THE IMPORTANCE OF MORNING AND EVENING STAR SIGHTS

Part 1 – Checking to see which stars and planets will be above the observer’s horizon during Nautical Twilight on a certain day. By Jack Case

INTRODUCTION

The Astronomical Position Line. A position line is a line drawn on a nautical chart along which a vessel’s position is known to lie. When a position line is derived from an observation of a celestial body, it is known as an astronomical position line.

The Observed Position. The position of a vessel can be established by the intersection of two or more position lines; such a position is known as a position fix. A position fix derived from astronomical position lines is known as an observed position and is marked on the chart as ‘Obs’.

Inaccuracy in Astronomical Position Lines Inaccuracy may be introduced into an astronomical position line by a number of contributory errors which are described here. For this reason, the accuracy of an observed position derived from only two astronomical position lines cannot be relied upon and therefore, it is generally accepted that at least three position lines are required in order to obtain an accurate fix.

Daylight Fixes. During the hours of daylight, we are mainly restricted to obtaining fixes from just one celestial body, the Sun. Sometimes, we can achieve a two point fix from the Sun and the Moon but mostly, all we can do is obtain two time-separated astronomical position lines using the Marcq St. Hilaire method to give us a two point fix.

Stars and Planets. There are 59 navigational stars and 4 navigational planets which we can use to achieve position fixes derived from three or more position lines but there are only two short periods during the day in which we can do this because we need it to be dark enough to see the bodies in the sky yet light enough to see the horizon.

Twilight Time. In general, the optimum conditions for taking observations of stars and planets occur during the times of civil twilight and nautical twilight when it is likely to be light enough for the horizon to be seen yet dark enough for those celestial bodies to be visible.

Civil Twilight. Morning civil twilight begins when the geometric centre of the Sun is 6^o below the horizon and ends at sunrise. Evening Civil Twilight begins at sunset and ends when the geometric centre of the Sun reaches 6^o below the horizon. During civil twilight, the horizon is clearly visible and the brightest stars as well as Venus, the brightest of the navigational planets, can be seen as long as they are above the horizon at that time.

Nautical twilight is the time when the centre of the Sun is between 6° and 12° below the horizon. Thus, Morning Nautical Twilight begins when the Sun rises to 12° below the horizon and ends when Morning Civil Twilight begins, that is when the Sun has risen to 6° below the horizon. Evening Nautical Twilight begins when Evening Civil Twilight ends, that is when the Sun has sunk to 6° below the horizon and ends when the Sun is 12° below the horizon . Nautical twilight is so named because it is when navigators are able to take reliable sights of stars and planets using a visible horizon for reference. During Nautical Twilight, the horizon is visible and most of the navigational stars and all of the navigational planets can be seen as long as they are above the horizon at that time.

How Do We Establish Which Stars/Planets Will Be Visible During Twilight? Unlike the Sun and the Moon which are easily identified, the approximate positions of stars and planets need to be established before observations can be made. The times of rising and setting of the Sun and Moon can be found in the daily pages of the Nautical Almanac so we know when they will be visible above the horizon. However, the risings and settings for stars and planets are not listed so we have to calculate these for ourselves.

The Stars. The stars are at such an immense distance from the Earth that the movement of their relative positions in the sky, which is so slow and so small, can be discounted without any great loss of accuracy and we can assume therefore, that they are in fixed positions in the celestial sphere. However, for the reasons explained in my articles ‘Stars for all Seasons’, the stars that we see in the night sky change from season to season and the ones that we do see, rise earlier each night.

The Planets. The planets in the solar system orbit the Sun in an anti-clockwise direction when viewed from the north pole of the celestial sphere. The apparent motions of the planets, when viewed from the Earth, are complicated by the facts that they are at varying distances from the Sun, have different orbital patterns, retrograde motions and orbital speeds. Only those planets that are sufficiently prominent to be observed with an ordinary sextant are considered to be ‘navigational planets’. These are: Venus, Mars, Jupiter and Saturn.

