Math Problem Statement

Calculate the azimuth of Sirius based on the provided navigation data and time conversions.

Solution

The task involves calculating the azimuth using the provided navigation data. Let's break down the given information to process it:

Provided Information:

  1. Date: Thursday, 14 April 2016
  2. Celestial Body: Sirius
  3. BT (Board Time): 22:15
    • BT Relation: BT = GMT + 6 hours
    • GMT = 16:15
  4. Analog Clock Time: 04:16:21 (need to interpret this in terms of GMT or BT alignment).
  5. DR (Dead Reckoning Position): 1914.2N19^\circ 14.2' \, \text{N}, 08802.3E088^\circ 02.3' \, \text{E}
  6. GP (Geographical Position of Sirius): 2490.5249^\circ 0.5'
  7. GK (Course Compass): 1510151^\circ 0'
  8. KK (Compass Course): 1530153^\circ 0'
  9. VlogV_{\text{log}} (Speed): 13.0 knots
  10. Variation: 714W7^\circ 14' \, \text{W}
  11. Deviation: 30W3^\circ 0' \, \text{W}

Steps to Solve:

The azimuth calculation generally involves:

  1. Converting the time accurately to GMT for the calculation of celestial positions.
  2. Determining the Local Hour Angle (LHA) using the observer's longitude and the Greenwich Hour Angle (GHA) of the celestial body.
  3. Calculating the azimuth using navigational formulas, such as: tanZ=sinLHAcosLHAsinlatitudetandeclinationcoslatitude\tan Z = \frac{\sin LHA}{\cos LHA \cdot \sin \text{latitude} - \tan \text{declination} \cdot \cos \text{latitude}}

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Math Problem Analysis

Mathematical Concepts

Celestial Navigation
Time Conversions
Trigonometry
Local Hour Angle (LHA)
Azimuth Calculation

Formulas

BT = GMT + 6 hours
LHA = GHA + Longitude (East positive, West negative)
tan Z = sin(LHA) / [cos(LHA) * sin(Latitude) - tan(Declination) * cos(Latitude)]

Theorems

Spherical Trigonometry

Suitable Grade Level

University-Level Navigation Studies or Advanced High School