Earth's Shape, Latitude & Longitude: Dividing the Globe for Navigation

uh it's time for us to dig into module two and we're going to be checking out the earth and the coordinates that are

used to um essentially divide it up and identify locations on the earth and uh so number one the Earth is uh actually

an oblate ellipsoid all right and uh greatly exaggerated and and in that it's not a perfect oblate ellipsoid it's

actually got kind of a funky shape and here on the right side you can see this is uh greatly exaggerated but

it kind of shows you how what the actual shape it is um for all intents and purposes though we can approximate it as

a sphere um the oblate ellipsoid concept comes from this our our spherical Earth

is spinning around and um we all know what happens when we try to spin something around right if you've ever

tried it in like a a bucket or a rock on the end of the string it tries to fly out and so that

causes our Earth to fly out and kind of bulges so it's actually uh larger in diameter around the equator than it is

around uh over the the poles and it's uh around the poles has kind of kind of been squished down a little

bit so um but if we if we just approximate it as a sphere um we can we'll be we're

doing we're doing just great and uh actually it was known that the Earth was a sphere and um way back about uh 250

BC uh a guy named arat Aristophanes uh was able to compute the

diameter of the earth pretty darn accurately he was actually within 15% and uh the way he did it he knew how

far apart two things were that were vertical on the Earth's surface and uh one of them the well at

Zing the um Sun's Rays on June 21st went straight down into it and he assumed that that well was was straight

down and uh then the following year he went to a a different place Alexandria and um measured the angle of

the sun's rays in relation to an oblisk at Alexandria he came up with uh 7 Dees and 12 minutes and uh using just like

basic geometry this Arc Length um and that angle measurement he was actually able to figure out the radius of the

earth now fortunately we don't have to get into that geometry but that's just kind of a a side note um how really a

lot of what we're going to be using in this class um either in a GPS happening for us automatically or um doing manual

calculations uses a lot of geometry and math and it's it's all it's all mixed in there so

so how do we divide the Earth up and um this concept has been around for a long long time ever since uh people started

needing to navigate around the earth and um so the way it split up at at the equator we all know what the equator is

and it uh goes right around the middle of the Earth it's kind of like it it splits it in half from north to

south and we have parallels and these are rings imaginary rings that go around the earth you can see the and these are

all parallels here and they are parallel to the equator hence that's that's the name of it so if we know what parallel

we're on um that tells us how far north and south we

are and then we also have meridians um and these run from the north to the South Pole kind of split it

up into a basketball looking thing or orange slices depending on how you want to think about it and so if we know

which parallel we're on and then which Meridian we're on that defines a a coordinate on the

earth so here um all right

my my drawing tool is not working quite right but you can imagine if we have a a Meridian going on around here and we've

we say we're at the intersection of the that Meridian and this parallel well then that's where we are on the

earth now these parallels are also called lines of latitude and

um and so the latitude you might have heard of latitude longitude the latitude gives us our north south

location and then meridians these are called lines of longitude and they give us our East West

value and um we're going to get super familiar with this concept as we move forward here so here's another view of

this latitude longitude concept uh we always specify latitude first and the latitude is the angular

measurement off of the Equator and so here Fossil Oregon happens to be at 45°

latitude and it's to the north it's north of the equator so that's the 45 degrees

north and then longitude is measured off of the prim Meridian the Prime Meridian is a

Meridian uh which reaches from the north to the South Pole and it goes through the uh through grenwich grenwich England

um the the W is silent uh and um that is our 0 degrees longitude so here if we

measure uh and these are all degree measurements so 120° um that away from the prime

meridian that gives us our East West location um and now those um the longitude you can also see here the um

the angular measurement and this this will help you with your questions for this uh

this getting started assignment so our um our latitude it starts out at zero at the

equator and it increases all the way up to 90 when it hits the North Pole or it starts at zero and increases all the way

to 90 uh when it hits the South Pole now longitude on the other hand it starts at zero at the Prime

