HND Nautical Science / BSC Navigation Obtaining Hour Angles and Declinations from the Nautical AlmanacThe Greenwich Hour Angle and Declination of any heavenly body, used in astro-navigation, can be found using the Nautical Almanac. The GHA and Dec of all the major navigational bodies are given in the Almanac for each whole hour of Greenwich Mean Time, for every day, throughout the year. In the case of stars, the Almanac gives the Sidereal Hour Angle and Declination of the star, however the Greenwich Hour Angle of Aries is tabulated for every hour. It is then a simple process to convert these to quantities into Greenwich Hour Angle of the star. At sea it is not practicable to take observation where the GMT is always a whole hour in value. Therefore we must be able to calculate the GHA and DEC for any time GMT. This is achieved by using the increment tables at the back of the Almanac. These tables have been devised to allow an observer to calculate how much in excess, of a tabulated hourly value, the actual GHA and Dec will have changed by. The increment tables are based on computed rates of change of Hour Angle of the various bodies used in navigation. We have already seen that the Sun is defined as having a rate of change of Hour Angle (HA) of exactly 15 degrees per hour. The First Point of Aries is defined as having a rate of change of HA of 15 o 02.5’ per hour. From the classroom we have discovered why this must be the case. The actual rate for the sun is not exactly 15o per hour, due to the eccentricity of the earth’s orbit, however any slight variations due to this are included in the tabulated hourly values of the Sun’s GHA. This has little effect when we are dealing with the accuracy obtainable using celestial observations. The planets and the moon are slightly different. All of these objects move along roughly the same path as the sun (ecliptic) but move at differing rates on a day to day basis or in the case of the moon on an hourly basis. The table below gives the actual variation in rates of change of HA for each body SUN ARIES VENUS MARS JUPITER SATURN MOON 15o per hour (assumed constant) 15o 02.5’ per hour (assumed constant) 14o 59.0 to 15o 05.0’ per hour 15o 00.0’ to 15o 03.4’ per hour 15o 02.0’ to 15o 03.4’ per hour 15o 02.0’ to 15o 03.4’ per hour 14o 19.0’ to 14o 37.0’ per hour v/d Correction BSc ASTRO DGR 2001 0’ 03. This is because the moon is the closest object to the earth and as such moves across the celestial sphere very rapidly. v/d Correction BSc ASTRO DGR 2001 . Therefore the “v” correction for mars will be = 15o 03.0’ is the slowest rate of Change of HA that the Moon can ever have.g the planet Mars has an hourly rate of change of 15 03. given above. Note except for the planet Venus the “v” correction is always added to the GHA of the body. the vast majority of which would be devoted to increment tables. however this would entail a much larger almanac. and is valid for the three days that particular page covers. In the case of the planets the “v” correction is simply the excess of the planets actual hourly rate of change of HA over that of the assumed value of the suns hourly rate of change. we can use the increment tables for the sun and apply the “v” correction as an additional correction. The Moon can only move faster than this lowest value depending on its changing distance from the earth.The “v” Correction It would be possible to create tables which would give the actual hourly rates of change for each of the planets and moon. In the case of the moon the values of “v” are given for each hour of GMT. e. The Moons increment tables are not based on the sun at all. In order to overcome these problems the “v” correction is used. (or if we are not looking at a whole hour of GMT then a pro rata proportion of the “v” correction must be applied.4’ 15o 00. Venus can either have an additive or negative “v” correction depending on the time of year.4’ per hour. due to its distance from the earth. The assumed hourly value of 14o 19. This ca be found at the bottom of the daily pages for each of the planets. The difference between the base value. It makes one complete revolution with respect to Aries in a period of some 27. in the case of a planet. The case of the Moon is slightly different.3 days.4’ Provided we always remember to allow for this small difference then. and the actual value is then tabulated as the “v” correction of the Moon. If the “v” correction for Venus is to be subtracted then it will appear at the bottom of the daily pages as a negative value. 5) Dec(obs) = = = 21o 02. The value of “d” given at the bottom of the respective tables indicates how much the declination of these bodies changes in one hour. When apply the “d” correction you should always look at the declination value for the following hour of GMT in the tables as this will show whether you need to add or subtract the correction. In the same way as the “v” correction must be taken on a pro rata basis for increments of time which are less than a whole hour.The “d” Correction You should also note that the Sun.3’ S o 21 02.0’ 6. depending on whether the declination is increasing or decreasing. unlike the stars whose declination to intents and purposes can be considered as fixed.5’N 0.4’ Dec (14h) (d = 0. Calculate the GHA and Declination of the Sun at 14h 32m 16s GMT on the 18th July 1995 GHA (14h) Inc (32m 16s) (v= ) GHA (obs) = = = = 28o 27. The “d” correction may be added or subtracted. tabulated alongside the hourly values of declination. or in the case of the Moon.2’N Calculate the GHA and Declination of the Moon at 07h 29m 12s GMT on the 8th March 1995 GHA (07h) = Inc (29m 12s) = ( v = 12. as the “v” and “d” corrections are usually fairly small.9’ Dec (07h) (d = 2. These tables have been constructed to allow the navigator to obtain the pro rata value of the “v” and “d” correction for the number minutes of each hour. Moon and planets all move along a path on or close to the ecliptic. so the “d” correction must be applied the same way. therefore the declination of these objects is continually changing.3 ) = GHA (obs) = 207o 01.4’N 18o 44.0’ o 214 05.0 N/A 26o 31. Aries and the Moon for every second of every hour. Moon and planets also have a “d” correction tabulated at the bottom of the page. There are also a set of tables which are labeled “v”/”d” tables.9’ 6o 58.7’N v/d Correction BSc ASTRO DGR 2001 .9) Dec(obs) = = = 18o 43. the incremental values of change of GHA are given for the Sun and Planets. Examples of each type of calculation are given below. In the increment tables at the back of the almanac.4’ 8o 04.3’N 1. The Sun. There is no need to worry about seconds. 3’ 158o 45.6’ 360o 00.7’S 0.0) Dec(obs) = = = 21o 00.0’ 0.7’S Calculate the GHA and Declination of SPICA at 02h 39m 58s GMT on the 29th May 1995 GHA γ(02h) Inc (39m 58s) (v= ) GHAγ (obs) SHA * GHA *(obs) .1’ 4o 58.6 )= GHA (obs) = 207o 55.0.1’ N/A 286o 09.4’S N/A o 11 08.8’ Dec (17h) (d = 0.2’ 10o 01.5’ 12o 30.0’ 84o 54.6’ Dec (02h) (d = ) Dec(obs) = = = 11o 08. It also contains worked examples similar to those above.2 ) GHA (obs) = = = = 110o 35.360o GHA *(obs) = = = = = = = = 276o 08.1) Dec(obs) = = = 05o 33.3’ 4440 54.7’S 0.4’S Note: All students would be well advised to look at pages 255 and 256 in the explanation section of the Nautical Almanac as these pages contain an explanation of the “v” and “d” corrections which would be suitable for an examination answer. v/d Correction BSc ASTRO DGR 2001 .0 21o 00.0N 05o 33.7’ o 115 33.7’S Calculate the GHA and Declination of Saturn at 17h 19m 52s GMT on the 19th April 1995 GHA (17h) Inc (19m 52s) ( v = 2.5’ -0.5’ 220o 25.Calculate the GHA and Declination of Venus at 23h 50m 02s GMT on the 11th February 1995 GHA (23h) = Inc (50m 02s) = ( v = .5’ Dec (23h) (d = 0.