Wednesday, February 27, 2019

Star Names

For navigational purposes, stars have two naming conventions: proper names such as Canopus and a Greek letter designation called the Bayer system such as Alpha Carinae, meaning the alpha star of the constellation Carina. The alpha star means most dominate, or if all are about the same brightness, the first one in a logical sequence of numbering, as in the Big Dipper, which goes alphabetically from Alpha Ursa Majoris (Dubhe) at tip of the cup to Eta Ursa Majoris (Alkaid) at the end of the handle. Officially the constellation name in this system is in the Latin genitive form (belonging to), but Alpha Ursa Major would be adequate for record keeping and communications.

Science fiction readers will likely know of Alpha Centauri, which navigators call by its proper name Rigil Kentaurus, because this is the nearest star to our solar system and perhaps an early one to visit or receive visitors from.

Figure 1. Sample of star names. The red labels have been added. Selected stars called navigational stars are assigned  unique numbers in the Almanac.

The USNO star chart above (from the support page of our cel nav text) shows how these names are used in the Almanac, sometimes using one name form and sometimes another. We see this also in the star charts from the Almanac, a sample of which is below.

Figure 2. Sample star chart from the Almanac.

Figure 3. Greek alphabet

Comparing the alphabet with Figure 1, see the points mentioned above. In Bootes, there is one dominant star and it is alpha, and the other letters are more or less random.  In the Big Dipper the stars are similar in prominence, so they are labeled sequentially along the figure. In Leo, the brighter Regulus  (magnitude 1.4) is alpha and Denebola (magnitude 2.1) is beta. The brightness of stars is specified in terms of magnitude (see Brightness of Stars and Planets.)  All magnitude-1 stars  and most magnitude-2 stars have proper names. Less bright stars typically do not.

Note on Constellations
We often think of constellations as groups of stars, but that is not the full picture. The full sky is divided up into sections with straight boundaries (SHA and Dec), much as a state is divided up into counties.  The full globe of the sky is divided into 88 constellations, which means that every point in the sky is in a constellation, even if there are no stars near it.  If you look up any constellation in the wiki it will include a nice vector image of the constellation boundaries. A sample is shown below.

Figure 3a. Outline of the constellation Ursa Major (white area).  See these for any constellation
 in the wikipedia.

Navigational Stars
There is yet another classification of stars that is crucial to navigators. The 57 stars listed on the daily pages are called navigational stars. They are also on the Index to Selected Stars in the back of the Almanac (p. xxxiii). These are bright stars, magnitude 1 or 2, but they are not chosen by brightness alone, but rather selected uniformly around the sky so that several of them will be in view at all times from any location. Polaris is notably not on that list, though it is used routinely for navigation and certainly qualifies as a "navigational star."

Figure 4. Index to Selected Stars—the navigational stars. 

This list has been on page xxxiii  of the Almanac for many years, which is easy to remember, and it is also printed on the yellow cardstock bookmark that comes with the Almanac.  Listing the stars by number and alphabetically is a handy feature of this list.  Cel nav apps, including our own StarPilot, often use these star numbers for a quick way to select a star.

There are another 116 stars listed in the back of the Almanac that do not show up on the daily pages. That full list (174 stars) includes the navigational stars, and is presented in a unique manner, illustrated in Figure 4. The first half of the year (January to June) lists the stars by their Bayer designation ("Greek-letter name"), whereas from July to December they are listed by their proper names. This can be an important nuance to know when it comes to some star ID questions. All navigational stars have a proper name.

Figure 5. Sections of two facing pages of the star list at the back of the Almanac.

Here we learn, for example, that the brightest star in the sky, Sirius, is also known as Alpha Canis Majoris, the alpha dog in the Dog constellation. It has still another name—you guessed it: the Dog Star.

Stars in this list are sorted according to increasing SHA. If you know the star but not its SHA, check the star maps in the Almanac or the USNO version linked above, which plots star locations on a Declination-SHA grid.

This list provides more stars for navigation but it is very rare that we need one from this list. The navigational stars usually carry us across the ocean. Indeed, any ocean can typically be crossed using the same few stars with the aid of a planet or two.  See a real example in Hawaii by Sextant.

