Celestial Navigation Chapter 6.1 Homework Solutions
Sight Planning
Homework Solutions
Global Navigation
Chapter 6
1
Objectives
Internet resources to identify & locate celestial
bodies.
Use an electronic sight planning tool,
Sight
Planner
in
Celestial Tools .
Set up a USPS star finder for any location &
time
.
Set up a USPS star finder for any location &
time
.
2
Objectives
(continued)
Select suitable bodies for fixes at twilight
or in daytime
.
Identify an unknown celestial body listed
in
NA.
3
Pratical Exercise
1
Set up the Star Finder for your present
location, at any convenient time on the
evening of the day you are reading this.
List the planets and first-magnitude stars
that will be visible with their azimuths
and altitudes to help in locating the
bodies. Then go outside and find as many
of the listed bodies as you can
.
2.
Use
Celestial Tools
to determine the
planets and first-magnitude stars that
will be visible with their azimuths and
altitudes
.
4
Question 3
To plot a body on the star finder, set the red
To plot a body on the star finder, set the red
template arrow to the value of
template arrow to the value of
:
:
a.
a.
LHA Aries.
LHA Aries.
b.
b.
GHA Aries.
GHA Aries.
c.
Right ascension (RA).
d.
d.
Declination.
Declination.
Ref: ¶ 46
Ref: ¶ 46
5
Question 4
If you rotate the blue template to mimic
the passage of time, the arrow will
indicate
:
a.
Increasing values of LHA Aries.
b.
Decreasing values of LHA Aries.
c.
Increasing values of right ascension.
d.
Decreasing values of right ascension.
Ref: ¶ 40
6
Question 5
Right Ascension of the sun is equal to
:
a.
GHA Aries – GHA sun.
b.
180° - SHA sun.
c.
180° + SHA sun.
d.
SHA sun – GHA sun.
Ref: ¶ 48
7
Question 6
Set your star finder for the northern hemisphere,
with the red template in place. Find the solution
to a. Then, using the appropriate blue templates
and appropriate side of the star base, find the
solutions to b, c, and d
.
a. What is the declination of?
Answer : 27°
(by inspection).
8
b. What is its altitude at meridian transit at
Latitude 75°N?
A
n
s
w
e
r
:
4
2
°
Solution 6b : Calculate RA of Alphecca?
RA = 360° - SHA = 360°-126°16,7’ =
233°43,3’ (rounded to 234°)
S
e
t
7
5
°
N
b
l
u
e
t
e
m
p
l
a
t
e
o
n
2
3
4
°
a
n
d
r
e
a
d
a
l
t
i
t
u
d
e
.
A
l
t
i
t
u
d
e
i
s
4
2
°
.
c. What is its altitude at meridian transit at
Latitude 25°S?
c. Answer : 38°
S
o
l
u
t
i
o
n
:
S
e
t
2
5
°
S
b
l
u
e
t
e
m
p
l
a
t
e
o
n
s
o
u
t
h
b
a
s
e
a
t
2
3
4
°
a
n
d
r
e
a
d
a
l
t
i
t
u
d
e
.
A
l
t
i
t
u
d
e
i
s
3
8
°
d. What is its altitude at meridian transit at Latitude
75°S?
d. Answer: Body is below the horizon.
d. Solution: Set 75°S blue template on south
base at 234° and read altitude. Body is below the
horizon.
Question 7 a
Use the Excerpts from the
Nautical
Almanac,
Appendix B, for the following
questions. You are at L35°N, Lo 62°W. It is
ZT 2000 on 30 June
.
a.
For this time, plot the planets on the star base
and list SHA, RA, dec and magnitude for each.
Plot the sun and moon for the same time and list
GHA, RA and dec for
each. Find LHA Aries?
9
Question 7 b
Use the Excerpts from the
Nautical Almanac,
Appendix B,
for the following questions. You are at L35°N, Lo 62°W. It
is ZT 2000 on 30 June
.
b.
Choose the bodies for a two-body
and three-body twilight fix
.
10
T
w
o
-
b
o
d
y
f
i
x
e
s
:
V
e
g
a
-
A
n
t
a
r
e
s
,
D
e
n
e
b
-
M
o
o
n
,
P
o
l
l
u
x
o
r
M
a
r
s
-
S
p
i
c
a
a
r
e
a
l
l
r
e
a
s
o
n
a
b
l
e
.
T
h
r
e
e
-
b
o
d
y
f
i
x
e
s
:
D
e
n
e
b
-
A
n
t
a
r
e
s
-
R
e
g
u
l
u
s
,
M
o
o
n
-
S
p
i
c
a
-
R
e
g
u
l
u
s
.
