Celestial navigation 2014 (pdf)

Celestial Navigation 3.0
2014.04.22 Yen @ NTU-AST
http://www.exploratorium.edu/neverlost

Navigation
is not about you, or your mind, or what you
can do. It's not about the sun and stars.
It's really about Everything.
-- Shorty Bertelmann, Navigator

# 1
Speed
- sandglass
- log, knot

# 2
Direction
-sun stone
-compass

# 3
Position Fix
(before 18 century)
-lead 測深儀
-astrolabe 觀象儀
-cross-staff 橫桿測天儀
-back-staff 背桿測天儀
-quadrant 象限儀
-octans 八分儀
( coastal sailing 海岸線航法 )
( lead )

( parallel sailing 平緯航法 )
(astrolabe)

The navigator always knows his Latitude,
but never knows his Longitude…
Until 18 century !

Tech Progress:
New Instruments in 18 century

## Before
Nocturnal – Only useful in the night

## New Instruments :
Chronometer & Sextant
1772, Harrison, H5

http://en.wikipedia.org/wiki/File:Using_sextant_swing.gif

Review :
3 Systems of Coordinates

## 1
The
Terrestrial
Coordinate
System
30oN

## 2
The
Celestial
Coordinate
System
North Celestial Pole
( Pn )
天北極
Local Hour Angle
( LHA )
當地時角
Polar Distance
極距
Declination
( Dec )
赤緯
Celestial Meridian
天子午線

## 2 ( test )
The
Celestial
Coordinate
System
Dec=23.5
Q1: where is LHA?
Q2: polar distance = ?
LHA=120

## 2
The
Celestial
Coordinate
System
春分點
North Celestial Pole
( Pn )
天北極
Sidereal Hour Angle
( SHA )
恆星時角
Declination
( Dec )
赤緯

## 2
The
Celestial
Coordinate
System
Greenwich
Celestial
Meridian
格林威治天子午線
Greenwich Hour Angle
( GHA )
格林威治天子午線

Summary for Hour Angle
All West
• LHA –
• SHA –
• GHA - Greenwich
## 2
The
Celestial
Coordinate
System
♈

## 3
The
Horizon
Coordinate
System
Zenuth
( Z )
天頂
Altitude
( Hc)
高度/仰角
Zenith Distant
( zd )
天頂距
Azimuth Angle
( Az)
方位角
Azimuth
( Zn )
真方位
Celestial Horizon
天水平線

## 3 ( test )
The
Horizon
Coordinate
System
Hc =50
Az=150
Q1: Zenith distance = ?
Q2: Azimuth = ?

## 1+2+ 3
Combine the
3 Systems of
Coordinates
Are you ready ?

Lat of =35oN
Hc=20o
Dec of = 20oS
Q1: zenith distance = ?
Q2: polar distance =?

## Position Fix :
in plane geometry (I)
Situation:
1. You do not know where you are.
2. All you know is the positions
of A and D , their altitudes
(60o,45o), and length of AB and
DE
How to solve your position ?
D
A
E
B
1
√3

## Position Fix :
Solution:
1.
for A, altitude = 60, RA=1
for D, altitude = 45, RD=1
2.
plot the circles with radius = RA
and RD.
3.
C must lie on the intersections.
A
√3

## Position Fix :
Solution:
1.
for A, altitude = 60, RA=1
for D, altitude = 45, RD=1
2.
plot the circles with radius = RA
and RD.
3.
C must lie on the intersections.
A
B
D
E
45
45
45
60
60
60
C
C
1
√3

## Position Fix :
in spherical geometry (I)
Where H1 > Hc > H2
Geometric Position
天體於地球之投影位置
Circle of equal Altitude
等高度圈
Pn
Assumed Position
假定船位

## Position fix :
in spherical geometry (I)
What is the length between AP and GP?
1) the angle of XZ = zenith dis.
2) 1 nautical mile = 1 海浬
(on earth) =1’arc
= 1/60° arc
≒ 1852 km
Problem of High Altitude Method (高高
度觀測法)
1) radius too large
2) distortion on sea chart
AP

Intercept Method
截距法
## Position fix :
in spherical geometry (II)

sine rule:
sin(a)/sin(A) = sin(b)/sin(B) = sin(c)/sin(C)
cosine rule:
cos(a) = cos(b) cos(c) + sin(b) sin(c) cos(A)
cos(b) = cos(c) cos(a) + sin(c) sin(a) cos(B)
cos(c) = cos(a) cos(b) + sin(a) sin(b) cos(C)
Positional Astronomy: Spherical trigonometry http://star-www.st-and.ac.uk/~fv/webnotes/chapter2.htm
Spherical Triangle
## Position fix :

A =當地時角(LHA)
B= 天體角
C =方位角(Az)
Terrestrial Triangle
a = 90 - Hc
b= 90 -L
c =90 -Dec
sin(Hc) =sin(L)sin(Dec)+cos(L)cos(Dec)cos(LHA)
sin(C) =cos (Dec)sin(LHA)/ sin(Hc)
@ Northern Hemisphere
North Pole
GP
AP
## Position fix :

