Question

Calculate the Sun’s hour angle for an observer in longitude 103◦ 40` W, keeping the mean solar time of zone +7, who has made an observation of the Sun at approximate zone time 16h 30m, June 1st. The chronometer time was 23h 31m 20s, the chronometer error being 1m 10s slow on GMT. The ephemeris transit of the Sun for June 1st was 11h 57m 41s (taken from The Astronomical Almanac).

Answer 1

Answer on Question #54954, Physics / Astronomy | Astrophysics

By equation :

$$\mathrm {G H A} _ {\odot} = \mathrm {G H A M S} + 1 2 ^ {\mathrm {h}} - \text {E p h e m e r i s t r a n s i t}.$$

Hence,

$$\mathrm {G H A} _ {\odot} = \mathrm {G H A M S} + 2 ^ {\mathrm {m}} 1 9 ^ {\mathrm {s}} (\mathrm {A})$$

We proceed by setting up the following scheme:

In the second last line, the longitude has been converted, thus:

$$1 0 3 {}^ {\circ} 4 0 ^ {\prime} = 6 \times 1 5 {}^ {\circ} + 1 3 {}^ {\circ} + 4 0 ^ {\prime} = 6 ^ {\mathrm {h}} + 5 2 ^ {\mathrm {m}} + 1 6 0 ^ {\mathrm {s}} = 6 ^ {\mathrm {h}} 5 4 ^ {\mathrm {m}} 4 0 ^ {\mathrm {s}}.$$

Answer: $6^{\mathrm{h}}54^{\mathrm{m}}40^{\mathrm{s}}$

http://www.AssignmentExpert.com/