1 Homework Q & A Junior Navigation Chapter 5 Celestial Coordinates

2 Objectives: ■ Define declination, hour circle, Greenwich hour angle (GHA), and local hour angle (LHA). ■ Understand how the geographical position (GP) of a body is located by celestial coordinates, and the relationships among hour angles. ■ Calculate LHA and declination from Nautical Almanac data

3 Practical Exercises: Problem 1. Follow the Student Manual for guidance

4 2. Greenwich hour angle (GHA) is: a. the arc distance, measured in an easterly direction, from the observer's meridian to the hour circle of a GP. b. the arc distance, measured in a westerly direction, from the Greenwich meridian to the hour circle of a GP. c. the arc distance, measured in a westerly direction, from the observer's meridian to the Greenwich meridian. d. the arc distance, measured in an easterly direction, from the Greenwich meridian to the observer's meridian. Ref: ¶ 8, 9

5 L = 15°19'N Latitude of the GP of a body is equal to the declination of the body. Dec = 15°19'N; therefore L of GP = 15°19'N. Lo = 16° 19'E If GHA of a body is greater than 180°, longitude of the GP of the body is equal to 360° - GHA of the body, and the GP is in east longitude. Longitude of GP = 360° - 343°41' =16°19'E. Ref: ¶ The declination of the sun is 15°19'N. Its GHA is 343°41'. What are the latitude and longitude of the GP of the sun? Ans:

6 4. Fill in the blanks: a.GHA is measured from ___________________ to _________________. b. Dec is measured from ___________________ to _________________. Greenwich meridian hour circle of GP the equator the GP of the body c. LHA is measured from ___________________ to _________________. c. LHA is measured from ______________________ ____________ ___________________. the local meridian of the observer to hour circle of the GP Ref: ¶ 8, 12 & 13

7 5. Declination is measured: a. south from the north pole and north from the south pole. b. from the pole of the hemisphere in which the observer is located. c. north or south from the equator. d. north or south from the observer's parallel of latitude. Ref: ¶ 12

8 6. LHA is measured: a. from the upper branch of the observer's meridian eastward to the hour circle of the celestial body. b. from the upper branch of the observer's meridian westward to the hour circle of the celestial body. c. from the hour circle of the celestial body eastward to the Greenwich meridian. d. from the hour circle of the celestial body westward to the Greenwich meridian. Ref: ¶ 13

9 7. Fill in the blanks: a. GHA sun + _____ = LHA sun. b. GHA sun - _____ = LHA sun LoE LoW Ref: ¶ 20

10 8. Given: Lo 150°E; ZT 0600; GHA sun is 120°. Find: UT and LHA of the sun. UT = 2000 previous day Solution: Compute ZD = Lo divided by 15 and rounded. ZD = Lo 150° / 15° = 10. Since Lo is E, the ZD is negative, ZD = -10 Compute UT: ZT 0600 ZD -10 UT hr - 1 day UT 2000 previous day Ref: ¶ LHA sun = 270° Solution: GHA computation: Since the mean sun will be over Greenwich at 1200 UT, GHA at 1200 will be 000°. At UT 2000, it's 8 hours later and the sun will have moved 8 hr x 15°/hr making the GHA 120°. GHA Sun 120° Lo E +150° LHA Sun 270°

11 9. Given: UT 2300, 29 Mar; Lo 115°30'E; GHA sun 163°50.8'. a. Find: ZT and date. Solution: Compute ZD: ZD = Lo 115°30.0' / 15 = 7.70, which rounds to 8. Lo is east so ZD is negative. ZD = - 8. Compute ZT: UT 2300 ZD - 8 (rev) ZT Mar - 24 hr + 1 day ZT Mar Mar 279° 20.8' Ref: ¶ GHA Sun 163°50.8' Lo E + 115°30.0' LHA Sun 279°20.8' b. Find the LHA of the sun.

The sun is directly overhead at your position. You note the time, and look up in your Nautical Almanac for this date and time that the GHA of the sun is 75° and its declination is 21° N. What do you know about your position? Ans: Since the sun is directly overhead, you are at the GP of the sun; your position is L 21° N, Lo 75° W Ref: ¶

13Q7 End Of Homework Q & A Junior Navigation Chapter 5 Celestial Coordinates