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Sunday, October 31, 2010

Extra-Tropical Low

An extra-tropical low is just a fancy name for any cyclone which forms north or south of the Tropics. I've heard them described as "cold hurricanes", which is somewhat true, except that they are typically much larger in area than hurricanes tend to be. This one in particular that is slowly marching our way is currently 938mb, certainly as low as the eyes of many hurricanes or typhoons. Out at sea, this thing is already spawning 50' significant wave heights, which means that statistically some of the waves are 100'. That's a lot of water.

As you can see, the cold front has already occluded the warm front, and the occluded front is wrapping around the low. All other things being equal, this would bring a LOT of rain to the Salish Sea basin.

However, there's more to the story. The low will follow the Rossby waves at the 500mb level. Here's the 500mb map:

Even though the jet stream is way down around Cape Mendocino, the 500mb contours appear to be steering the low even more northward into the Gulf of Alaska. So, we won't expect to see even the backwash of this until Friday (the rains tonight and tomorrow are from another cold front), and depending on how things shape up we may get no more than a typical late-autumn occluded front out of it at this latitude.

Will post more when I know more.

Have a happy and safe Halloween!!

Fox News Science does it again.

Wow. Okay, so, the rocket scientists over at Fox News just posted an article about, um, rocket science.

The headline is "Is NASA Covering Up the 100-Year Starship?"

The short answer is, no, they're not. This is possibly the worst-informed piece of science "journalism" I've ever seen, even coming from Fox. There are so many problems with this article I don't even know where to begin. Basically Fox has managed to conflate the Orion starship project and the Mars missions into one single (cough) one million dollar program.

So, the quick debunks, and then I'm going to use this as a jumping off point later to discuss some of the very cool things NASA is in fact planning as far as solar planetary exploration and colonization, and also deep-space exploration of the nearest stars.

1) Yes, NASA has had plans for a starship that would get humans to the nearest stars in about the span of a human lifetime. All of the technology to do so existed in 1958. It would have cost about the same amount as the Apollo 11 mission, and could have been completed and ready for launch as early as 1960. Had we launched to Alpha Centauri in 1960, we would be more than halfway there by now. The problem with the Orion starship was that it utilized atomic bomb blasts for propulsion, which is fine for a launch from orbit but at the time we had no way of doing that, so it would have needed to be a ground launch, which would have been a Very Bad Idea. Now we have the ability to construct a ship outside of the earth's atmosphere, and this is less of an issue. The current administration has given the green-light to dusting off and continuing this research, which is excellent. But it's hardly a secret, and certainly not a "cover up".

2) Yes, NASA has several different ideas about how best to accomplish a manned mission to Mars and other planets and moons within our solar system. Yes, some of these methods presume that a trip to Mars (or Europa or wherever) would be a one-way trip. So what? A hundred years ago many families and individuals set out westward in Conestoga wagons, fully aware that they were heading into a hostile wilderness with no hope of ever returning to their homelands. Yes, many of them died in the process. And many of them didn't. But in any case, while it might take 90 years to get to Alpha Centauri, it will in no way take 100 years to get to Mars. It might however take several years, depending on how we do it.

3) The missions to Mars and to Alpha Centauri are completely separate missions and completely separate projects. That said, the technology for the Orion starship could make one hell of a fine interplanetary craft as well. I will devote an entire post (or several) to the Orion mission, it's important and fascinating stuff.

3) Yes, it is easier to modify the human body to adapt to an alien world than it is to modify an entire planet to adapt to the human body. Of course Fox News would be surprised to learn this.

Here's the link to the Fox article.

Hold your nose

Halloween Weather Update (Seattle area)

Right now it looks like the extratropical low which is continuing to deepen south of the Aleutians will not be dumping QUITE as much rain on us as previously anticipated. Better news still is that it looks like we have a small window of dry weather for the trick-or-treaters tonight. If NOAA's modelling holds up, the rains shouldn't start until around 11pm tonight.

Will post more later about the extratropical low, both the one in the Gulf right now and ETLs generally. 

