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Microsoft PowerPoint - UCTM Handout C - Student Packet - drh041009c [Read-Only] fn:drh041009c
Academy for Math, Engineering, and Science
Where in the
World Are We?
Student Packet
Latitude
Suns
Altitude = 62
Zenith Distance
90 - Suns Altitude
= 28
Suns Declination = 13
North Pole
Earth fn:drh041009c
Academy for Math, Engineering, and Science
Plot these locations on the world map
San Francisco
38
o
N 122
o
W
Rio de Janeiro
23
o
S 42
o
W
Jerusalem 32
o
N 35
o
E
Melbourne 38
o
S 145
o
E
Papeete
17
o
S 150
o
W
Review of Latitude and Longitude fn:drh041009c
Academy for Math, Engineering, and Science
Protractor
Straw
Weighted string shows
Polariss altitude
Latitude by Polaris
North Pole
South Pole
Earth
Horizon
Line
Observer
Polaris
(North Star)
Latitude
Polaris
Altitude
The angle of Polaris
above the horizon
equals the
observers
approximate
latitude
Possible 0.7
o
error
North Pole
South Pole
Earth
North Pole
South Pole
Earth
Latitude
Horizon
Line
Observer
Polaris
(North Star)
Latitude
Polaris
Altitude
Observer
North Pole
South Pole
Earth
North Pole
South Pole
Earth
Measuring the altitude of Polaris is easy to
do with simple tools such as this.
However, the Polaris method has
one major problem. It doesnt
work in the majority of the world. fn:drh041009c
Academy for Math, Engineering, and Science
Source: Emergency Navigation, David Burch
Any of these constellations can be used to find Polaris. The + or - signs indicate that
the distances from the pointer stars to Polaris are slightly larger of smaller than
exactly five times the pointer spacings labeled as x. However, if you just remember
distance = 5 times x then that will get you close enough to find Polaris. fn:drh041009c
Academy for Math, Engineering, and Science
Noon Sun Shot On April 26
Latitude
Suns
Altitude = 62
Zenith Distance
90 - Suns Altitude
= 28
If the SUN IS SOUTH OF YOU, then your
Latitude = Suns Declination + Zenith Distance
Example: Alt = 62 so ZD = 28, and then Lat = 13 + 28 = 41
Suns Declination = 13
North Pole
Earth
The Noon-Time Sun:
On ANY day of the year
Latitude
Suns
Altitude = 62
Zenith Distance
90 - Suns Altitude = 28
If the SUN IS NORTH OF YOU, then your
Latitude = Suns Declination - Zenith Distance
Example: Alt = 62 so ZD = 28, and then Lat = 13 - 28 = -15 = 15 SOUTH
Suns Declination = 13
Remember:
If Sun is South of You, Add If Sun is North of You, Subtract
(SSA) (SNS)
North Pole
Earth
Noon Sun Shot On October 17
Latitude
Suns
Altitude = 62
Zenith Distance
90 - Suns Altitude = 28
If the SUN IS SOUTH OF YOU, then your
Latitude = Suns Declination + Zenith Distance
Example: Alt = 62, so ZD = 28, and then Lat = -9 + 28 = 19
Suns Declination = -9
(South = NEGATIVE)
North Pole
Earth
The Noon-Time Sun:
On ANY day of the year
Latitude
Suns
Altitude = 62
Zenith Distance
90 - Suns Altitude = 28
If the SUN IS NORTH OF YOU, then your
Latitude = Suns Declination - Zenith Distance
Example: Alt = 62, so ZD = 28, and then Lat = -9 - 28 = -37 = 37 SOUTH
Suns Declination = -9
(South = NEGATIVE)
North Pole
Earth
North = Positive South = Negative
Latitude
Suns
Altitude
Zenith Distance
= 90 - Suns Altitude
If the suns declination is SOUTH of the
equator, write the declination as a NEGATIVE
NUMBER, then the rules of adding and
subtracting will still be the same as before.
Suns Declination
North Pole
Earth
Finding Latitude From a Noon Sun Shot fn:drh041009c
Academy for Math, Engineering, and Science
How to find
the suns
declination on
April 26
April 26
April 26
April 26
Declination
is 13 degrees
North
Declination
is 13 degrees
North
Student exercise:
What is the suns declination on
June 15? ________
Sept 7? ________
December 18? ________
If the suns noon-time altitude is 41 degrees and it is SOUTH of you, what is
