Re: Latitude and meridians

On Jan 18, 4:09 pm, noneag...@xxxxxxxxx wrote:
On Jan 16, 3:18 pm, oriel36 <kelleher.ger...@xxxxxxxxx> wrote:



On Jan 16, 9:28 pm, Frogwatch <ohara...@xxxxxxxxxxxxxx> wrote:

On Jan 16, 12:13 pm, oriel36 <kelleher.ger...@xxxxxxxxx> wrote:

On Jan 16, 3:48 pm, noneag...@xxxxxxxxx wrote:

Hello,
A newbie question -- Why are the meridians not parallel like latitude
and why do they converge at the poles. Why do they have to measure
degrees and not distance like the latitude. If even meridians were
parallel, don't the intersecting lines of latitude and longitude give
the location of a place.
Sorry about so many why's. I am trying to understand the significance
of the origin of meridians.

Thanks for your help in advance.

You are asking questions which are actually a joy to answer and give
yourself a pat on the back for asking questions which few have asked
before  and even fewer have considered.Far from being a dull
exercise,the answers tell you much about human history in all sorts of
areas such as navigation and astronomy and just how brilliant men are
when they put their minds to it and although it is not possible to
discover the origins of most of your questions as to when and who
created the Lat/Long system as parts stretch back to remote
antiquity,it is possible to see how and why they organised things as
they did.

For instance,sailors used the altitude of the North star to determine
their latitude,they could do this as the star is a fixed point when
looking out at the night sky -

http://www.youtube.com/watch?v=XTTDWhky9HY

The higher you are in latitude,the higher in the sky Polaris will be -
90 degrees at the geographical poles and 0 degrees at the Equator -

http://lasp.colorado.edu/~bagenal/1010/images/latitude.jpg

Columbus held to the 28N Latitude in his first voyage West using this
method in tandem with the favorable trade winds -

http://www.reformation.org/columbus-route2.jpg

--------------------------------------------------------------------------- --------------------------------------------------------------------------- --------------------

Longitude is an altogether different story and even though it is a
little more complicated that latitude,you should be able to get the
basics.

The reason that longitude lines converge is due to the practicalities
of determining location East and West using time.A location at the
Equator is travelling at roughly  a maximum 1000 miles per hour at the
Equator while further North it diminishes to 0 miles at the North and
South poles yet both locations along the same line of longitude begin
and end the day at the same time.The trick is that once you know where
you are North or South in  Latitude (using Polaris for instance),you
can determine how many miles span the globe at that latitude location
-

http://www.thefreedictionary.com/_/viewer.aspx?path=hm/sci&name=ASlongit

A degree of Longitude at the 0 degree latitude ( Equator)  is 69 miles
while at 45 degrees latitude the value shrinks to 49 miles and all the
way to 0 miles at poles,they even jokingly have a tradition to 'race
around the world' based on this longitude relationship -

http://erikkawasaki.blogspot.com/2006/03/race-around-world_27.html

So,once you know how far North and South you are on the planet,you
then know how many miles circle the 360 degree globe at that
latitude.The next thing to do is to convert that 360 degrees of
longitude into 24 hours of time where 4 minutes of time equals 1
degree of longitude/geographical separation, 1 hour equals 15 degrees
and 24 hours makes 360 degrees in total -

http://academic.brooklyn.cuny.edu/geology/leveson/core/graphics/mapgr...

Now for the tricky part !.I assure you all scientists get lost on this
section and if you find difficulties here then you are in good
company.

Look at the image of celestial motion again -

http://www.youtube.com/watch?v=XTTDWhky9HY

While there is a fixed point for North and South  namely the star
Polaris,there is no fixed point East or West so you then you turn to
the daily cycle as daily rotation returns to noon.The great astronomer
Christian Huygens showed how to use natural noon as a fixed point so
that clocks can be used to determine how far East or West your
position is based on the difference where 4 minutes of clock time
equals 1 degree of longitude and therefore geographical separation -

http://www.xs4all.nl/~adcs/Huygens/06/kort-E.html

What Huygens does not explain,but I will if you so wish,is how they
managed to use natural noon as a basis for creating the 24 hour day
and then to use that for creating the notion that daily rotation is a
constant 24 hours/360 degrees and I hope others would too  as it
provides the foundation by which John Harrison created accurate
watches -

http://www.sailingwarship.com/harrisons-h4-chronometer-1760.html

Despite the enjoyable history behind the evolution of timekeeping and
its link to geography,navigation and especially astronomy,scientists
today are extremely careless with the value for daily rotation through
360 degrees and offer an alternative value (23 hours 56 minutes 04
seconds) and the reasoning behind that value.

Oriel, a good explanation.
However, the lines of latitude actually do sorta converge toward the
center of the earth if you consider the Lat and Long. coords to be the
angular coordinates of a spherical coordinate system using radius,
polar and azimuthal angle.

 That is, if you move toward the center of

the earth, you do so along a line of constant latitude  but decreasing
radius.  Likewise if you move directly away from the center of the
earth you do so on a line of constant latitude.

