the available astronomical data for the sun and moon to determine their tidal potential at an instant in time and compare it to concurrent actual tide data.

I am still not sure whether I should be using Astrometric Position or Apparent Position. And for the sun should I be including the equation of time (analemma)?

This is a hobby project.

I appreciate any help on guiding me onto the right track.

 

[D H]

I am not trying to do astronomical observations. I am trying to use the available astronomical data for the sun and moon to determine their tidal potential at an instant in time and compare it to concurrent actual tide data.

Whoa, dude. You are neck deep, or deeper, in an extremely complicated subject. NOAA hires PhD oceanographers and very smart computer programmers by the boatload because tides are complex. You are asking very, very basic questions. You have at least five years of education ahead of you to even begin such a venture. Even with that education at hand, you are still but one person. You appear to be trying to undertake a task that would nominally be assigned to a boatload of freshly minted PhD oceanographers.

This is a hobby project.

Then treat it as one. Don't dive neck-deep into a PhD level research project. I suggest that you use some already existing tide calculation software. There is plenty of that that is freely available on the web, no charge, not even a postcard. Xtide, http://www.flaterco.com/xtide/, is one such package. There are plenty of others.

 

[Studiot]

Tidal timings, directions and heights are significantly affected by terrain.

A good book, if you can get hold of one, is the Admiralty Manual of Tides.

go well

 

[Gannet]

Thanks Studiot

I'll be on the lookout for "Admiralty Manual of Tides"

Tidal timings, directions and heights are significantly affected by terrain.

I agree with your statement. I just want to do some real world analysis, instead of just reading about it. Also, I believe by doing this, I will become more knowledgeable about tides, astronomy, fluid dynamics, etc. Even though it is complex, I think it is a lot more simpler than climate modeling.

 

[Studiot]

Look in Google or Abe.

It used to be published by Her Majesty's Stationery Office (HMSO) along with the Admiralty Manual of Hydrographic Surveying (In 2 large volumes) this also has tidal information.

The Admiralty Manual of Navigation has the astro stuff if I remember correctly.

It's all old stuff but the mechanics hasn't changed since these books were written.

go well

 

[Gannet]

Thanks again,

Speaking of old books, the best book I found so far for Fluid Dynamics on Tidal Waves is Lamb's Hydrodynamics, Sixth Edition from 1932.

If you know of any others, please let me know.

 

[Studiot]

There is indeed a great deal in Lamb.

You should also look in

Solitons an Introduction

Drazin and Johnson

Cambridge University Press

Solitons are the mathematical term for 'solitary waves' such as the Severn Bore, which are a tidal phenomenon.

 

[DoggerDan]

Solitons are the mathematical term for 'solitary waves' such as the Severn Bore, which are a tidal phenomenon.

There seems to be some confusion on this. Wikipedia's entry says: "The Severn bore is not a self-reinforcing solitary wave or soliton but rather a shock wave which is formed because the wave is traveling faster than the wave speed in water above the Bore."

Meanwhile, I found three other entries (below) which claim it is a soliton:

1. http://neohumanism.org/s/so/soliton.html

2. http://www.scientific-computing.com/features/feature.php?feature_id=42

3. http://www.daviddarling.info/encyclopedia/S/soliton.html

I'm familiar with the differential equation definition of a soliton, and it appears to me that while the Severn bore shares many of the same characteristics as a mathematical soliton, it is not actually a soliton, but has been mischaracterized as one for many years.

Support? Dissent?

 

[BobG]

Just dealing with the original question:

1) Declination will be close to the geodetic latitude, so it depends how much accuracy you need. At the equator and the poles, it will equal geodetic latitude. The error will get up to around 0.2 degrees or so in the mid-latitudes.

2) Subtract the current Greenwich Mean Sidereal Time from Right Ascension to get the longitude. There's plenty of downloadable spreadsheets or programs on the internet that can calculate Greenwich Mean Sidereal Time - or you can calculate it manually using an Astronomical Almanac (they list GMST for midnight of each day of the year, and you just have to add Universal Standard Time to it).

An astronomical almanac should have the formula to convert from declination (which matches geocentric latitude) to geodetic latitude. As DH mentioned, you have to compensate for the oblateness of the Earth, and the Earth's flattening factor is 1/298 (plus some odd change - check your WGS-84 constants if you need the exact value).

It's a bit of work to correct such a small error, but if you're plugging this into a spreadsheet or program, it can be worth it.

 

[Gannet]

Thank you BobG for replying to my Original Post. Your answers are very helpful.

