A Task for Geographers (or maybe Pilots?)

[TheBramble]

I'd like to be able to calculate at which 2 points on the Earth's surface (cloud cover notwithstanding!) the Sun is at exactly the same angle given the Lat/Long of one point.

Is it as simple as +/-90 degrees of Latitude for the Vertical angle and 180 degrees of Longitude for the Horizontal?

 

[Salty Gibbon]

Are you designing a new trading strategy Tony ?

 

[SOCRATES]

No, Salty what he wants is to pinpoint the dome.

Bramble what you need to do is to calculate the Azimuth of the sun for a particular location for a particular point in time, because as the Sun is stationary but the earth revolves so the bearing of the sun changes.
This calculation is derived by entering arguments, latitude, hour angle and declination (of the sun) in tables of Azimuth or ABC tables. The three coefficients derived from this calculation will give you the bearing you seek. This bearing is called the Azimuth and is presented as a true bearing. Then if you have a compass the bearing so derived has to be converted to Magnetic Bearing by adding or subtracting the compass error.

Kind Regards As Usual.

 

[Salty Gibbon]

I remember you said before you went to Navigation School Soc.

Tres impressive.

 

[SOCRATES]

Fact.

Kind Regards As Usual.

 

[TheBramble]

Thanks Socco. I'm OK with deriving the appropriate coefficients for Azimuth (and also for Altitude).

What I'm attempting to establish is how I can calculate for which Lat/Long points (plural) on the surface of the Earth effective equality of Solar Azimuth and Solar Altitude exist at any given instant in time.

 

[TWI]

To be accurate you also need to account for atmospheric refraction? may need localised temperature and pressure components for that.

 

[TWI]

Maybe I am misunderstanding the question but as far as I can tell there will not be more than one place on Earth where the sun has the same Azimuth and Altitude. Azimuth is always measured North(0) to North(360).
No two points in the sky have the same right ascension and declination after all.

 

[SOCRATES]

You are quite correct in saying that there will not be more than one place on earth where the sun has the same Altitude. It's height above the horizon varies with location. Also for example at sunset on the equator it descends nearly vertically whereas in high latitutes it slopes.The azimuth of the sun is valid for a particular location at a particular point in time also. But because the azimuth is a straight line, therefore it cuts arcs of longitude and latitude symetrically. That is what we are talking about and not about changes.
In point of fact any course steered or set is an azimuth. We can extend this understanding to mean that a bearing is also a form of azimuth. we conclude that if we choose an azimuth that crosses two or more points these can be identified in terms of geographical location, that is, in terms of latitude and longitude.

Kind Regards.

 

[TheBramble]

Maybe I am misunderstanding the question but as far as I can tell there will not be more than one place on Earth where the sun has the same Azimuth and Altitude. Azimuth is always measured North(0) to North(360).
No two points in the sky have the same right ascension and declination after all.

That is why I attempted to fudge with 'effective equality'.

Taking the strict definition of Azimuth: A point on the celestial sphere the angular distance of which measured towards the east, from north, along the astronomical horizon to the intersection of the great circle passing through the point and the astronomical zenith with the astronomical horizon.

So measured from Magnetic or True North (doesn't matter for purposes of this discussion which), regardless of location selected, the Azimuth is going to be the same. True?

However, surely the Altitude will be identical in two places. Logically, one person's Sunrise is another's Sunset?

 

[Salty Gibbon]

However, surely the Altitude will be identical in two places. Logically, one person's Sunrise is another's Sunset?

Surely that would only be true if the earth were a perfect sphere - which it is not.

 

[SOCRATES]

Braaaaaamble, what you are doing is taking the celestial definition of Axzimuth. That definition is a very different one to the one used for navigation and position finding and finding of direction in practical terms when the time, latitude, hour angle and declination is known. In colloquial navigation parlance it is also understood to mean a bearing, from the object or planet or star to the observer's position or a given location in terms of Longitude and Latitude predetermined or given in advance.

Kind Regards.

 

[TWI]

Surely that would only be true if the earth were a perfect sphere - which it is not.

This is just an added complication which brings in all sorts of nightmares including gravity and precession and tectonic plate movement. So it will only actually be true for a time "t". Also have to consider a sidereal day of ~23hrs 56mins

Anyway in simplistic terms the altitude of the sun should be solved by

ASIN(SIN(Latitude of observer).Sin(Declination of Sun) + Cos(Latitude of observer).Cos(Declination of Sun).Cos(Greenwich hour angle of Sun + longitude East of Greenwich of Observer))

If you set that equal you can solve it quite simply so you original assumption is correct.
(Greenwich hour angle + longitude East of Greenwich of Observer is the Local Hour Angle which in turn equals Local Sidereal Time - The Suns Right Ascension)

I think....

Unfortunately the sun as investments can go both up and down.

 

[TheBramble]

Thanks to all for responding and for pointing me in the right direction.

May the Sun never set on your Umpire.

 

[Salty Gibbon]

Good luck with your celestial trading plan.

 

[TheBramble]

Tying up Loose Ends

If you define a plane that passes through the centre of the Earth and the centre of where the Solar disk appears to be, nearly half of the Great Circle that defines that plane will have the same Azimuth. Almost one half will have one Azimuth and almost the other half will have an Azimuth 180 degrees different. It's only 'almost' half because there are two points on the Great Circle where the Sun is at the Zenith and at the Nadir. At those points, Azimuth is undefined.

There also exists a terrestrial Small Circle for which the Solar Altitude is identical at any given time.

Took some time...