Friday, October 29, 2010

Great World-Wide Star Count UPDATED

Tonight begins the annual Great World Wide Star Count! It runs through November 12th, and is an excellent opportunity for amateur astronomers all over the world to collect data for determining the extent of regional light pollution. 
Star Count

All you need to do is go outside, look at a constellation (Cygnus if you're in the northern hemisphere, Sagittarius if you're in the southern hemisphere) and compare what you see with the diagrams provided. Then correlate this with the time and your location (by GPS or Google Earth) and submit your data to the good folk at Windows to the Universe, a subsidiary of NESTA (the National Earth Science Teachers Association). Here is the pdf of the Activity Guide:  
Star Count Activity Guide

UPDATE: If you use Google Earth and cut-and-paste your decimal latitude and longitude from it into the blocks on the Reporting page, you must delete the degree symbols on both or it won't be able to recognize the string of numbers as a latitude or longitude.

Incidentally, from the park by my house I could see fourth magnitude stars in Cygnus.

And a really lovely meteor, probably part of the Orionid shower, although it was awfully early in the evening. 


The great thing about Seattle weather this time of year, if it's not one damned thing after another it's the same damned thing over and over.
Yes, we have another frontal system setting up to park itself over the Puget Sound basin on Sunday. No, it won't be quite as windy as last weekend. No, we won't see the flooding that's predicted for the western slope of the Cascades. But a bit sloppy for the Trick or Treaters.

This is the beginning of our first Pineapple Express of the season, spawned by the (still nasty, currently 940mb) remnants of Typhoon Chaba. More on this as it progresses.

Thursday, October 28, 2010

Starpath School of Navigation courses at Windworks Sailing Center

Starpath School of Navigation
2011 General Navigation Series 

at Windworks Sailing Center

Starpath courses are tailored toward the recreational mariner as well as the professional. They are designed to teach the principles of navigation in a clear and concise manner. They are not intended as "license prep" courses, but rather as training for actual navigation. 

All Starpath classes are Tuesday and Thursday evenings from 1800-2100. Testing time is not built into
the schedule.

Radar Navigation Jan 4 – Jan 6
A practical guide to safe, versatile and efficient use of small-craft radar, radar principles and operation,
navigation by range and bearing, use of EBL and VRM in navigation and collision avoidance,
identifying radar targets and interpreting their motions, and how to apply the Rules of the Road. Also,
how to interpret land masses seen of the radar. This course is guaranteed to increase the safety and
efficiency of your radar watch many fold and greatly reduce the anxiety of those encounters with
converging radar targets that cannot be seen visually.

Electronic Navigation Jan 11 – Jan 13
Covers the best guidelines to safe and efficient use of GPS both independently and directly interfaced
with electronic charting software as a primary navigation system. Also covers use of electronic depth
sounding for bathymetric navigation.

Navigation Rules and Collision Avoidance Jan 18 – Jan 20
Covers all aspects of the Rules of the Road, starting with the basics and ending with all you need to
safely navigate in accordance with the Rules and avoid a collision with another vessel. It is for power
and sail vessels, large and small, professional and recreational. The Rules are the same for “...every
description of water craft used as a means of transportation on the water”. We will discuss collision
avoidance with vessels held visually, as well as by radar alone in conditions of reduced visibility.
Special emphasis will be placed on the obligations of sailing vessels and small power-driven vessels
interacting with each other, and interacting with larger vessels operating in the traffic lanes.
Prerequisite: No prerequisite, but Radar Navigation class is strongly recommended.

Marine Weather Feb 1 – Feb 17
A plain-language, practical course for inland and ocean sailing, guaranteed to make your sailing safer
and more efficient. Combine your own observations of wind, sea, clouds and barometer to better
interpret the official forecasts obtained from radio, satellite or facsimile as well as make your own
forecast if you lose the official sources. Develop practical rules of thumb which contribute to sound
decision making at the dock and underway.

Starpath School of Navigation
2011 Celestial Navigation Series 

at Windworks Sailing Center

Basic Celestial Navigation Feb 22 – Mar 3
Confidently use a marine sextant and chronometer to derive latitude by Local Apparent Noon and
Polaris, and precompute, shoot, compute and plot a three-star fix using Pub 249 Vol 1. This is the very
barest-bones minimum celestial navigation and ocean dead reckoning needed as an adjunct to GPS to
safely navigate an offshore passage.

Intermediate Celestial Navigation Mar 8 – Mar 17
Obtain and plot a celestial line of position of the sun, moon, planets and stars, using a marine sextant,
chronometer, Nautical Almanac and Pub 249 volumes 2 and 3. Plot a running fix of the sun, and
precompute sights of sun, moon, stars and planets using the 2102D Starfinder. Student will be familiar
with routine sight-averaging techniques necessary to utilize a plastic marine sextant.
Completion of this class along with Basic Celestial Navigation will prepare the student for most
Celestial Navigation exams, including US Sailing.
Prerequisite: Basic Celestial Navigation or equivalent.