 How to Pronounce a Star's Name
My answer would be, just about however you want to.  These are often complex names; many evolved from the Arabic, although Arabic speaking persons might not recognize the present form of the word. Alnilam, Alioth, Altair, are examples, as is, by the way, Alcohol. In fact, many of the prominent stars have many names, or many spellings for the same name, although there is now an official list of names and spellings as of June, 2018.  You will see that most of these were only formalized in 2016 or 2017.

The wiki has good presentations of stars organized by constellations, which include detailed maps of the constellation. Standard pronunciation guides are complex, so here is a starting point for the navigation stars, plus a few others we use in the course.  There are more alternatives than I have listed here.

Name                Pronunciation
Acamar               AH-kuh-mar
Achernar             AK-er-nar
Acrux                A-krucks
Adhara               ad-HAR-a
Al Nair              all-NAYR
Aldebaran            al-DEB-ah ran
Alioth               AL-lee-oth
Alkaid               AL-kade
Alphecca             al-FECK-ah
Alpheratz            AL-fer-rats
Altair               AL-tair
Ankaa                ANG-kah
Antares              an-TAIR-ease
Arcturus             arc-TOUR-russ
Atria                AH-tree-a
Bellatrix            BEL-la-trix
Betelgeuse           BET-el-jooz
Canopus              can-OH-pus
Capella              kah-PELL-ah
Caph                 KAF
Castor               CASS-ter
Deneb                DEN-ebb
Denebola             de-NEB-oh-la
Dubhe                DOOB-huh
Elnath               EL-noth
Eltanin              EL-ta-nin
Enif                 EEN-if
Fomalhaut            FO-mal-oh or FOH-mal-owt
Gacrux               GAK-kruks
Gienah               JEEN-ah
Hadar                HAH-dahr
Hamal                HAM-al or hah-MAHL
Kaus Australis       KOWSS ow-STRAH-liss
Markab               MAR-kab
Megrez               meg-REZ or MEG-rez
Menkar               men-KAHR
Menkent              men-KENT
Merak                MER-ak
Miaplacidus          mee-a-PLASS-id-uss
Mintaka              MIN-ta-ka
Mirfak               MERE-fak
Mizar                MYE-zahr
Nunki                NUN-kee
Peacock              pea-COCK
Polaris              poe-LAIR-is or poe-LAHR-is
Pollux               POL-lucks
Procyon              PRO-see-on
Rasalhague           RAHS-al-haig
Regulus              REG-you-luss
Rigel                RYE-jel
Rigil Kentaurus      RYE-jel ken-TAW-russ
Sabik                SAH-bik
Saiph                SAFE
Scheat               SHEE-at
Schedar              SHED-er
Segin                SEG-in
Shaula               SHOWL-a
Sirius               SEER-ee-us
Skat                 SKAHT
Spica                SPEE-ka or SPY-ka
Suhail               soo-HALE
Vega                 VEY-ga or VEE-ga
Zubenelgenubi        zoo-BEN-el-je-NEW-bee

Zubeneschamali       zoo-BEN-ess-sha-MAH-lee

My suggestion is choose a way to say it and then whenever you do say it, say it bold and clear. Anyone hearing who might have thought it was done another way would then pause, and likely take your word for it. It would be difficult in many cases to argue what is right.

For more, the definitive study of star names is the classic Victorian text  Star Names Their Lore and Meaning by Richard Hinckley Allen, which is online, being a remarkable work of Bill Thayer, formerly of University of Chicago.  There are also tons of used print copies online for a dollar or two, being the Dover edition from the early 60s. We have a copy of that one which we scanned, OCRed, and cleaned up to make an ebook long before Bill Thayer's work and also long before Google got into the practice of scanning all books.

The best stargazing program for Mac or PC is the amazing free one called Stellarium. Has a short learning curve, but is a remarkable and beautiful tool.  You can read digital values of height and bearing for cel nav studies as well.

Saturday, February 23, 2019

Check Assumed Positions After Plotting Cel Nav Fix

A question about DR came up in our cel nav course that took us back to a couple basic points. One is the difference between manual cel nav solutions using tables and plotting sheets compared to doing sight reduction and position fixing with a computed solution using a computer or mobile app. We discuss most of these differences in our textbook, but realized today that one important difference is not stressed in the book, although it is covered in many places in our online course.