So what we need is a method that will enable us to calculate not only which of the navigational stars and planets will be above the celestial horizon during civil and nautical twilight but also what their approximate position in the sky will be during those times. There are various methods and devices that can be used for this purpose such as celestial navigation star-globes, star Identifiers, ABC tables and navigation software systems. However, my book ‘Astronomy For Astro Navigation’ describes my ‘Where To Look’ Method which is a simple ‘rule of thumb’ method of predicting which stars and planets will be visible during during civil and nautical twilight without the need to clutter the chart table with cumbersome globes, computers and large books of tables, some of which are quite expensive and complicated. The Where To Look Method, of which I claim ownership, is particularly advantageous in the close confines of a small-boat chart table and is cost-free.

The ‘Where To Look’ Method. The ‘Where To Look’ Method enables us to quickly and easily establish whether or not a particular star or planet will be above the celestial horizon during civil and nautical twilight and if it is, what it’s approximate position in the sky will be. It is emphasised that this is not intended to be a method of accurately pin-pointing the position of a celestial body; it is just a method of locating it so that we can begin the process of using it to calculate an astronomical position line.

Before proceeding with the explanation, I would like to say that Although it will take many words to explain this method thoroughly, it is something which, once fully understood, can be put into practice quickly and easily with just a little mental arithmetic and logic.

Planning which stars and planets will be above the celestial horizon during civil and nautical twilight . We should remember that unlike the navigational planets which will be in the sky at some point during a 24 hour period, the stars that we can see will change from season to season because of revolution as explained in ‘Stars For All Seasons Part 1’. We should also remember that even those stars that are ‘in season’ will not necessarily be visible during Nautical Twilight because of reasons of rotation which is also explain in ‘Stars For All Seasons Part 1’. By studying all seven of ‘Stars For All Seasons’ articles you will come to know which stars will be available for your star sights throughout the year.

Method. Firstly, in the Nautical Almanac, look up the time of nautical twilight for your latitude. To find out if a star or planet will be above the celestial horizon at your position during nautical twilight, you need to take two things into account, its local hour angle and its declination.

Local Hour Angle (LHA). For a star or planet to be visible, its geographical position must be within 90^o east or west of our estimated longitude at the time of the planned observations. If a celestial body’s LHA is greater than 0^o but less than 90^o , then the body will be above the celestial horizon to the west of the observer’s longitude. If a body’s LHA is greater than 270^o but less than 360^o then 360^o – LHA will be less than 90^o and the body will be above the celestial horizon to the east of the observer’s longitude.

We can formulate the above statements as follows:

Body is above horizon to the west if: LHA = 0^o to 90^o.

Body is above horizon to the east if: LHA = 270^o to 360^o

or 360^o – LHA = 0^o to 90^o

We can demonstrate what has been discussed above with the aid of the following diagram.

In the diagram, Point O is the position of an observer on the Earth’s surface at latitude 50^oN.

NS is the meridian of the observer and in terms of LHA is 0^o.

WE is the celestial equator.

The limits of the observer’s western and eastern horizons are at LHA 90^o and LHA 270^o which are both 90^o from the observer’s meridian.

Suppose that point A in the diagram represents the position of a celestial body whose LHA is 40^o and that point B represents the position of another celestial body whose LHA is 295^o. Since the LHAs of these bodies is either less than 90^o or between 270^o and 360^o, they will be visible above the celestial horizon to the west and the east respectively.

Bodies whose LHAs are greater than 90^o but less than 270^o would be below the celestial horizon and therefore would not be visible.

The articles ‘Stars For All Seasons’ on this site will give help in establishing which navigational stars will be visible above the horizon during Nautical Twilight at certain times of the year. Chapter 5 of my book ‘Astronomy For Astro Navigation’ will give more detailed help of the same topic.