Advanced Celestial Navigation Mar 22 – Mar 31
Obtain and plot celestial sights using a marine sextant and chronometer along with Pub 229, NAO
tables, the Kolbe Long-Term Almanac or a programmable scientific calculator. Navigate safely using
the smallest amount of publications, and without access to regularly updated almanac information (as
may be necessary for circumnavigating the globe).
Prerequisite: Basic and Intermediate Celestial Navigation or equivalent.

Emergency Celestial Navigation Apr 5 – Apr 14
Use the sun, moon, planets and stars to successfully navigate across an ocean without benefit of a
chronometer, sextant, almanac or sight-reduction tables. Many of the techniques covered will be based
on Polynesian celestial navigation principles.
Prerequisite: Basic and Intermediate Celestial Navigation or equivalent. Advanced Celestial Navigation
or the equivalent is not required but is strongly recommended.

Register for Starpath courses at:

Windworks Sailing Center
7001 Seaview Avenue NW, Suite 110 Seattle, WA 98117, USA
Toll-free 877-223-1993 Tel (206) 784-9386 Fax (206)784-2995

Zenith Maritime Academy Class Calender

Below is a list of the USCG licensing courses I'm teaching this winter, posted here mainly so that I can then transfer it to the "Calender" link to the right. If you don't happen to be interested in sitting for a captain's license, this will likely not interest you.

Schedule for Zenith Maritime Academy licensing courses at Windworks Sailing Center

These courses are approved by the USCG for the licensing of US Merchant Mariners. They are linked from the Windworks website as Seattle Merchant Mariner Training.
For registration contact:

Windworks Sailing Center
7001 Seaview Ave NW
Suite 110
Seattle WA 98117
206-784-9386, fax 206-784-2995

All Zenith classes are Monday through Friday 0900-1700, with a 1-hour lunch break. Testing time is
built into the schedule, with additional testing time for the Master 200 ton upgrade course available the
following week.


32 hour (1 week: 4.5 days plus 0.5 days testing) Master 100 to Master 200 Upgrade Nov 8 – Nov 12 $375

4 hour Auxiliary Sail Nov 15 $75
4 hour Commercial Assistance Towing Nov 17 $75
4 hour Marine Radio Operator Permit (FCC) Nov 19 $75

56 hour (2 weeks: 8 day plus 2 day testing) Operator of Uninspected Passenger Vessel (“Six Pack”) Nov 29 – Dec 10 $800
24 hour (1 week: 3.5 days plus 1.5 days testing) Operator of Uninspected Passenger Vessel to Master 100 Upgrade Dec 13 – Dec 17 $375
32 hour (1 week: 4.5 days plus 0.5 days testing) Master 100 to Master 200 Upgrade Dec 20 – Dec 24 $375

4 hour Auxiliary Sail Dec 27 $75
4 hour  Commercial Assistance Towing Dec 29 $75
4 hour Marine Radio Operator Permit (FCC) Dec 31 $75


56 hour (2 weeks: 8 day plus 2 day testing) Able Seaman Jan 3 – Jan 14 $800
56 hour (2 weeks: 8 day plus 2 day testing) Operator of Uninspected Passenger Vessel (“Six Pack”) Jan 17 – Jan 28 $800
24 hour (1 week: 3.5 days plus 1.5 days testing) Operator of Uninspected Passenger Vessel to Master 100 Upgrade Jan 31 – Feb 4 $375
32 hour (1 week: 4.5 days plus 0.5 days testing) Master 100 to Master 200 Upgrade Feb 7 – Feb 11 $375

4 hour Auxiliary Sail Feb 14 $75
4 hour  Commercial Assistance Towing Feb 16 $75
4 hour Marine Radio Operator Permit (FCC) Feb 18 $75

56 hour (2 weeks: 8 day plus 2 day testing) Operator of Uninspected Passenger Vessel (“Six Pack”) Feb 21 – Mar 4 $800
24 hour (1 week: 3.5 days plus 1.5 days testing) Operator of Uninspected Passenger Vessel to Master 100 Upgrade Mar 7 – Mar 11 $375
32 hour (1 week: 4.5 days plus 0.5 days testing) Master 100 to Master 200 Upgrade Mar 14 – Mar 18 $375