The issue at hand is evaluating a fix based on the dimensions of the plot itself. In other words, we look at the lengths of all the lines involved. There are two kinds of lines on the plot of a cel nav fix: the lines of positions (LOPs) themselves, and the lengths of the azimuth lines that run from the assumed positions to the LOPs (the a-values). A sample is shown in Figure 1.

Figure 1.  Crucial lengths defined.  If any of these are approaching 60 nmi long, we should use the fix for a new DR and redo the sight reduction.

The crucial lengths are the a-values, a1 and a2, as well as the lengths along the LOPs from the fix to the azimuth line (L1 and L2).  Chances of long lines is enhanced when the DR is about halfway between two whole latitudes, because we must choose one of these for the assumed latitude. 

We make the assumption in standard manual plotting procedure that the circle of equal altitude near our position can be approximated as a straight line (the LOP), and that the azimuth lines, which are segments of a great circle, can be approximated by a straight line as well.  Both of these approximations can break down if any of these lines gets too long.

Below is a new addition to textbook Section 11.24, followed by examples and background of this concern.

Evaluate Assumed Positions in Manual Sight Reductions

Before we start to evaluate a full set of sights for optimum accuracy, we should pause at the end of the sight reduction to check that our basic assumptions are in order for the sights at hand.  How we do this depends on how we are doing the sight reduction. If we are using a computer or nav app for sight reduction and position fixing,  this step can be skipped completely, because the location of the assumed position (AP) does not matter when computing a fix. With calculator solutions, we generally use our DR at the fix time as the basis of the computations, and even if the DR is way off, the programs will work around this either by solving for intersecting circles of position, or iterating lines of position (LOPs) automatically, as explained in the manual approach below. In any event the choice of AP is not a concern for computed solutions, but we must consider this when doing manual solutions using plotting.

When doing sight reduction by hand using tables and manual plotting, we must check that none of the lines leading to our plotted fix are too long. This can happen with manual sight reduction as we must choose an AP based on the minutes part of the GHA and our DR Lat and Lon. We can always choose the AP to be within 30' of the DR, but even then with various configurations of body bearings and APs, we can end up with large a-values. If the DR position was wrong by a lot, meaning the distance between the DR position and the fix found using the APs chosen properly for each sight, then the a-values can get even much larger.  In this case the distance between the fix and the azimuth line measured along the LOP can get large as well. The lines that can get too long are illustrated in Figure 1, above.

We might consider that any crucial line in our plotted fix that is over (or approaching) 60 nmi should be considered too long for best results, meaning they may violate our basic assumptions in the plotting. Underlying the manual plotting solution is the assumption that the LOP itself is a valid straight-line approximation to a segment of a circle of equal altitude (see textbook Section 10.6), and we assume that the azimuth line is a segment of a great circle, even though we are plotting it as a straight rhumb line. These approximations can break down when the lines get too long. The consequences of this also depends on the direction they are oriented, but a generic filter on the lengths should catch all cases.

The solution to long lines on the plot, is to plot the fix in the normal way, then read that Lat and Lon and call that the new DR for these sights.  Then do the sight reduction again using this DR, which will call for new APs, and then the lines will all be shorter, and the fix you get will be more accurate.

In most cases of routine cel nav—see Hawaii by Sextant for examples—we can proceed as normal, and will not find any excessively long lines, but if we do, we can fix it. On the other hand, if we suspect ahead of time that our DR could be wrong by over 40 miles or so, then we might do a quick 2-LOP fix to check the lines and find a new best DR to use before any further analysis.

The instructions to Pub 229 include a Table of Offsets for curving the LOPs to help with this correction. That table shows corrections of several miles for lines L1 or L2 of just 45 miles. Errors due to long a-values are more subtle and depend on the azimuths; they occur when a straight line approximation to the azimuth line diverges from the curved great circle tract between AP and GP.

In summary, any of the crucial lines in a fix plot approaching 60 nmi long should call for getting a new DR from the fix and redoing the sight reduction. Errors of several miles can occur without this precaution. Such errors are larger for high sights, above 70º or so, and line lengths can get enhanced when  DR Lat is about half way between two parallels.

More Background on this Topic

This section goes into more detail to look at how these errors actually come about and the sizes of them in a few examples.  At this point, you can say "I know the rule now, and I will use it as needed," and then skip this section!  