Test: 已知兩邊夾一角，求對邊
觀測者所在緯度45度N，天體赤緯5度N，當地時角(LHA)60度，
試求:天體之高度。
Hint: sin(Hc) =sin(L)sin(Dec)+cos(L)cos(Dec)cos(LHA)
Solution:
sin(Hc) =sin(L)sin(Dec)+cos(L)cos(Dec)cos(LHA)
=sin(45)sin(5)+cos(45)cos(5)cos(60)
=0.41384
Hc = 24°26.8’#
周和平<天文航海學> 第七章 217頁例1
## Position fix :

That’s okay ! ( pad )
There are some Tables, e.g. No.229
,that keep you away from mathematics
during Sight Reduction !
We will be soon there !

Hc H0
GP
90-Hc
Altitude
Intercept
Hc > H0 , Away
H0 > Hc , Toward
(Homoto, H0 more Toward)
AP
## Position fix :

## Position fix :

AP
Intercept
Line of Position 天文位置線
## Position fix :

## Position fix :
We got the
Position !

Sight Reduction
using
Nautical Almanac and Table No.229

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
λ17°10.5W，於ZT 20-01-56，以船用六分儀觀
測Pollux ( 北河三 )，得H028°02.1’。試以航海
曆及229表，求AP、a (截距 ) 及Zn。
( key: GP,LHA,AP )
Aztec sailing: http://www.aztecsailing.co.uk/theory/ch6%20sect%202.html
周和平<天文航海學> 第九章 314頁例2改寫

Nautical Almanac
Parameter:
1.GMT
Download @ http://navsoft.com/downloads.html

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
測Pollux，得H028°02.1’。試以航海曆及229
表，求AP、a及Zn。
( key: GP,LHA,AP )
Zone time ( ZT ) 20-01-56
Zone difference ( ZD) +1
_________________________________________________
Greenwich mean time (GMT) 21-01-56

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
( key: GP,LHA,AP )
Greenwich mean time (GMT) = 21-01-56
GHA ♈ 209°01.5’
SHA ( Pollux ) 243°49.1
____________________________________________________
GHA ( Pollux ) 452°50.6’
=93°19.7’

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
( key: GP,LHA,AP )
GHA ( Pollux ) = 93°19.7’
Aλ 17°19.7’W
____________________________________________________
LHA ( Pollux ) 76°
Dec. (Pollux) 28°03.1’N
aL 42°

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
( key: GP,LHA,AP )
LHA ( Pollux ) 76°
Dec. (Pollux) 28°03.1’N
aL 42°
____________________________________________________
已知兩邊一夾角，求對邊 ( Hc ) 與方位角 ( Z ) 。
Help me, Table No.229 !!

Table No.229
Parameter:
1. LHA
2. Dec
3. aL
Download @National Geospatial-Intelligence Agency ( https://www1.nga.mil/‎)
Online sight reduction ( http://www.csgnetwork.com/directnautsrt1.html )

Warm up
1990年6月5日，某船2000 DR L41°34.8’N,
λ17°10.5W，於ZT 20-01-56，以船用六分儀觀測
Pollux，得H028°02.1’。試以航海曆及229表，求
AP、a及Zn。 ( key: GP,LHA,AP )
LHA ( Pollux ) = 76°
Dec. (Pollux) = 28°03.1’N
aL = 42°
____________________________________________________
Z 76 .4°
Rule 360 °
_____________________________________________________
Zn = 283.6 °
Hc = 28 °13.3'

Warm up
Pollux AP
Line of Position
42°N
17°W
AP (aL , aλ ) ( 42°00.0N , 19°19.7W)
A = Hc-Ho 11.2’Away
Zn 283.6°

Practice
2013年5月2日，某船 0200 DR L45°00.0’N,
λ23°23.0’W，於ZT 02-01-59，以船用六分儀
觀測 Deneb( 天津四 )，得H052°18.0’。
試以航海曆及229表，求：LHA、Hc、Z、a以及
天文位置線 ( LOP )。

2013年5月2日，某船 0200 DR L45°00.0’N,
λ23°23.0’W，於ZT 02-01-59，以船用六分儀觀測
Deneb( 天津四 )，得H052°48.0’。試以航海曆及229表，
求：LHA、Hc、Zn、a以及天文位置線。
Solution:
ZT 02-01-59
ZD +2 e
GMT 04-01-59
GHA ♈ 280°14.3’
SHA + 49°31.5’ 45°19.5N
GHA 329°45.8’
aλ - 23°45.8’
LHA 306°
Dec 45°19.5’
aL 45°00.0’
Hc 52°33.0’
Z 70.2°
Hc 52°33.0’
H0 52°48.0’
a 15.0’Toward
Z 70.2°
Rule -) 360.0°
Zn 289.8°

Reference
周和平 <天文航海學>
www.owenpalmiotti.com

Celestial navigation 2014 (pdf)

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Celestial navigation 2014 (pdf)