4 hour Auxiliary Sail Mar 21 $75
4 hour  Commercial Assistance Towing Mar 23 $75
4 hour Marine Radio Operator Permit (FCC) Mar 25 $75

56 hour (2 weeks: 8 day plus 2 day testing) Operator of Uninspected Passenger Vessel(“Six Pack”) Mar 28 – April 8 $800
24 hour (1 week: 3.5 days plus 1.5 days testing) Operator of Uninspected Passenger Vessel to Master 100 Upgrade April 11 – Apr 15 $375
32 hour (1 week: 4.5 days plus 0.5 days testing) Master 100 to Master 200 Upgrade Apr 18 – Apr 22 $375

4 hour Auxiliary Sail Apr 25 $75
4 hour  Commercial Assistance Towing Apr 27 $75
4 hour Marine Radio Operator Permit (FCC) Apr 29 $75

Washington DC weather for rallies Saturday

For those planning to attend the combined Jon Stewart and Stephen Colbert rallies in Washington DC this weekend, the weather could not be more cooperative. Sunny and around 60° F, light winds, generally excellent weather for a late autumn rally and/or march on the Mall.

Those attending the satellite rallies in Seattle will find the weather somewhat more, ah, Seattle like. 

For information regarding the rallies click Rally to Restore Sanity or March to Keep Fear Alive

Wednesday, October 27, 2010

More storm stuff from around the country

While we in the Pacific Northwest have been focusing on this weird (really weird) low that hung out off the Vancouver Island coast this past weekend, some other really large storms have been happening east of the Rockies that are considerably noteworthy as well.
Right now we're seeing the deepest low ever recorded in Minnesota (954.8 mb at Bigfork Airport, comparable to a category 3 hurricane if the isobars had been stacked up closer). Today the cold front marching out in front of that is spawning tornadoes from Alabama to Virginia (my oldest daughter just texted me from NC, they've just canceled the latest tornado warning there, where three tornadoes have touched down in the past few hours).
There's a lot of discussion going on right now over at the Cliff Mass blog about whether or not the low over Minnesota should really be considered "the biggest storm of all US history", as some media outlets are hyping it as. Cliff Mass correctly points out that many of the extra-tropical lows which are generated in the Gulf of Alaska and spin down to the coasts of southeast Alaska, British Columbia, Washington, Oregon and northern California have deeper lows than any midwest storm, and even deeper than many hurricanes, but that for whatever reason these are under-reported by most media outlets and even textbooks, especially those based in the east coast.
So, having lived on the east coast, the west coast, and the midwest, I'd like to throw my opinion into the fray and say that the different types of big storms which affect each region are simply DIFFERENT TYPES OF BIG STORMS. I've been through hurricanes on the Atlantic seaboard (and in the middle of the Atlantic), tornadoes in Kansas (including the F5 that leveled Topeka in 1966, pictured above), and I've been through huge extra-tropical lows in both the Atlantic and Pacific oceans. And each has its very own unique characteristics and problems. I don't think one can categorize one as being "worse" than another.  
What is much more interesting to me than the squabble of "my storm's bigger than your storm", is the fact that the strange extra-tropical low in the Pacific Northwest and the low in Minnesota happened in such close time-proximity to each other. Correlation does not prove causation, but it does "waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there'", as Randall Munroe of the brilliant comic XKCD once put it. The fact that we're seeing such strange weather all across the US is at least worthy of further investigation.

Tuesday, October 26, 2010

Three day Low

Winds should be diminishing late this afternoon as the (now 990mb) low moves inland into British Columbia.

This storm has taken almost everything I thought I knew about extra-tropical lows and blown it out the window. This thing has been sitting off of Vancouver Island since Saturday, sitting and spinning like a buzz-saw. Lows aren't supposed to do that. High are supposed to be stationary, lows are supposed to move around the stationary highs. This is meteorology 101. Except that apparently this particular storm played hooky that day, or didn't crib some smarter storms notes or something, because it clearly didn't get the word.

If a bigger low, like a hurricane or typhoon, decided to make landfall and then just park itself for three days over a densely populated region, that would be a real problem. Hopefully the good folk at NOAA, Environment Canada and UW Meteorology are getting some good modeling data out of this storm.