How To Calculate The LHA Of A Star. The LHA of stars is not listed in the Nautical Almanac so we must calculate this ourselves. The following method can be used.

From the nautical almanac daily pages, find the Greenwich Hour Angle (GHA) of Aries (to the nearest degree) at the planned time of the observation.
From the ‘Index to Selected Stars’ in the Nautical Almanac, find the Sidereal Hour Angle (SHA) of the chosen star to the nearest degree.
Calculate your estimated longitude (to the nearest degree) at the planned time of the observation.
Combine the SHA, GHA Aries and the estimated longitude to find the approximate LHA.

Example. Using the following scenario, calculate LHA of Arcturus.

Scenario:

Date and Time: 30 May 2017, 21^h 00^m(+3)

Assumed Latitude and Longitude: 45^oN, 47^o30’W

Sunset: 19^h 37^{m (from Nautical Almanac)}

Civil twilight: 20^h 13^{m (from Nautical Almanac)}

Naut. twilight: 21^h 00^{m (from Nautical Almanac)}

Chosen Star: Arcturus (‘Stars For All Seasons Part 7’ tells us that this star will be visible during nautical twilight on 30 May).

SHA of Arcturus: 146^o, Declination Arcturus: N19^{o (from Nautical Almanac)}

To Calculate LHA of Star Arcturus

SHA Arcturus: 146^o

GHA Aries : 203^o33’.6

SHA + GHA: 349^o33’.6

Assumed Long: -47^o30’ (w) (subtract if long is west, add if long is east)

LHA Arcturus: 302^o03’

Since LHA is greater than 270^o but less than 360^o, Arcturus will be above the horizon to the east of the observer’s position. (i.e. 360^o– 302^o03’ = 57^o57’ so we can conclude that the meridian of the GP of Arcturus will be 57^o57’ to the east of the observer’s longitude during nautical twilight).

Declination. We have discussed how we ascertain, from a celestial body’s LHA, whether or not it will be above the celestial horizon to the west or the east of the observer’s position. We also need to discuss how we can ascertain from the body’s declination whether or not it will be above the horizon to the north or south of the observer’s position. To be visible above the horizon to the north or south, a celestial body’s declination must be within 90^o of the latitude of the observer’s position. If the latitude is north, then the declination must be within the range 90^o north to (90^o – latitude) south. If the latitude is south, then the declination must be within the range 90^o south to (90^o – latitude) north. We can formulate the above statements as follows:

Latitude North: visible range = 90^oN to (90^o – Lat)S.

Latitude South: visible range = 90^oS to (90^o – Lat)N.

Returning to the example above, given that the declination of Arcturus is 19^oN we can calculate whether or not it will be above the horizon to either the north or south of the observer’s position as follows:

The latitude of the observer = 45^oN so by the rules stated above, the visible range of celestial bodies from the observer’s position will be 90^oN to 45^oS. Furthermore, since the declination of Arcturus is 19^oN, we can conclude that the latitude of its GP will be 26^o to the south of the observer’s latitude during nautical twilight.

Conclusion. Arcturus will be visible above the observer’s horizon to east and south of his position during nautical twilight.

Planets. The procedure for calculating whether or not a planet will be above the horizon during civil and nautical twilight is the same as that for stars except for one thing. Whereas the Nautical Almanac does not list the GHA for stars, it does for planets, so for this reason, the procedure is made simpler as shown below:

GHA Mars : 117^o04′

Assumed Long: -47^o30’ (w) (subtract if long is west, add if long is east)

LHA Mars : 69^o34’ (i.e. visible above the horizon to the west)

Calculating Approximate Altitude And Azimuth. It is all very well knowing whether or not a particular star or planet will be above the horizon during nautical and civil twilight but if we intend to use it to calculate an astronomical position line, we also need to know where to look for it in the sky; that is, we need to know its approximate azimuth and altitude. We will discuss this problem in part 2 of this series.