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Author
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Topic: CelNav Practice Problems Section 5.8
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Bill Hayles
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posted February 02, 2026 03:06 PM
I am working on the 10 problems on page 73 (Section 5.8) in the “Celestial Navigation” book. I have the following three questions.
Question #3
Part of the calculations for question #3 I am confused about. Basically, the answer on page 225 indicates that the a-value is 13.6.
I get 46.3. Here are my values. Hs 41d 30.5m. Index correction is +4.0 DIP is -3.1 these give you Ha 41d 31.4m. Altitude correction is 15.1 this make Ho 41 d 46.5 m. Since Hc is 42d 00.2m, I get an a-value of 46.3
Question #5
How do you get an a-value of 1d 20.9m from an Ho of 71d 20.6m and an HC of 69d 59.7m?
Question #6
The answers in the book indicate that LHA is 360. I get 359. UTC time is 00h 51m 00s
GHA is 183d 58.8m. GHA (m.s.) is 12d 45.0m. This gets a GHA of 196d 03.8m. A-Lon is +162d 56.2m. These are my calculations. What am I doing wrong?
From: Brockport NY
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RobertR
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posted February 02, 2026 11:16 PM
Hello!
I'll take these in order--
#3
If Hc is 42°00.2' and Ho is 41°46.5', to subtract Ho from Hc I would first convert 42°00.2' to 41°60.2'. This simplifies the problem to 60.2'- 46.5', which = 13.7'
#5
This is similar. (71°21.6' - 69°59.7') can be restated as (70°80.6' - 69°59.7'). 70°-69°=1°, and 80.6'-59.7'= 20.9', so our answer is 1°20.9'
#6
GHA hours is 183°58.8' + GHA min/sec 12°45.0' = GHA 196°43.8'
You are in East longitude, so DR Lon 163°16'E becomes aLon = 163°16.2' + GHA 196°43.8' = LHA 360°00.0' (000°00.0')
Note that because this is a noon sight, the LHA will always be 000°/360°, by definition, which is a good way to check your arithmetic when working a problem this way.
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Bill Hayles
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posted February 03, 2026 10:35 AM
Hello and thankyou for a quick response. I am still confused on #3 and #4 but lets take number 6 first. I see that I made a mistake in my math for calculating GHA (minutes in particular). Thanks I get this one now.
For #3
If you read the text on page 67 Step 8 in the Sight Reduction process.... It states that if the degrees for Hc and Ho are not the same, write the larger of the two so that it has the same degrees as the smaller. That would make Ho 41d 46.5m and Hc 41d 00.2m making the a-value 46.3. Do you always subtract Hc from Ho or do you subtract the smaller number from the larger in all cases?
Same question for #5.... Ho is 71d 20.6m and Hc is 69d 59.7m. By the writeup in the book for Step 8, this makes Ho 69d 20.6m and Hc 69d 59.7m. This would make the a-value 39.1
Thanks so much for your patience on this one.
From: Brockport NY
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RobertR
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posted February 03, 2026 01:02 PM
Hello again! When we "write the larger of the two so that it has the same degrees as the smaller," we are re-stating the value of Hc or Ho in different terms in order to simplify our arithmetic, but we are not actually changing the value. So if we take 1° away from the "degrees," we must add 60' to the "minutes," and vice versa.
So for #5, our Ho is 71°20.6' and our Hc is 69°59.7', we must subtract the smaller from the larger to determine our Intercept.
To subtract 59.7' from 20.6' we need to borrow 1° (60') from the 71° column and add it to the Ho minutes. This gives us an Ho of 70°80.6' and an Hc of 69°59.7'. 80.6' - 59.7' = 20.9'
Then we subtract 69° from 70° to get 1°. Together, 1°20.9' is our difference between Ho and Hc. This is our Intercept, or "a-value."
Next, we must determine which direction to apply our intercept to our Assumed Position, along the line of the body's azimuth (Zn).
If our Ho is More than our Hc, our intercept is Toward the celestial body along our azimuth (HoMoTo). If our Hc (Computed) is Greater than our Ho, our intercept is Away from the celestial body along its azimuth (CGA, Computed Greater Away).
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RobertR
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posted February 03, 2026 01:12 PM
Problems # 5 and 7 here are somewhat unusual, in that the intercepts are larger than 1°. So in the case of #5 for example we don't really "write the larger of the two so that it has the same degrees as the smaller," as that would have given us an Ho of 69°140.6', which would have meant converting 60 of those minutes back into a whole degree. (Which is fine, but it adds two more steps, and two more opportunities to introduce a math error.)
The real point of carrying the degree over to the minutes column is just to keep our subtraction in the same units.
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Bill Hayles
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posted February 03, 2026 03:27 PM
Thank you that is very helpful. Is it safe to say that for computing the a-value that the smaller of the two values for Ho and Hc is subtracted from the larger?
From: Brockport NY
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RobertR
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posted February 03, 2026 03:41 PM
Yes, always.
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