Rising, Setting and Twilight

Transcription

1 Rising, Setting and Twilight The rotation of e ear on its own axis causes e phenoenon of e rising and setting of all celestial bodies. Generally, e celestial bodies see to appear at e eastern horizon, cross e sky and en disappear to e western horizon. However, soe bodies are always visible above e horizon or always visible below e horizon, depending on e latitude of e observer and e declination of e celestial body. The body at is always visible above e horizon is called circupolar; in is case, e body is in e lower eridian and e zeni distance of e body is less an 90 (body A). A heavenly body is always invisible if it never rises above e horizon when its zeni distance is greater an 90 at e instant of upper eridian passage (body B). Tie of Rising and Setting In navigation, rising or setting is when e upper lib of e body is on e visible horizon. The tie of sunrise and sunset is given on e right-hand side of e right-hand page in e daily pages of e Nautical Alanac. The figure is e Local Mean Tie (LMT) for e iddle day of e ree days on each page. In e low and oderate latitudes, e daily change of e tie of sunrise or sunset is very little over ree days, so e tie of iddle day can be used for oer dates on e sae page wiout interpolation. In e high latitudes, interpolation ay be necessary for ore accuracy. In order to obtain UT, apply e longitude in tie to LMT as follows: + West Longitude UT = LMT East Longitude

2 Procedure for finding ties of sunrise and sunset 1. Fro e daily page of e Nautical Alanac, extract e LMT for e latitude, which is e next nueral saller an e 2. Extract e LMT for e latitude, which is e next nueral higher an e 3. Calculate e difference between e above LMTs, and use Table I in e back of e Nautical Alanac to obtain e correction for 4. Apply e above latitude correction (3) to e LMT in (1) to obtain e LMT for e 5. Apply e longitude in tie to e LMT (4) to obtain UT. Exaple 1 Find UT of sunrise and sunset on 18 of July 2008 for latitude N and longitude W: Sunrise Sunset LMT (45 N) d h d h LMT (50 N) difference 20 d h d h Latitude LMT (47 28 N, Longgitude in tie ( UT (47 28 N, d h d h h h d h d h Exaple 2 Find UT of sunrise and sunset on 24 of October 2008 for latitude S and longitude E: Sunrise Sunset LMT (50 S) d h d h LMT (52 S) d h d h difference 5 5 Latitude S correction (table I) LMT (50 43 S, Longgitude in tie ( UT (50 43 S, d h d h h h d h d h In e exaple above, e tie of sunrise and sunset of 24 of October uses e sae table as 25 and 26 of October, where 25 is e iddle day. Basically, e inforation obtained fro e table is at of 25 of October. There is only a slight change in LMT

3 between each day, so interpolation is unnecessary. Generally, in e low latitudes, e ties of setting and rising of e sun change very slightly over ree days, so interpolation can be oitted. Finding e tie of oonrise and oonset is siilar to finding e tie of sunrise and sunset, but ore coplicated due to e rapid change of GHA and e declination of e oon at an irregular rate. Therefore, e ean ties of rising and setting at e Greenwich Meridian cannot be considered as e LMT for any oer eridians, as in e case of e sun; hence, e extra correction in longitude is needed. Thus, e tie of oonrise and oonset are given in e Nautical Alanac in daily basic; en, if in east longitude, interpolation is needed wi e preceding day, and if in west longitude, interpolation is needed wi e following day. For convenience, e ties of oonrise and oonset of e day following e last day in e period are also given. Procedure for finding ties of Moonrise and Moonset 1. Fro e daily page of Nautical Alanac, extract e LMT for e latitude next saller an e 2. Extract e LMT for e latitude next higher an e observer s latitude; 3. Calculate e difference between above LMTs and use table I at e back of e Nautical Alanac, to obtain e correction for 4. Repeat steps 1, 2 and 3 for e day following e given date, if in west longitude; or for e day preceding, if in east longitude. 5. Calculate e difference between ese two days and use table II also at e back of e Nautical Alanac, to obtain e correction for observer s longitude, or by e following forula: longitude Longitude Correction = Daily difference Apply longitude in tie to LMT to obtain UT.

4 Exaple 3 Find UT of oonrise on 18 of July 2008 for latitude N and longitude E: LMT (40 N) LMT (45 N) difference Latitude difference (17 and 18 ) Longitude E correction (table II) LMT (42 42 N, Longgitude in tie ( Proceeding Moonrise Day d h d h d h d h d h d h UT (42 42 N, d h h 7 23 d h Exaple 4 Find UT of oonset on 26 of October 2008 for latitude S and longitude W: LMT (20 S) LMT (30 S) difference between 20 S and 30 S Latitude S correction (table I) difference (26 and 27 ) Longitude W correction (table II) + 12 LMT (20 56 S, h Longgitude in tie ( UT (20 56 S, Following Moonset Day d h d h d h d h d h d h 53 d h d h + + Twilight Twilight is e period of incoplete darkness before sunrise and after e sunset. So e orning twilight ends at sunrise, when e upper lib of e sun just appears above e visible horizon, and evening twilight starts at sunset, when e upper lib of e sun just disappears below e visible horizon. The period of twilight is very iportant to e navigator, because in is period e visible horizon can still be seen and e celestial bodies on e sky are bright enough to be observed by e sextant. There are ree stages of twilight: 1. Civil twilight is e interval of tie between visible sunrise or sunset and e tie when e centre of e sun is 6 below e rational horizon.

5 2. Nautical twilight is e interval of tie between visible sunrise or sunset and e tie when e centre of e sun is 12 below e rational horizon. 3. Astronoical twilight is e interval of tie between visible sunrise or sunset and e tie when e centre of e sun is 18 below rational horizon. The twilight period is longer in higher latitudes an in lower latitudes. The period of astronoical twilight is e liit of e full darkness; it is too dark for observation, so only civil twilight and nautical twilight periods are considered for navigational purposes. The procedure to find e twilight is sae as finding e sunrise and sunset. Exaple 5 Find UT of e orning twilight on 17 April 2008 for position N, W: Nautical Civil LMT (35 N) d h d h LMT (40 N) difference 10 d h d h Latitude LMT (38 45 N, Longgitude in tie ( UT (38 45 N, d h d h h h d h d h In e exaple above, siilarly to finding e tie of sunrise and sunset, e tie of twilight of 17 April uses e sae table as 15 and 16 April, where 16 April is e iddle day. Basically, e inforation obtained fro e table is at of 16 April. There is only a slight change in LMT, so interpolation is unnecessary. Generally, in e low latitudes, e ties of setting and rising change very slightly over ree days, so interpolation can be oitted.