Since then I found this http://bowie.gsfc.nasa.gov/hw95/" The HW95 tidal potential catalogue. One of the data files states

Note that there exist in the catalogue some tidal waves which have the same frequency but are generated by different celestial bodies or are related to different degree of the tidal potential. These waves are sorted to increasing degree, and for the same degree, to the sequence Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn.

This link should help me as a "go-by". I never knew that these tidal potential models also to into account: Mercury, Venus, Mars, Jupiter, and Saturn. So if they include them, I better try to be at the state of the art accurate.

Thank you again BobG and D H for pointing out the errors.

Studiot I found the above link while looking for "Admiralty Manual of Tides" A lot of Nautical Bookstores on line are selling it.

 

[D H]

This link should help me as a "go-by". I never knew that these tidal potential models also to into account: Mercury, Venus, Mars, Jupiter, and Saturn. So if they include them, I better try to be at the state of the art accurate.

You would be much better off starting with the basics.

You haven't given a clear picture of what you are trying to accomplish with your endeavor. Are you

• Trying to see how well the predictions for existing tidal model for some specific location matches up with your observations for that location?
  If this is the case you need to use whatever terms that model says needs to be used. If, for example, you are using a Doodson-based model you had better use a Doodson model of the tides rather than something more recent. The nice thing about using an existing model is that it already exists. You can download free software that implements these models and free (at least in the US) data coefficients for these models. One downside of this approach is that the number of locales for which detailed tidal coefficients exist is rather limited. Even worse, in some places you have to pay for that formerly public domain data.
  
  
• Trying to develop your own tidal model for some specific location?
  If this is the case you would be much better off starting with a very simple model, gradually adding complexity as you accumulate data. You definitely do not want to start with a full-blown HW model (or something even "better"); you will have to accumulate data for decades before you can even start crunching the numbers -- and even then you will have to be very careful about your number crunching. One problem with any large model is that it is very easy to come up with a model that not only can't extrapolate accurately (predict the tides next week or next month), it can't even interpolate accurately (post-dict the tides at some point in time between your measurements). Unmodeled effects such as the weather will creep into your derived coefficients unless you go to extreme pains to eliminate these unmodeled effects -- and that means even more data.
  
  
• Trying to develop your own tidal model for the world?
  If this is the case I strongly suggest you redirect your efforts. This is a huge research program that requires extremely expensive equipment such as satellites and cryogenic gravimeters and requires thousands of well-trained people working over the course of multiple decades and across multiple continents. This is not an undertaking for a hobbyist.
  
  
• Trying to do something different?

The tidal potential at some location by itself is pretty much worthless when it comes to predicting the tides at that location. To illustrate, let's take a trip down the coast of England starting at Huntstanton at 20:51 on October 15, 2011. This was the time of a high tide at Huntstanton. Imagine moving with that high tide as it moves down the coast. About 60 kilometers down the coast, the town of Cromer experienced a high tide at 21:10. Moving further down the coast, Winterton-at-Sea experienced high tide at 21:57, Great Yarmouth at 23:14, Lowestoft at 00:16 (on October 16), Southwold at 01:21, Aldeburgh at 01:46, Felixstowe at 02:16, Clacton-on-Sea at 02:40, and Southend-on-Sea at 03:18. That's a 6 hour and 27 minute delay in the arrival of high tide over a distance of less than 200 kilometers. The tiny change in tidal potential across this short distance does not explain this huge difference in timing. (You can verify these numbers by visiting this site: http://www.tidetimes.org.uk/.)

I intentionally picked an area where tides are very complex. The North Sea has two amphidromic points plus an incomplete amphidromic system, making for some rather beastly tides. It is always high tide at some point in the North Sea. The coast of Argentina is another area where tides vary drastically over a very short distance.

To model the tides at some location, oceanographers develop a location-specific set of magnitudes and phases of the various contributors to the tides at that location. This requires a good amount data gathered over a long period of time. A good amount of data are needed because the weather also affects the measured values. For example, my office at work overlooks a bayou. The tide tables suggest that on Wednesday morning when I get to work I should see the bayou being nearly full of water. I doubt that will be the case: I most likely will see a mudflat instead. Our first good cold front is expected to blow through on Tuesday night.

 

[Gannet]

You would be much better off starting with the basics.

You haven't given a clear picture of what you are trying to accomplish with your endeavor. ...

My personal goal for this endeavor is a complete understanding of tides.

The reason I am pursuing this is because it involves a lot of subjects that I am interested in.

Since starting this endeavor, I have learned a lot things I didn't knew before.

Where all this will lead too. I do not know.

Thank you D H you have been very helpful.