If you can move towards and away from the center of the Earth then
good for you but the topic and the questions asked relate to finding
location on the surface of the planet where latitude lines do not
converge to all intents and purposes while longitude meridians
converge at the geographical North and South poles from a maximum
distance apart  at the Equator -

http://plantwatch.sunsite.ualberta.ca/library/images/lat.jpg

http://plantwatch.sunsite.ualberta.ca/library/images/long.jpg

There is an incredible amount of history involved in determining
location by means of a watch  and the relationship between the daily
cycle and longitude meridians which help determine a geographical
position and I enjoy presenting this facet when I can -

http://www.esri.com/lewisandclark/locationthen.html

Do you wish to explain how the 24 hour day is linked to daily rotation
through 360 degrees as the principles set out by Huygens,the creation
of the  accurate by John Harrison and the use of it by Lewis and
Clark ?.This is the tricky part which few people can handle but you
are welcome to try.- Hide quoted text -

- Show quoted text -

Thank you all for the input.
Oriel,
  Thanks for your excellent explanation to my questions. I don't get
much time to read thru all this and therefore today finally I finished
reading all that you have sent. It was very fascinating to know all
this facts. I would sure like to know about the 24 hour day is linked
to 360 degree. I just saw that you posted this info in another
message. I will check that out later. Thanks again for the
explanation.

To discover how 24 hours is linked to daily rotation through 360
degrees requires a small detour into the astronomy of Copernicus and
Kepler but it is well worth the effort.It may seem like a lot of
tedious work but you are passing through some of humanity's greatest
discoveries and inventions.

Before Copernicus ,the geocentric astronomers had the Earth at the
center of the solar system * and watched as the other planets moved
against the background stars,the longer it took a planet to return to
the same spot ,the further away it was therefore the geocentric
astronomers put the Sun's position between the 225 days of Venus and
the 687 days of Mars as the Earth's cycle dictated by the Sun is 365
days .That is how they understood the solar system until Copernicus
changed it and he did it in a way that can now be easily understood
with modern imaging.

The geocentric astronomers noticed that the planets did not move
against the background stars in a predictable way night after night
but one day they would stop and a few days after that they would
appear to move backwards (retrograde) and then a long time after that
they would move forward again and modern imaging shows this as Jupiter
and Saturn move against the background stars over the course of a year
-

http://antwrp.gsfc.nasa.gov/apod/image/0112/JuSa2000_tezel.gif

What Copernicus discovered was that the orbital motion of the Earth
caused this effect as it overtakes the outer planets just as a car
going round a traffic circle in an inner lane overtaking cars in an
outer lane .So rather than having the Sun between Venus and
Mars,Copernicus replaced it with the motion of the Earth and the other
planets around the central Sun **.

This left daily rotation to explain the daily cycle of day and night
and this is where the 24 hour day comes in.If you get this far in
separating orbital motion from daily rotation then that is a good
day's work for the next part is really tricky and trips up just about
everyone.













* THE ORDER OF THE HEAVENLY SPHERES Chapter 10
"Of all things visible, the highest is the heaven of the fixed stars.
This, I see, is doubted by nobody. But the ancient philosophers wanted
to arrange the planets in accordance with the duration of the
revolutions. Their principle assumes that of objects moving equally
fast, those farther away seem to travel more slowly, as is proved in
Euclid's Optics. The moon revolves in the shortest period of time
because, in their opinion, it runs on the smallest circle as the
nearest to the earth. The highest planet, on the other hand, is
Saturn, which completes the biggest circuit in the longest time.
Below
it is Jupiter, followed by Mars.

With regard to Venus and Mercury, however, differences of opinion are
found. For, these planets do not pass through every elongation from
the sun, as the other planets do. Hence Venus and Mercury are located
above the sun by some authorities, like Plato's Timaeus [38 D], but
below the sun by others, like Ptolemy [Syntaxis, IX, 1] and many of
the modems. Al-Bitruji places Venus above the sun, and Mercury below
it. "

http://www.webexhibits.org/calendars/year-text-Copernicus.html


"Finally by what arguments do you prove that the centre of the Sun
which is at the midpoint of the planetary spheres and bears their
whole system - does not revolve in some annual movement,as Brahe
wishes,but in accordance with Copernicus sticks immobile in one
place,while the centre of the Earth revolves in an annual movement.
Argument 10
" The 10th argument,taken from the periodic times, is as follows; the
apparent movement of the Sun has 365 days which is the mean measure
between Venus' period of 225 days and Mars' period of 687
days.Therefore does not the nature of things shout out loud that the
circuits in which those 365 days are taken up has a mean position
between the circuits of Mars and Venus around the Sun and thus this is
not the circuit of the Sun around the Earth -for none of the primary
planets has its orbit arranged around the Earth,as Brahe admits,but
the circuit of the Earth around the resting Sun,just as the other
planets,namely Mars and Venus,complete their own periods by running
around the Sun."
Johannes Kepler -Epitome Copernican astronomy





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