Meridian here we're going to the West around the earth and it goes to the West until it hits 180 degrees 180 degrees

that's considered the anti- meridian and that is as the highest longitude value that you can get is 180

degrees um now if you go beyond that if you keep going west beyond that then you actually start getting longitude

measurements that are measured from the opposite direction so if you go from from the prime radian and circle around

to the east that'll go 180 Dees and max out when it meets uh the anti- Meridian going the other way

around way all right and so here's just another view on that may it kind of clears up

what's going on there you can see these are latitude measurements and here's all of our

parallels or our lines of constant latitude and as we move away from the equator you can see how they tick up

until we get to uh 90° uh similar thing for longitude here's our prime meridian you

can see there's the prime meridian it's running right through grenwich England right there and um as we move to the

West we are increasing that and it increases around till it hits 180 right or if we go to the east it

increases until it hits 180 going the opposite way and so

um if we know our latitude and our longitude we know where our exact location is on the

Earth all right so now latitudes and longitudes if you if you just have a um say you know what I'm at

45° latitude and 120 degrees longitude West um that does does not give us enough

accuracy that's there's a a whole bunch of leadway and it won't get us close enough to where we need to be so usually

latitude and longitude are broken up into degrees and then further broken up into

minutes and then further broken up into seconds so this is just a visual on that here's one degree and there are actually

60 minutes in a degree and then within a minute there are 60 seconds and so in the work that

we'll be doing in this class we always get our location down to the nearest nearest

Second and um as as long as that that makes sense to you there we'll we'll be kind of

going over this over and over again and um the degrees minutes seconds that's just a way of splitting up a degree so

that it is gets it accurate enough for us and uh here this is just um just a visual on what we were talking

about as far as the uh oblate ellipsoid and what's going on there since it's the Earth is spinning

around it's actually going a 1,40 mil hour uh at the equator up here the closer you get to

the North Pole since it's not as far from the axis of rotation it's actually going slower so what does that do it

kind of pulls it out at the equator and makes it not quite a perfect sphere

um and uh here's just another visual on what's going on there so not a perfect sphere but for all intents and purposes

we can really assume that it is one and and stay well within the accuracy that we

need now so let's look at U how did the the early Sailors early

Navigators how did they use these latitude values and longitude values and why were they using degrees and

um the reason is they would look at um celestial bodies either the Sun or the North Star and based on the angle of

those so for example the angle to Polaris which is the North Star so if you the further up towards the north

North Pole that you go the angle

between the North Star and the Horizon will increase so here if you're right at the North Pole and you look at

the North Star it's going to be straight above you if you're where we are which is not

too far from 50° latitude and you look at the North Star the North Star

is going to be up in the sky a little bit and actually it will be up in the sky the angle from The

Horizon to the north star is going to be the same as our latitude value so this is just geometry just the way it works

out this 50° measurement off of The Horizon is the same as this 50° measurement off of the Equator so that

was really easy for Navigators to figure out they could just get that measurement and they would know how far north or

south they were on the earth um what happens if you're below the equator though right you you um

really can't see the North Star anymore and uh they would actually use a formation of four stars it's called The

Southern Cross and um that would allow them to figure figure out how far south of the Equator they

were uh this is a tool it's called a seant and um we'll look at a video in class and have a little bit more of a

discussion on it but that allows us to measure the angle of a Celestial body uh from The Horizon to that Celestial

body all right um next thing we need to talk about is notice that these meridians converge as they get closer to

the North Pole all right and and also notice that uh so so if you start out on one

Meridian you start walking North eventually you're going to run into the North Pole and any Meridian for any

Meridian that's that's true so if there's two people they start out at the equator way far apart along the Equator

and they start walking North through the ocean and everything they're eventually going to meet at the North

Pole and so let's say let's say they were 30°

of longitude apart and that's um a really long way along along the Equator down here well

the closer they get to the North even though they stay 30° of longitude apart they are getting closer and closer

together their actual physical distance on the earth is getting closer together

um and um yeah so the um and however

parallels and so so what that means really in the bottom line what that means is one degree of longitude our

East West measurement it's worth a lot more down at the equator than it is up here in