Monday, October 25, 2010

Rules of the Road

For those who found my last post entertaining, you can read every single one of the Rules of the Road right here!

Nav Rules Download

Public Service Announcement

Traffic Separation Schemes

(i) A vessel engaged in fishing shall not impede the passage of any vessel following a traffic lane.
(j) A vessel of less than 20 meters in length or a sailing vessel shall not impede the safe passage of a power-driven vessel following a traffic lane.


I know, weird, right?

Yes, it means that fishing boats (and their nets and gear), sail boats of any size and any vessel at all of less than 66' in length must stay out of the way of shipping traffic navigating within the designated traffic lanes. Even if the fish happen to be running in the lanes, even if a sailboat is becalmed in the lanes, even if the middle of the lanes seems like the very most fun place to be.

Because fishing in the lanes, sailing in the lanes, or motoring in the lanes in anything smaller than 20 meters is about as smart as riding a tricycle on I-5.

Fortunately, the boundaries of the traffic lanes are printed right on the navigation charts, so there's no reason to not know where they are and be able to stay well clear of them. Electronic versions of all US navigational charts are available free of charge from NOAA, at the link to the right. The traffic lanes are the big purple stripey part that runs right up the middle.

Navigation is fun!

Storm update

Here is the barograph for West Point Lighthouse in Seattle for yesterday's atmospheric "bomb". Note that even though the barometer is now rising, the winds and seas are continuing to build. Click on the Cliff Mass blog to the right, he has a lot more information about this storm, which is turning out to be truly extraordinary.

Sunday, October 24, 2010

Weekend storm update

Just got back from run to Victoria. Wind and seas significantly bigger in Puget Sound and Admiralty Inlet than in the Strait of Juan de Fuca, which was surprisingly calm. This morning the swell off the coast was between 20' and 30' "westerly". We knew that if "westerly" meant from the southwest we wouldn't get much swell in the east entrance, but if it was from the northwest we could expect about half the swell height of the west entrance, or about 12'. The swell turned out to be southwesterly, so we had none at all in the east entrance of the strait.

Tomorrow's forecast for Puget Sound in the vicinity of Seattle:


Overnight: S wind 18 to 22 kt, with gusts as high as 29 kt. Rain likely. Wind waves around 3 ft.

Monday: SSW wind 20 to 25 kt, with gusts as high as 38 kt. Showers likely. Wind waves around 4 ft.

Monday Night: S wind 12 to 20 kt, with gusts as high as 30 kt. Showers likely. Wind waves 2 to 3 ft.

Friday, October 22, 2010

Hourly predictions for this weekend's storm

Wind, wave and swell predictions for Cape Flattery and the west entrance of the Strait of Juan de Fuca this weekend.

Nothe that "Significant Wave Height" is the average height of the highest 1/3 of the wind waves. So statistically, a predicted SWH of 10' means that you occasionally see wind waves of 20', in addition to the swell. These "statistical waves" are sometimes erroneously called "rogue waves", but they are actually a normal and expected part of the bell-curve of wave heights at a given time.

Thursday, October 21, 2010

Weather update for this weekend

Like, no joke, that's a 957mb low.

Storms in the Strait of Juan de Fuca

Guh-narly. Sustained winds to 45 knots, combined seas 
at Cape Flattery 35', including a west swell of 25'.  
For more and better information, click on the Cliff Mass 
blog to the right.
These predictions are for Cape Flattery, NOT Puget Sound 
or the Strait of Juan de Fuca. 

 8 FT. SW SWELL 13 FT.




Wednesday, October 20, 2010

Comet Hartley 2

Comet Hartley 2 will be faintly visible tonight and in the early hours of tomorrow morning. Once Orion is up, imagine another "person" standing on Orion's shoulders. Where that person's head would be is the bright star Capella, in Auriga the Charioteer. The comet will be a faint fuzzy blob just below Capella.

If you happen to be far away from city lights, the diffuse coma of this comet is apparently quite large; right now twice as large as the diameter of the full moon. For urban areas, only the inner portions of the comet will be visible.

Salish Sea

In my last post I made reference to the Salish Sea. I realize that this terminology is not yet in common usage, but it is now the official designation for the body of water comprised of the Straits of Juan de Fuca and Georgia, Puget Sound and Hood Canal, and adjacent navigable waters. Here is the official USGS map of the Salish Sea, as of 15 November 2009.