Below is a sample of the Pub 229 Table of Offsets and how it is used to make the corrections for curved LOPs.

Figure 2.  Table of Offsets from Pub 229 and their example of how they are used.

We see from the Table that for a sight that has Ho about 73º, an LOP line length (L1 or L2 in Figure 1) of 45 nmi (45') would cause an error of 1 nmi (1') on the LOP position.  At 60 nmi, the error would be much larger. All in all, it is likely faster to just get a new DR leading to shorter lines than to correct the individual LOPs this way, and with that in mind, we generally do not cover the use of the Offsets in our course.

Here is a way to approximate this correction if you might care to.

Figure 2a.  We see the 0.9' at 72º in the Pub 229 table, and then can estimate that at 100 nmi, the correction would be about 4.6'. ( To be redrawn when we can. )

Errors due to large a-values are a bit more subtle and there is no easy table for the correction. The situation is illustrated in the graphics below, starting with cel nav data from the USNO.

Figure 3. Cel Nav data from

The Mars and Markab sights are plotted below in OpenCPN, using a neat feature of that program that lets us plot a line segment as rhumb line or great circle, or both.

 Figure 4. Geographical positions (GP) of two bodies showing the great circle track to them from the assumed position (AP). 

Here we see an interesting example of spherical geometry.  From this AP at this time, we would actually be looking just north of west to see a star that is a long way south of us!  The direction we look to see a star is called its azimuth, 279.8 T to Markab in this example. This azimuth generated in the sight reduction process is numerically the same as the initial heading of a great circle (GC) track from the AP to the GP.  Below we expand the section near the AP.

Figure 5. Deviation of a rhumb line along the initial heading of a great circle track.

In the case of Markab, we would plot the azimuth line in direction 279.8, and then plot the LOP perpendicular to that line. However if the a-value is ~60 miles or so long, this line is some 4 nmi off the GC track as computed in OpenCPN. This, in itself, would not matter, but the offset will effectively rotate the LOP by some small amount. In this simple picture the rotation would be arctan (4/60) which is about 4º—but this example overestimates the effect. We get a better feel for the effect by breaking the GC track down into smaller steps, which is easy to do with a program like StarPilot.

Figure 6. Start of the great circle track to Mars from the AP in 0.25º of Lon steps (~ 12 nmi).

In this example we see that an a-value of 85 nmi would yield an LOP that is rotated by 1º off the true orientation.  This could lead to a relatively large fix error if the lines L1 or L2 were also large.  On the other hand, a quick redo of the sight reduction using new DR removes this error.

A real example
As a practical example that includes a bit of each of these long-line errors, we look at  Problem 8 from the real sight data included in Hawaii by Sextant (HBS).

Figure 7. Sample sights from HBS.

In this voyage and the documentation of it, we did a running fix between two sun lines taken at 1102 and 1334, which led to the fix labeled FIX 1334.  For now, we do not care about running fixes and just treat these two sights as if we were dead in the water.  That would lead to the fix marked with a red circle, where no line was advanced.  That is the fix we are studying in light of the fact that L2 from the 1334 sun line is indeed over 60 nmi long.

In the next picture we used the 1334 fix to get a new DR and then did the sight reduction again, using Pub 229 (without any offsets). That is shown below with the new APs.

Figure 8. Redo of Problem 8 sight reductions with new DR position.

The red data are the original plotting using original APs shown in Figure 7. The green plotting is the new fix using the previous fix position as a new DR. You can view both work forms to see where all the numbers come from.

This correction moved the fix by 3.5 nmi, which is a significant amount if we are striving to get the best possible cel nav fix.


To follow up on the point that these long-line problems do not arise in a computed solution, we look at a computed solutions using the raw data from the initial sights, including the inaccurate DR.

Here is the raw sight data of the two sights and the computed LOPs 
using 1802 DR 36º 31' N, 133º 28' W. Times in UTC
July 10, 1982, HE = 9 ft, IC=0, 
18:02:02, Hs 49º 24.5',   a = 21.5' T 098.0
20:34:46, Hs 74º 42.0',   a = 10.7' T 158.0

For a fix at 36º 27.8' N, 133º 01.6' W.... which is what we got by plotting, but only after one iteration of the AP.