your latitude if the date is
June 15? ________
Sept 7? ________
December 18? ________
What if the sun were NORTH of you when you did the measurements and got
41 degrees? What would you latitude be then if the date is
June 15? _______
Sept 7 ________
December 18? ________ fn:drh041009c
Academy for Math, Engineering, and Science fn:drh041009c
Academy for Math, Engineering, and Science
360 degrees/day = 15 degrees/hour = 0.25 degrees/minute
If the time in Greenwich is 4:15 p.m.
when its noon where you are, then your local noon is
4 hours and 15 minutes after Greenwich, which means your
longitude = ((4*60)+15)*0.25 = 63.75
o
West
Assume its June 15.
(Youll find out later why thats important.)
360 degrees/day = 15 degrees/hour = 0.25 degrees/minute
If the time in Greenwich is 5:39 a.m.
when its noon where you are, then your local noon is 6
hours and 21 minutes before Greenwich, which means your
longitude = ((6*60)+21)*0.25 = 95.25
o
East
Assume its June 15.
(Youll find out later why thats important.)
Finding Longitude From a Noon Sun Shot fn:drh041009c
Academy for Math, Engineering, and Science
Local noon usually does NOT occur
exactly at 12:00 even in Greenwich!
Because the Earths orbital path is elliptical rather than
circular, the timing of local noon changes throughout the
year. On some days the sun reaches its noon-time peak
altitude at Greenwich before 12:00, and on other days it
reaches that peak altitude after 12:00.
Sun
Earth
Nov. 2
The sun is
fast by 16
minutes on
this day.
Local noon
occurs at
11:44 a.m.
in Greenwich
The sun is
fast by 16
minutes on
this day.
Local noon
occurs at
11:44 a.m.
in Greenwich
The error
resulting from
ignoring this
time change is
NOT trivial.
You can miss
your destination
by almost
300 miles! fn:drh041009c
Academy for Math, Engineering, and Science
The date is November 2
Local noon in Greenwich occurs at 11:44 a.m.
Local noon for you is 10:27 GMT. Where you are?
360 degrees/day = 15 degrees/hour = 0.25 degrees/minute
Your local noon occurs 1 hour and 17 minutes
before Greenwich, which means your
longitude = ((1*60)+17)*0.25 = 19.25
o
East
Student exercise:
How many minutes fast or slow is the sun running on
March 15? ________ minutes Fast or slow? ___________
October 21? ________ minutes Fast or slow? ___________
If local noon for you occurs at 2:15 p.m. GMT, then what is your longitude if
the date is
March 15? ________
October 21? ________
If local noon for you occurs at 7:52 a.m. GMT, then what is your longitude if
the date is
March 15? ________
October 21? ________ fn:drh041009c
Academy for Math, Engineering, and Science
Putting it all together. Calculating both latitude and
longitude from the noon sun shot.
Nort
h
53.7
degrees
3
:
07 G
M
T
Nov
e
mber 27
Nort
h
60.3
degrees
23:40 G
M
T
July 14
Sou
t
h
42.6
degrees
17:32 G
M
T
F
e
b
r
uar
y 3
What i
s
y
our
longitude?
What i
s
y
our
latitud
e
? a
nd th
e n
oon-
time s
un
i
s

South/North
of y
ou
a
n
d
y
o
u
m
easu
re
that altitud
e

to be

a
nd th
e
su
n
reac
hes its
peak noon-
tim
e
a
l
titud
e

in y
our
loc
a
tion at
If the date i
s

Find the latitude and
longitude of all three
positions above and
plot them on the
world map. fn:drh041009c
Academy for Math, Engineering, and Science
Measuring the Noon-Time Sun
H
S
ArcTan (H/S) = Altitude
Altitude
Yard Stick
Shadow
Weighted string shows
if stick is not vertical
20.00
22.00
24.00
26.00
28.00
30.00
32.00
34.00
9:00
10:30
12:00
13:30
15:00
If you take measurements over a three-
hour period like this example, then you will
also have all the data needed to calculate
both latitude and longitude.
Su
ns Altitude
Time fn:drh041009c
Academy for Math, Engineering, and Science
20.00
22.00
24.00
26.00
28.00
30.00
32.00
34.00
9