Question 7 c
Use the Excerpts from the
Nautical Almanac,
Appendix B,
for the following questions. You are at L35°N, Lo 62°W. It
is ZT 2000 on 30 June
.
c.
What is the sun’s azimuth at sunset? At
sunrise
?
11
At sunset, Sun Zn is 298°.
At sunrise, Sun Zn is 062°.
Question 7 d
Use the Excerpts from the
Nautical Almanac,
Appendix B, for the
following questions. You are at L35°N, Lo 62°W. It is ZT 2000 on 30
June.
d.
Is the approximate altitude of the sun at
meridian transit determined by the blue
overlay reasonable for a sight
?
At meridian transit, altitude of the sun is
78°. This is a high altitude sight, so care
must be taken to make an accurate
observation
.
12
Question 7 e
Use the Excerpts from the
Nautical Almanac,
Appendix B, for the
following questions. You are at L35°N, Lo 62°W. It is ZT 2000 on 30
June
.
e.
Were the sun and moon available for a 2-
body fix earlier in the day on 30 Jun
e
?
No sun-moon fix is possible. The sun is
setting as the moon is rising
.
13
Question 7 f
Use the Excerpts from the
Nautical Almanac,
Appendix B, for the
following questions. You are at L35°N, Lo 62°W. It is ZT 2000 on 30
June
.
f.
From the
Almanac
, what is the time of
meridian transit of Venus on 30 June? Do
you expect it to be visible during the
daylight
?
MT is at ZT 1007. It is 2hrs 5 minutes
away from MT of the sun and its
magnitude is such that it should be visible
in the daytime
.
14
Question 7 g
Use the Excerpts from the
Nautical Almanac,
Appendix B, for the
following questions. You are at L35°N, Lo 62°W. It is ZT 2000 on 30
June
.
g.
Due to cloud cover at twilight, the only
bodies available for observation that
evening were Antares and a bright body
low on the eastern horizon. What is that
body
?
With the 35° N blue template set at
evening twilight, the only bright body low
in the
east is Altair
.
15
Question 8-a
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the sun a
short time before transit and a meridian transit
LOP. An azimuth cut of 45° between the LOPs
should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20 Mar
2004)
.
16
a.
What is the azimuth of the sun at transit and
LHA Aries when the sun is at transit
?
Using the Star Finder: Zn = 000°, LHA Aries=
001° (By inspection)
Using Celestial tool: Zn = 360°, LHA Aries = 001°
Question 8-b
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the sun a
short time before transit and a meridian transit
LOP. An azimuth cut of 45° between the LOPs
should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20 Mar
2004
).
17
When the azimuth of the sun is 045°, what is the
LHA of Aries
?
Star Finder : 332
°
C
e
l
e
s
t
i
a
l
t
o
o
l
:
3
3
1
°
S
o
l
u
t
i
o
n
:
Z
n
0
4
5
°
o
c
c
u
r
s
f
r
o
m
1
0
0
4
t
o
1
0
1
0
.
U
s
i
n
g
m
i
d
p
o
i
n
t
1
0
0
7
,
L
H
A
A
r
i
e
s
=
3
3
1
°
Question 8 c
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the sun a
short time before transit and a meridian transit
LOP. An azimuth cut of 45° between the LOPs
should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20 Mar
2004
).
18
C
e
l
e
s
t
i
a
l
t
o
o
l
:
3
0
°
.
S
o
l
u
t
i
o
n
:
(
3
6
0
°
-
3
3
1
°
)
+
0
0
1
°
=
3
0
°
S
t
a
r
F
i
n
d
e
r
:
2
9
°
W
h
a
t
i
s
t
h
e
d
i
f
f
e
r
e
n
c
e
b
e
t
w
e
e
n
t
h
i
s
L
H
A
A
r
i
e
s
a
n
d
t
h
e
L
H
A
o
f
A
r
i
e
s
a
t
L
A
N
?
Question 8 d
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the sun a
short time before transit and a meridian transit
LOP. An azimuth cut of 45° between the LOPs
should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20 Mar
2004
).
19
What is the LHA difference, converted to time
?
S
t
a
r
F
i
n
d
e
r
:
1
h
o
u
r
5
6
m
i
n
u
t
e
s
.
S
o
l
u
t
i
o
n
:
2
9
°
X
4
m
/
d
e
g
r
e
e
=
1
1
6
m
i
n
u
t
e
s
/
6
0
=
1
h
o
u
r
5
6
m
i
n
u
t
e
s
.
C
e
l
e
s
t
i
a
l
t
o
o
l
:
2
h
o
u
r
s
.
