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V And D Correction

Outlines v and d correction in Nautical Almanac

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HND Nautical Science / BSC Navigation Obtaining Hour Angles and Declinations from the Nautical Almanac The 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 the Alma Almana nacc give givess the the Side Sidere real al Hour Hour Angl Anglee and and Decl Declin inat atio ion n of the the star, star, howe howeve verr the 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 15 o 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 v/d Correction 15o per hour (assumed constant) 15o 02.5’ per hour (assumed constant) 14o 59.0 to 15 o 05.0’ per hour  15o 00.0’ to 15 o 03.4’ per hour  15o 02.0’ to 15 o 03.4’ per hour  15o 02.0’ to 15 o 03.4’ per hour  14o 19.0’ to 14 o 37.0’ per hour  BSc ASTRO DGR 2001 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, however this would entail a much larger almanac, the vast majority of which would be devoted to increment tables. In order to overcome these problems the “v” correction is used. This ca be found at the  bottom of the daily pages for each of the planets, and is valid for the three days that particular   page covers. In the case of the moon the values of “v” are given for each hour of GMT. This is because the moon is the closest object to the earth and as such moves across the celestial sphere very rapidly. It makes one complete revolution with respect to Aries in a  period of some 27.3 days. 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. e.g the planet Mars has an hourly rate of change of 15 03.4’ per hour. - 15o 03.4’ 15o 00.0’ = 03.4’ Therefore the “v” correction for mars will be Provided we always remember to allow for this small difference then, in the case of a planet, we can use the increment tables for the sun and apply the “v” correction as an additional correction. (or if we are not looking at a whole hour of GMT then a pro rata proportion of the “v” correction must be applied. The case of the Moon is slightly different. The Moons increment tables are not based on the sun at all. The assumed hourly value of 14 o 19.0’ is the slowest rate of Change of HA that the Moon can ever have, due to its distance from the earth. The Moon can only move faster than this lowest value depending on its changing distance from the earth. The difference between the base value, given above, and the actual value is then tabulated as the “v” correction of the Moon.  Note except for the planet Venus the “v” correction is always added to the GHA of the body. Venus can either have an additive or negative “v” correction depending on the time of year. 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. v/d Correction BSc ASTRO DGR 2001 The “d” Correction You should also note that the Sun, Moon and planets also have a “d” correction tabulated at the bottom of the page, or in the case of the Moon, tabulated alongside the hourly values of  declination. The Sun, Moon and planets all move along a path on or close to the ecliptic, therefore the declination of these objects is continually changing, unlike the stars whose declination to intents and purposes can be considered as fixed. The value of “d” given at the bottom of the respective tables indicates how much the declination of these bodies changes in one hour. The “d” correction may be added or  subtracted, depending on whether the declination is increasing or decreasing. 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, so the “d” correction must be applied the same way. In the increment tables at the back of the almanac, the incremental values of change of GHA are given for the Sun and Planets, Aries and the Moon for every second of every hour. There are also a set of tables which are labeled “v”/”d” tables. 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. There is no need to worry about seconds, as the “v” and “d” corrections are usually fairly small. Examples of each type of calculation are given below. Calculate the GHA and Declination of the Sun at 14h 32m 16s GMT on the 18 th July 1995 GHA (14h) Inc (32m 16s) (v= ) GHA (obs) = = = = 28o 27.4’ 8o 04.0 N/A 26o 31.4’ Dec (14h) (d = 0.5) Dec(obs) = = = 21o 02.5’N 0.3’ S o 21 02.2’N Calculate the GHA and Declination of the Moon at 07h 29m 12s GMT on the 8 th March 1995 GHA (07h) = Inc (29m 12s) = ( v = 12.3 )= GHA (obs) = v/d Correction 207o 01.9’ 6o 58.0’ 6.0’ o 214 05.9’ Dec (07h) (d = 2.9) Dec(obs) BSc ASTRO = = = 18o 43.3’N 1.4’N o 18 44.7’N DGR 2001 Calculate the GHA and Declination of  Venus at 23h 50m 02s GMT on the 11 th February 1995 GHA (23h) = Inc (50m 02s) = ( v = - 0.6 )= GHA (obs) = 207o 55.5’ 12o 30.5’ -0.5’ o 220 25.5’ Dec (23h) (d = 0.0) Dec(obs) = = = 21o 00.7’S 0.0 o 21 00.7’S Calculate the GHA and Declination of  Saturn at 17h 19m 52s GMT on the 19 th April 1995 GHA (17h) Inc (19m 52s) ( v = 2.2 ) GHA (obs) = = = = 110o 35.1’ 4o 58.0’ 0.7’ o 115 33.8’ Dec (17h) (d = 0.1) Dec(obs) = = = 05o 33.7’S 0.0N o 05 33.7’S Calculate the GHA and Declination of  SPICA at 02h 39m 58s GMT on the 29 th May 1995 GHA γ (02h) Inc (39m 58s) (v= ) GHAγ  (obs) SHA * GHA *(obs) - 360o GHA *(obs) = = = = = = = = 276o 08.2’ 10o 01.1’ N/A 286o 09.3’ 158o 45.3’ 4440 54.6’ 360o 00.0’ 84o 54.6’ Dec (02h) (d = ) Dec(obs) = = = 11o 08.4’S N/A o 11 08.4’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. It also contains worked examples similar to those above. v/d Correction BSc ASTRO DGR 2001