In other words, again, if you compute the fix with a standard navigation program you do not have to worry about this factor.  The crucial feature of a proper cel nav program is it will iterate the results automatically that we are illustrating here manually, meaning it gets a fix from the user input DR, then replaces the DR with the fix, then computes the fix again to see if it changes, and it if did, it repeats again till there is no change. Alternatively, a program can intersect the two circles of position directly and not use any DR at all.


As a closing note on this topic, in the informational section at the back of the Nautical Almanac, called Sight Reduction Procedures: Methods and Formulae for Direct Computation, in Section 11, Position from intercept and azimuth by computation, they address the topic we covered here. 

They propose that the distance to be monitored (equivalent to our fix to AP) should be less than 20 nmi and if not, change AP to fix and recompute.  They can afford to make the distance smaller because they are computing the solution, as we noted that all programs do.  When doing it by hand, we can stick with the "anything approaching 60 nmi" for our trigger.

Thursday, February 21, 2019

Does Accurate DR Matter in Cel Nav—Verb vs. Noun

When doing cel nav by traditional books and plotting, we often stress that our choice of the assumed position (AP) based on our DR position does not matter—we can always find out where we are; we do not have to know where we are to find out where we are. Once we have a fix, we can then look over the plot to see if we might gain accuracy by redoing the AP, but this is not often called for.

In other words, we do not need an accurate DR position to ultimately get an accurate fix.  Indeed, at the end of this note, we will illustrate this by doing a fix in the middle of the Pacific using the Golden Gate as our as our initial DR position.

This reasoning rather quickly brings up a conflict that sharp students spot immediately. And, indeed, we got this vary question again just recently. Namely, do we need accurate DR for cel nav? Let's answer the cel nav part first, because more broadly speaking accurate DR is the absolute fundamental aspect of all navigation,  especially ocean navigation. We address this topic numerous places in our textbooks and courses. The short answer for why is simply that no matter how guarded, all or parts of our electronic nav aids may fail us, in which case we must depend on our DR, and if we have not practiced it, we will never know how well we can do it.  Or, when relying on cel nav, it could well be cloudy at the time we depend most on navigation.

So accurate DR is fundamental to good navigation, but to get specific about its role in cel nav, we have to look at dead reckoning or DR as a verb, meaning how well am I doing the process of dead reckoning, versus DR as commonly used to refer to a DR position, which is a noun.

As far as getting an accurate cel nav fix, DR as a noun, i.e.,  how well do I know where I am when I start, does not matter at all. See example at the end.

But once we start moving, then all fixes are running fixes, and the accuracy of the fix depends on how well you know how you are moving, which is DR as a verb.

In other words, to get an accurate cel nav fix when moving, I do not need to know where I am—i.e. I do not need an accurate DR position—but I do need to know how fast I am going and in what direction, and I must have some estimate of current and leeway, which means I need to know good DR as a verb.


An example showing that DR position is not crucial to a cel nav fix. Below are the two sights taken well offshore used in a different post, but this time we start with our DR position artificially set at the Golden Gate, which leads to large a-values.  You can view all work forms to see where the numbers come from.

 Figure 1. A grossly wrong DR leads to large a-values that require an expanded plot.

To accommodate the large a-values we make an exaggerated plot sheet with latitude parallels set at 6º apart. This generates a fix marked FIX GG1.  We then use that fix to improve the DR and do the sight reduction again, shown below.

Figure 2.  Using the Fix from Figure 1 as the new DR, we get very close to the True Position.

We cannot see quite yet how close we are, which would take another plot on a different scale, but we are close, and certainly one more iteration would be enough to get an accurate fix.

Refer to the work forms to note that we are not quite there yet.  The fix is still about 10 mile off, and indeed one a-value was over 60 nmi, which is our flag to redo it.  Then we do one more iteration and get right to the true position.

In this example, it took 3 iterations of manual plotting starting from a DR that was about 500 nmi wrong. Had we done this analysis with a computer program such as the StarPilot, we would home in immediately. In passing, I note that we show elsewhere that it is really difficult to get lost by 500 nmi, even much less than that takes effort when you are conscious the whole time. In other words, what do I have to do in my own boat for how long to not know if I am in WA or CA?

A more practical example of checking that the APs are close enough for a good fix is discussed in the article linked above ( Check Assumed Positions After Plotting a Cel Nav Fix ).