Greenland um however uh one degree of latitude for parallels one degree of latitude is worth the same amount no

matter where you are it might be down at the equator it might be way up here at the North Pole and one degre is worth

the same physical distance on the earth okay so we actually see that difference in the amount that a degree

of latitude is versus a degree of longitude on a lot of our Maps so if you look at U 1 to 24,000 000 map and we'll

be using a lot of those in this uh in this class it's actually rectangular shape has anyone ever wondered why in

the heck are those rectangular shaped um here in South Dakota and um maybe you've you've looked at like a a topographic

map and usually they are rectangular shape and the reason is they have the same

in longitude the longitude the change of longitude along the east

west side to side measurement is in this case it's 7 and a half

minutes the change of latitude up and down is also 7 and 1 half minutes but remember as we go north 7

and 1 12 minutes of longitude side to side is worth less than 7 and a half minutes of change of

latitude and so that's that's where we we see that now if this were at the equator down at the

equator a degree of longitude is worth the exact same as a degree of latitude and uh so there a 7 and 1 half

minute quadrangle would be would be a perfect square when you get all the closer you get to the North Pole the

more and more stretched out these things get and eventually they stop because it's not too practical to have a long

skinny uh map and so they they start using um reducing the amount of of latitude

that they show or they keep the same amount of latitude but they include more longitude as you get further north

so all right and um so all the the other thing we can notice here on on this map is that um all navigational type Maps

will have some way of locating figuring out what the latitude and the longitude is on it and so here this one this

corner starts out at with a latitude of 44 degrees 30 minutes and as it goes

up a lot of times they leave off the 44° so this is actually 44° 32 minutes and 30 seconds this one 44° 35 minutes and

all the way up here this is 44° 37 minutes and 30 seconds so we've changed by

72° or 7 and 1/2 minutes sorry or 7 minutes and 30 seconds same thing goes here for

longitude here at this corner we start out at 123° 15 minutes and then as we're going

this way we're increasing so this is actually 123 17 minutes 30 seconds and when we

get all the way out to here we're at 123° 22 minutes and 30 seconds if we look at a um a nautical chart they

also show latitude and longitude on here and so here this is our we don't see the this map since it's

cut off we don't see a full latitude degree measurement but uh as it's they're somewhere along here

we would see what the degree measurement is and then these are the minutes associated with it here for our

longitude here we do see it right here this is 122° and 40 minutes this back here would be 122 degrees and 38 and

then 36 minutes uh this is an example of an aeronautical chart and they lay it out a

little bit differently so this line right here is 170° of

longitude uh this line going across right here is 50° of latitude or 53 degrees of latitude and so when you get

up to here uh this would somewhere along this line there would be a label that tells us what latitude we are there and

somewhere along this line right here it would tell us what how many degrees of longitude we are

there so yeah so north south lines those are constant longitude East West lines those are going to be constant

latitude all right and um we we can also figure out um you may have seen like survey markers out there

maybe it's on top of a mountain or maybe it's at the corner of a property something like that the these someone

has figured out what the ex precise latitude longitude of those are and we can figure out other locations off of

those um and then um on maps there's there's there's been as um technology has improved and math

has improved and our knowledge of the shape of the Earth has improved the um the accuracy of where

these latitude longitude values are on a map has changed a little bit and um so there are different um

models uh that are used to approximate where they are and so you might see a map that has

two different locations for latitude and longitude and uh where the corners of

the map should be and um we'll get into that a little bit more in the future but it just it just tells us where which one

of those Corners depending on which system we're using we measure from one corner or the other to figure out our

location uh so so at this point and we're going to get into this a lot more in class in our classroom discussion but

um we want to be able to figure out the distance on the earth for a degree of longitude and a degree of

latitude right and so one degree on the earth for for latitude so if we change a degree how

much is that actually worth and uh the equations that we'll be using for that we just use the equation

for circumference of a circle 2 * pi * the radius and the radius that's going to be the radius of the

Earth and there's 360° in a circle so if we take that circumference and we divide it by 360

Degrees we figure out how much one degree of latitude is worth

um and one degree of latitude like we were talking about before is worth the same amount no matter where you are on

the Earth but one degree of latitude is worth different amounts depending on how far north or south you

are from the equator and so we actually have to use this equation right down here we figure out how much one degree

of latitude is and then we multiply it by the cosine of whatever latitude we are at uh so

think about that a little bit let it digest um we'll dig into it more in our lecture um on

campus and uh so that's all we need to go through today your next step is going to be uh to do um a few questions

questions in um in module two and um they are directly related to this PowerPoint and the discussion we've had

there's five questions true false multiple choice get you warmed up for this module and um then bring questions

to class and we'll talk about the exercises and some of the key points that we went over

today