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

Navigation

is about…

# 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)

( back-staff )

(quadrant)

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


Dec=23.5

Q1: where is LHA?

Q2: polar distance = ?

LHA=120

## 2

The


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

♈

Relation between

## 1 & ## 2

## 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 =?

Theory : Fix Position

## 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

Time Zone

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 )

Zone time ( ZT ) 20-01-56

Zone difference ( ZD) +1

_________________________________________________

Greenwich mean time (GMT) 21-01-56

Warm up


( 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


( 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


( 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

Thank you for listening !

celestial navigation 2014 (pdf)

Education