Monday, February 18, 2019

Moving Files Around on an iPhone and iPad

In a recent post I discussed a slick way to transfer files among iOS, Android, PC, and Mac wirelessly at sea (away from the internet)—or at home as needed using your normal wifi connection. The process works great, and away from the internet you can use any local network of your own. The Iridium Go device creates such a network, as does the RedPort Optimizer and the Ocens SideKick—the latter two being devices used to wirelessly share files downloaded from a sat phone to apps on other devices.

We also show (in a video linked in the post) that the $20 HooToo portable router does this job fine if you do not have any of those satcom instruments, and it is literally plug and play. Just use the USB cable provided to plug it into your computer or a phone charger, and you will see, in the wifi setup of all devices in the room, a new network (TripMateNano-xxx) that you can use to share files.

At this point, if you only care about Apple products (iOS devices and Mac Computers), you are done.  Connect all devices to your local network and use Airdrop to move them around.

The bigger challenge is connecting PCs and Android devices into the Apple devices, and that takes a couple extra easy steps.

We also need a free app from the App Store to carry out the transfers. There are several free options. Such things are also numerous on an Android system. Transfers then work among iOS, Android, PC, and Mac... or whatever else you have with a wireless connection option.

The only snag in this system, it turns out, is handling the files within the iPhone or iPad itself. This step is tied to the app you choose to do the transfer.  The first free app we tried (described in the post) worked fine for a while, then failed.  Now we have found a better one called, fairly enough, File Transfer App.  Also free, and so far I have not seen any ads.

Having now attempted several videos to illustrate moving files around in the phone, I realize we need an outline of what it involves and a review of how the phones work with files.

• Phones deal with photos and videos in a special way. Generally if they see anything with an image or video extension they try to force it to the Photos directory on the phone.  That is not a problem, because all of the transfer apps we are dealing with assume the main thing you want to transfer is photos, music, and videos so they have this all dialed in. Usually with special buttons for each of these and then another button for "files."  The navigator can need to transfer images, but we are mostly involved with files: GRB, GPS, TXT, PDF, etc.

• The primary app for moving files on an iOS device is called, simply, Files. I believe this is a stock app that comes with the iOS, but not sure since this one can be deleted, and most stock apps cannot be deleted. If Files is not there (a blue folder icon) then it can be downloaded from the App Store.  The attached video shows the use of this app.

• We also must be aware that there are only certain iOS apps that can work with external files. Any GRIB viewer app is an example, as they download and display GRIB files and then save them, and some offer the opportunity to share these files. A navigation program is another example, as they can create and then share GPX files of routes, tracks, and waypoints. Likewise some can import a GPX file created elsewhere. And the Mail program is another one that can send and receive attached files.

• Some but not all apps that work with external files provide access to them through the Files app, but many others do not, i.e., ebooks apps Kindle and Apple Books keep books in their own private libraries.

• Email attachments such as GRIB files from Saildocs can be transferred without using the Files app.

• In fact, any file in the phone that can be shared can usually be done without the Files app, but the Files app is often a convenient holding tank.

• In many cases the extension of the file is associated with an appropriate app on your phone. This facilitates some aspects of moving files around.

If we get, for example, an email attachment with extension .pdf, then a long press on the attachment will reveal a list of all the apps that can read a PDF file. When you choose to open the PDF in Adobe Digital Editions (ADE) for example, it will copy that file into its own library. On an iPhone—in contrast to an Android phone—that then is a dead end for the file. You can access it from the ADE app but can't move it from there, only delete it.  If you had subsequently deleted the email that had it as an attachment, then that file is gone.

What you can do is, instead of immediately loading into a specific app, save the file in the Files app, just putting it any convenient folder. Then from there you can open it later in any of several apps.

The contrast with Android is, we can go into the Android file directory and see where ADE is storing their library files, and so on, which is not doable in an iOS device.

• The other two videos show how the transfers work, the main step left to cover is the preparation of the files in the phone so the app can send them. Here are some scenarios to be demo-ed.

1) Import a GRIB file as an email attachment and move it LuckGrib folder or open it directly from the email.

2) Transfer a LuckGrib GRIB file to a transfer app so it can be sent to a PC.

3) Move a Bad Elf GPX track to Files app then share it to MotionX GPS

4) Take a screencap or photo and send it to the Transfer app via Files app (only option).