S
o
l
u
t
i
o
n
:
3
0
°
X
4
m
i
n
/
d
e
g
r
e
e
=
1
2
0
m
i
n
/
6
0
=
2
h
o
u
r
s
Question 8 e
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the
sun a short time before transit and a meridian
transit LOP. An azimuth cut of 45° between the
LOPs should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20
Mar 2004
).
20
W
i
t
h
t
r
a
n
s
i
t
o
c
c
u
r
r
i
n
g
a
t
1
2
0
7
,
w
h
e
n
s
h
o
u
l
d
y
o
u
t
a
k
e
t
h
e
e
a
r
l
i
e
r
s
i
g
h
t
?
S
t
a
r
F
i
n
d
e
r
:
1
0
1
1
.
S
o
l
u
t
i
o
n
1
2
0
7
–
0
1
5
6
=
1
0
1
1
C
e
l
e
s
t
i
a
l
t
o
o
l
:
1
0
0
7
.
S
o
l
u
t
i
o
n
:
1
2
0
7
–
2
h
o
u
r
s
=
1
0
0
7
(
Z
n
=
0
4
5
°
)
Question 8 f
With a DR position of L35°S, Lo 165°W on 20
March, plan a running fix with an LOP of the sun a
short time before transit and a meridian transit
LOP. An azimuth cut of 45° between the LOPs
should be adequate. The
Nautical Almanac
indicates that MT will occur at 1207 for your
longitude, so plot the sun on your star finder at
ZT 1207. Answer the following questions, first
using the star finder, then with
Celestial Tools
(when using
Celestial Tools
, use the date 20 Mar
2004
).
21
A
f
t
e
r
m
e
r
i
d
i
a
n
p
a
s
s
a
g
e
,
y
o
u
c
a
n
d
o
t
h
e
s
a
m
e
t
h
i
n
g
t
o
o
b
t
a
i
n
a
n
o
t
h
e
r
r
u
n
n
i
n
g
f
i
x
.
A
t
w
h
a
t
t
i
m
e
s
h
o
u
l
d
y
o
u
t
a
k
e
t
h
e
a
f
t
e
r
n
o
o
n
s
i
g
h
t
?
S
t
a
r
F
i
n
d
e
r
:
1
4
0
3
.
S
o
l
u
t
i
o
n
:
1
2
0
7
+
0
1
5
6
=
1
4
0
3
C
e
l
e
s
t
i
a
l
t
o
o
l
:
1
4
0
7
.
S
o
l
u
t
i
o
n
:
1
2
0
7
+
2
h
o
u
r
s
=
1
4
0
7
(
Z
n
=
3
1
5
)
Sight Planning
End of
Global Navigation
Chapter 6
22
Explore the challenges and solutions to celestial navigation through practical exercises involving star finders, celestial bodies identification, and sight planning tools. Enhance your knowledge of astronomy by setting up tools, locating planets and stars, and mastering the use of templates for plotting celestial bodies.
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Presentation Transcript
Sight Planning Homework Solutions Global Navigation Chapter 6 1
Objectives Internet resources to identify & locate celestial bodies. Use an electronic sight planning tool, Sight Planner in Celestial Tools . Set up a USPS star finder for any location & time. Set up a USPS star finder for any location & time. 2
Objectives (continued) Select suitable bodies for fixes at twilight or in daytime. Identify an unknown celestial body listed in NA. 3
Pratical Exercise 1 Set up the Star Finder for your present location, at any convenient time on the evening of the day you are reading this. List the planets and first-magnitude stars that will be visible with their azimuths and altitudes to help in locating the bodies. Then go outside and find as many of the listed bodies as you can. 2. Use Celestial Tools to determine the planets and first-magnitude stars that will be visible with their azimuths and altitudes. 4
Question 3 To plot a body on the star finder, set the red template arrow to the value of: a. LHA Aries. b. GHA Aries. c. Right ascension (RA). d. Declination. Ref: 46 5
Question 4 If you rotate the blue template to mimic the passage of time, the arrow will indicate: a. Increasing values of LHA Aries. b. Decreasing values of LHA Aries. c. Increasing values of right ascension. d. Decreasing values of right ascension. Ref: 40 6
Question 5 Right Ascension of the sun is equal to: a. GHA Aries GHA sun. b. 180 - SHA sun. c. 180 + SHA sun. d. SHA sun GHA sun. Ref: 48 7
Question 6 Set your star finder for the northern hemisphere, with the red template in place. Find the solution to a. Then, using the appropriate blue templates and appropriate side of the star base, find the solutions to b, c, and d. a. What is the declination of? Answer : 27 (by inspection). RA = 360 - SHA = 360 -126 16,7 = 233 43,3 (rounded to 234 ) Set 75 N blue template on 234 and read altitude. Altitude is 42 . c. What is its altitude at meridian transit at Latitude 25 S? c. Answer : 38 Solution : Set 25 S blue template on south base d. Answer: Body is below the horizon. d. What is its altitude at meridian transit at Latitude 75 S? b. What is its altitude at meridian transit at Latitude 75 N? Answer: 42 Solution 6b : Calculate RA of Alphecca? at 234 and read altitude. Altitude is 38 d. Solution: Set 75 S blue template on south base at 234 and read altitude. Body is below the horizon. 8