US and Canadian Tides

Here in the Salish Sea region we are frequently (in my case, daily) traveling between the waters of Washington and British Columbia. It is critical that we understand the differences between the conventions used on US charts and tide tables and Canadian charts and tide tables for this region, because in many cases they overlap.

In addition to the fact that US and Canadian charting agencies use different sounding units (metric in Canada, imperial in the US, alas), US and Canadian charts also use a different reference point for their soundings.

US charts and tide tables are based on Mean Lower Low Water (MLLW), that is, the average of all of the daily lower low water heights over a 19 year metonic (earth/sun/moon) cycle. By definition then, 50% of the lower low waters over that same 19 year period will be "minus tides", meaning that they are below the chart datum.

Canadian charts and tide tables, on the other hand, use Lower Low Water Large Tide (LLWLT), also called Lowest Normal Tide (LNT). LLWLT is the average of the 19 lowest low waters for the same 19 year metonic cycle, or rather the average of all of the lowest tides for each year over that same period. So it is still possible to have a tabular "minus tide" in Canadian waters, but for any given tide station you should see no more than 10 of these total over a 19 year cycle, as opposed to some 3500 minus tides for the same location on US charts for the same time span. 

In both cases, the Tide Tables inherently compensate for this datum difference, so if you were to take the combined charted depth and tide at a given moment for a given station from both US and Canadian sources (and convert from metric to imperial), the total depth of water would be presumably exactly the same. 

However, if we mix US tide tables with Canadian charts, we will find that we have significantly more water at a given location than what we have computed. This is mostly only a problem for bathymetric navigation. 

The much worse scenario is that if we mix Canadian tide tables with US charts, we will actually have significantly less water than what we have computed. The first scenario is a navigational embarrassment, the second may well result in a grounding.  

Monday, October 18, 2010

Starfinder: Arc to Arcturus

This is the first installation of an ongoing series of star identification posts, focusing mainly on stars commonly used for navigation.

The very bright reddish star to the west early in the evening this month is Arcturus, by far the brightest star in the constellation Bootes, the herdsman. Arcturus is most easily found by following the handle of the Big Dipper to the nearest bright star.

Arcturus is most immediately notable for the fact that there are no other bright stars anywhere close by it. It also has a proper motion which is inconsistent with that of other stars in our neighborhood. In other words, Arcturus is moving against the flow of traffic of the other stars in the area, including our sun. One possible explanation for this is that Arcturus may actually be a remnant of another galaxy which long ago merged with the Milky Way.

And that, I think, is pretty cool.

Sunday, October 17, 2010

Home grown space flight, on the cheap!

The Brooklyn Space Flight Program combined a weather balloon, video camera, GPS and chemical hand warmers to get this amazing footage! Hopefully this will inspire many other backyard astronauts.

Brooklyn Space Program balloon flight video

Saturday, October 16, 2010

Lunar Distances with Jupiter

Tonight and over the next few nights (if the weather holds) should be excellent for lunar distance practice to obtain Universal Time (formerly known as Greenwich Mean Time) by measuring the distance between the moon and Jupiter. Remember to align the moon's limb to the center of the planet, as Jupiter's present apparent diameter is large enough to affect your sextant readings.

The easiest method to compute UT by lunar distance is of course with a calculator or computer, but most of the point of computing them in the first place is to be able to derive UT at sea without any electronic means whatsoever, such as might occur after a lightning strike of a sailboat's mast (an all-too-common occurrence at sea). So instead, a set of tables such as those created by Bruce Stark are probably the best method of clearing lunar distances and deriving UT from them.

The other primary purpose of measuring lunar distances is to afford sextant practice to the landlocked celestial navigator. No visible horizon is necessary, so the sights may be taken from any location (and at any time) from which the moon and another bright object in the ecliptic may be seen.

An interesting astronomical application for this method which requires no special tables at all, but does require about a month's worth of observations, is comparing the moon's apparent diameter with it's hourly eastward rate of motion across the sky. With a simple marine sextant and a little patience, you can correlate the moon's daily relative distance based on apparent diameter (or actual distance, based on a mean lunar diameter of 3474 km, but this is in no way necessary) with its daily rate of movement relative to the sun, a planet or a star in the ecliptic. Armed with a months worth of data, you can easily demonstrate the elliptical nature of the moon's orbit and prove Kepler's three laws of planetary motion.