A video demo of the above 4 operations.

Monday, February 11, 2019

Brightness of Stars and Planets

In our cel nav course we provide two textbooks: Celestial Navigation and The Star Finder Book.  A question came up in class the other day that reminded us that we have many folks learning cel nav on their own using our main textbook who may not have the second book. These folks were then missing our discussion of star brightness. This note corrects that. In the next printing of the book, we will replace Section 11.20 with this new section of star brightness. Sadly enough, Section 11.20 was the one covering time tics and storm warnings from the NIST on the HF broadcasts from WWV and WWVH. These were both discontinued on Jan 31, 2019. I will have a post on that topic later. 

*  *  *
The brightness of a star is often a valuable aid to its identification. Brightness is specified by the body's magnitude. Star magnitudes are given in the star list at the back of the Nautical Almanac, not on the daily pages; star magnitudes change very little, if at all, throughout the year. The magnitude of the selected "navigational stars" are also reproduced in the Index to Selected Stars at the back of the Almanac (for years on page xxxiii). The latter is often reproduced on a yellow card bookmark.

Planet magnitudes are listed at the head of the planet columns on each daily page, because their brightness changes slowly throughout the year. The same magnitude scale applies to stars and planets. Samples are shown in Figure 11.20-1.

 Figure 11.20-1 Star and planet magnitudes listed in the Nautical Almanac. Planet values, i.e., -3.4 for Venus, are on the daily pages; star values are in the star list at the back of the Almanac (see below). The yellow card insert shows the values for the selected navigational stars. The list at the back includes many more stars.

Figure 11.20-1a. Star list sample pages from back of the Almanac, showing facing pages with different star name conventions. 

The Figure above shows a nuance in the star lists at the back of the Nautical Almanac. They list the star data by month, but they only show the star's proper name in the second half of the year.  Thus we learn that sigma Puppis does not have a proper name, whereas alpha Geminorum (of Gemini) is the alternative name to Castor.   We also learn that Sirius is the alpha star of the constellation Canis Major.  An "alpha star" is just what you think it is—the dominant star in the constellation.

There is not a simple correspondence between the numerical magnitude of a star and the visual brightness that we perceive. Each magnitude difference of 1.0 implies a brightness difference of 2.5. The magnitude scale is logarithmic, which means we need special tables, such as Table 11.20-1, to figure the actual brightness difference between two stars, or between a star and planet. And to complicate things even further, the scale is inverted; the lower the magnitude, the brighter the star.

(The system dates to Ptolemy in about 150 AD, who decided that the brightest stars we see are 100 times brighter than the faintest we can see, and then choose to divide the range into 5 magnitudes, so we end up with each being a factor of the fifth root of 100 (2.511) brighter than the next.)

The faintest stars we might navigate by would have a magnitude of about 3.0 although it would be rare to use such a faint star. A typical bright star has magnitude 1.0, which we could say is "two magnitudes brighter" than a faint magnitude 3 star. But the actual brightness difference between the two would not be a factor of 2.0; the bright one would appear just over 6 times brighter than the faint one.

The magnitude scale can also go negative for very bright objects. Venus, for example, at magnitude -4.0 would be 5.5 magnitudes brighter than a star with magnitude 1.5. Only two stars, the southern stars Sirius (-1.5) and Canopus (-0.7), are bright enough to have negative magnitudes. Venus and Jupiter are always negative, meaning always very bright, but Mars and Saturn are only rarely negative.

The sign of the magnitude difference is not important; the object with the lower magnitude is always the brighter object. Remember -1 is less than +1; and -3 is less than -2, and so forth. Objects with the same magnitude are equally bright—in Table 11.20-1 this is indicated by showing that a zero magnitude difference means an object is 1.0 times brighter than another object with the same magnitude.

For all practical star identification it is not necessary to be very technical about brightness and magnitudes. It is sufficient to classify stars in three rough categories:

Magnitude-one stars are the 20 or so brightest ones—pick a favorite and use it as your standard.