Question 7 a Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. a. For this time, plot the planets on the star base and list SHA, RA, dec and magnitude for each. Plot the sun and moon for the same time and list GHA, RA and dec for each. Find LHA Aries? Body GHA RA Dec LHA Magnitude Body 360 -SHA =RA 100 Dec GHA Soleil 179 23 N Venus 360 291 069 18 N -4,4 211 Moon 22 257 26 S Mars 360 234 126 20 N +1,8 152 279 217 23 Jupiter 360 195 165 8 N -1,9 114 Saturn 360 253 Rounded to 107 22 N +0,1 172 217 9
Question 7 b Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. b. Choose the bodies for a two-body and three-body twilight fix. Two-body fixes: Vega-Antares, Deneb-Moon, Pollux or Mars-Spica are all reasonable. Three-body fixes: Deneb-Antares-Regulus, Moon-Spica-Regulus. 10
Question 7 c Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. c. What is the sun s azimuth at sunset? At sunrise? At sunset, Sun Zn is 298 . At sunrise, Sun Zn is 062 . 11
Question 7 d Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. d. Is the approximate altitude of the sun at meridian transit determined by the blue overlay reasonable for a sight? At meridian transit, altitude of the sun is 78 . This is a high altitude sight, so care must be taken to make an accurate observation. 12
Question 7 e Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. e. Were the sun and moon available for a 2- body fix earlier in the day on 30 June? No sun-moon fix is possible. The sun is setting as the moon is rising. 13
Question 7 f Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. f. From the Almanac, what is the time of meridian transit of Venus on 30 June? Do you expect it to be visible during the daylight? MT is at ZT 1007. It is 2hrs 5 minutes away from MT of the sun and its magnitude is such that it should be visible in the daytime. 14
Question 7 g Use the Excerpts from the Nautical Almanac, Appendix B, for the following questions. You are at L35 N, Lo 62 W. It is ZT 2000 on 30 June. g. Due to cloud cover at twilight, the only bodies available for observation that evening were Antares and a bright body low on the eastern horizon. What is that body? With the 35 N blue template set at evening twilight, the only bright body low in the east is Altair. 15
Question 8-a With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). a. What is the azimuth of the sun at transit and LHA Aries when the sun is at transit? Using the Star Finder: Zn = 000 , LHA Aries= 001 (By inspection) Using Celestial tool: Zn = 360 , LHA Aries = 001 16
Question 8-b With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). When the azimuth of the sun is 045 , what is the LHA of Aries? Star Finder : 332 Celestial tool : 331 Solution : Zn 045 occurs from 1004 to 1010. Using midpoint 1007, LHA Aries = 331 17
Question 8 c With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). What is the difference between this LHA Aries and the LHA of Aries at LAN? Star Finder: 29 Celestial tool: 30 . Solution : (360 -331 ) + 001 = 30 18
Question 8 d With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). What is the LHA difference, converted to time? Star Finder : 1 hour 56 minutes. Solution : 29 X 4m/degree= 116 minutes/60 = 1 hour 56 minutes. Celestial tool: 2 hours. Solution : 30 X 4min/degree = 120 min/60 = 2 hours 19
Question 8 e With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). With transit occurring at 1207, when should you take the earlier sight? Star Finder : 1011. Solution 1207 0156 = 1011 Celestial tool: 1007. Solution : 1207 2 hours = 1007 (Zn = 045 ) 20
Question 8 f After meridian passage, you can do the same thing to obtain another running fix. At what time should you take the afternoon sight? With a DR position of L35 S, Lo 165 W on 20 March, plan a running fix with an LOP of the sun a short time before transit and a meridian transit LOP. An azimuth cut of 45 between the LOPs should be adequate. The Nautical Almanac indicates that MT will occur at 1207 for your longitude, so plot the sun on your star finder at ZT 1207. Answer the following questions, first using the star finder, then with Celestial Tools (when using Celestial Tools, use the date 20 Mar 2004). Star Finder: 1403. Solution : 1207 + 0156 = 1403 Celestial tool: 1407. Solution : 1207 + 2 hours = 1407 (Zn = 315) 21
Sight Planning End of Global Navigation Chapter 6 22