Magnitude-two stars are stars about as bright as the Big Dipper stars. There are only about 70 of these, each two to three times fainter than magnitude-one stars. And finally the

Magnitude-three stars  are like Pherkad, which is the lesser of the two Guards on the cup edge of the Little Dipper. Kochab, nearest the Pole is a magnitude-two star; Pherkad below it is a perfect 3.0 magnitude-three star. The two trailing stars of Cassiopeia, Ruchbah (2.65) and Segin (3.35), are both magnitude-three stars. There are only about 200 of these in all of the sky. The vast majority of celestial navigation is done with magnitude-one stars, and magnitude-three stars are hardly ever used.

Tip on star ID

It is rare to see stars below 10º or so (a hand width) on the horizon, because there we view them through the thickest layer of the earth’s atmosphere, where much of their light intensity is lost to scattering. Even the brightest stars fade as they descend toward the horizon, as shown in Fig. 11.20-2. Consequently, if you see an isolated star low on the horizon, you can bet it is a bright one, even if it appears faint. Since bright stars are well known stars, this observation alone often identifies the star for you.

Figure 11.20-2. How star brightness changes with the height of the star.  All stars fade as they descend toward the horizon because more of their light is lost to scattering. Polaris, for example, can rarely be seen at latitudes lower than about 5º  to maybe 10º N.

Or, an isolated low “star” could be Venus or Jupiter. But this confusion is unlikely since navigators tend to keep pretty close track of where these guys are, and even low on the horizon they remain notably bright. On a clear night, a low, bright Venus can startle a weary helmsman who sees it for the first time.

For more sophisticated star ID, it helps to know that several stars are distinctly reddish. These are in a class of stars called the Red Giants, and knowing these can be a valuable aid to their identification. See The Star Finder Book for more details on star and planet ID.

Practice with magnitudes

(1) Arcturus has magnitude 0.2 and Dubhe has magnitude 2.0. The magnitude difference is 2.0 - 0.2 = 1.8, and from Table 11.20-1, Arcturus is 5.2 times brighter than Dubhe.

(2) Sirius has magnitude -1.6 and Antares has magnitude 1.2 The magnitude difference is 1.2 - (-1.6) = 1.2 + 1.6 = 2.8, and from Table 11.20-1, Sirius is 13 times brighter than Antares.

(3) Jupiter, on some date, has magnitude -2.1 and Canopus has magnitude -0.9. The magnitude difference is -2.1 - (-0.9) = -2.1 + 0.9 = -1.2, and from Table 11.20-1, Jupiter is 3 times brighter than Canopus.

(4) Venus can be routinely as bright as magnitude -4.3 and the North Star, Polaris, has magnitude 2.1. The magnitude difference is 2.1 - (-4.3) = 6.4. From Table 11.20-1 we can estimate that Venus is roughly 400 times brighter than Polaris. Venus can be as bright as -4.8.

Tips on Planet Identification

The planet Mercury can be seen with the naked eye, and it can even be quite bright. But it is only rarely visible, and when it is, it will be low on the horizon, just before sunrise or just after sunset, and very near the sun. Since it is rare to be seen and always very low on the horizon it is not used for navigation. Its Dec and SHA are not listed in the Nautical Almanac.

Venus and Jupiter always stand out nicely among the stars. When either of these two are visible, they are always much brighter than any stars around them. Mars and Saturn, on the other hand, appear only as bright or medium bright stars. The main function of Mars and Saturn is to confuse the navigator by appearing as stars where no stars should be. Mars can sometimes appear reddish, and most planets will appear as tiny disks, rather than points, when viewed through 10-power binoculars.

Another identifying characteristic of planets is their lack of twinkle. Stars twinkle, planets do not. The reason can be traced to the apparent size of the light source—distant stars are point sources of light; the much closer planets are disk sources. A patch of warm air can momentarily refract all of the star light out of our eye, causing it to twinkle; but such transient refraction cannot remove all of the light from a planet since it comes from slightly different angles depending on its origin on the disk.

The relative location of the planets can also sometimes confirm or assist in their identification. The sun, moon, and all planets always lie along the same arc across the sky. On those occasions when 3 or more of these objects are visible (say, moon and two planets), this alignment can sometimes aid in their identification.

A consequence of the above, which comes about because the orbits of all of these bodies lie within the same plane (± 9º or so), is that planets are always found within a Zodiac constellation. With that said, the concept of constellation, let alone the Zodiac,  does not come up much in cel nav as we do not need it for anything. We do refer to groups of stars, but these are groups we make up from stars of neighboring constellations, such as the Summer Triangle.