By the Light of the Moon

My daughter just wrote to ask me just who can see the moon at any given moment in time.  If she can see it, can people in other countries see it too?  I wrote her a fun answer, and I'll share it here...

It's fascinating to picture how the moon works; what parts are lit, where it can be seen from, and so on.  The best thing to do is to imagine, or actually hold, two balls in front of you, like a golf ball and a grape perhaps. Hold them with your hands out a foot or so from you and from each other. Now imagine the sun as a big beach ball across the street. Effectively, the sun is "infinitely" far away, so the light always shines on the same side of the two balls you're holding, with all sun beams pretty much perfectly parallel. As you move the balls around each other you can see how the lighting on each changes relative to each other. This can help you visualize the phase of the moon as seen from the earth, and how the moon is visible from almost a full half of the earth at all times.

One cool detail I figured out one day is that if you look at the moon in the sky and imagine yourself standing up around the top edge, as though gravity there was pulling in the same direction as where you're standing on the earth, some interesting information comes to light. Another way to say this is to imagine a flag pole on top of the moon, sticking straight up from the moon's surface, exactly parallel and pointing in the same direction as a flag pole you're standing next to... okay, now look at where the sunlight is on the whole sphere of the moon around and under that flagpole. Is the flagpole on top up in the light or in the dark?  Then realize that the light on the whole earth under your feet is exactly the same. This is because the sun is so far away and both the earth and moon are lit in "parallel", or at exactly the same angles.  Looking at the moon in this way you can visually imagine how the earth is currently lit up too.  If the flag pole up around the top corner of the moon looks like it's in the dark, then you're probably looking at the moon in the dark too.

As far as who can see the moon at any given momnent, reverse the situation and imagine you're standing on the moon. From there you can see almost half of the earth at all times.  Anyone standing on the earth where you could see their location can look up and see your location on the moon too. This "line of sight" explanation can help you imagine where the moon must be visible from at any given moment.

A globe of the earth can help with this visualization. Find your location on the globe of the earth, put your eyes out away from the globe at about the angle the moon is up in the sky, and then see what half of the globe you can see.  Be sure to hold the globe far enough away from you to be able to see almost a full half of the earth. The moon is far enough away from the earth that almost (but not quite) a full half of each is visible from the other.

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Astronomical algorithms are a favorite subject on mine. This past month I republished a 2012 edition of Sun Position, my Kindle book that presents two very high accuracy algorithms for calculating exactly where in the sky the sun can be found... invaluable for solar energy research, development, and applications.

"Dark Side of the Moon"

Today the space probes Ebb and Flo crashed into the mile-high edge of a crater on the moon after an extremely successful mission to map the subtle gravity changes all over the moon's surface. Yesterday, one well-meaning news reporter stated the lunar satellites were to crash on the "dark side of the moon", and man, did he get a bunch of people writing to set him straight!  

You see, supposedly there really is no dark side of the moon, because the sun shines on all parts of the moon over a one-month period. This makes sense, but I'm here to tell you there really IS a dark side of the moon after all, and here's why.

Standing on the moon looking up towards earth, you'd discover that the phase of the earth is exactly opposite the current phase of the moon. If the moon is full, the earth is barely lit (a "finger nail earth"), and when the moon is but a fingernail of light, the earth is full and very bright in the lunar sky.  This is all because of the way the earth-moon-sun geometry all works out, with the sun at a very long distance away from the relatively close-together earth and moon system.

This all means that from the perspective of someone standing on the near side of the moon, the sun is very bright when its up for half a month, and the earth is very bright in the sky for the other half of the month.  If you're on the near side of the moon, the earth always hangs up there pretty much in the same spot in the sky, always looming large, especially when the sun is down and the earth is all lit up. 

Now consider the view of the sky for a lunar explorer standing on the far side of the moon, where the earth is never visible. Half of the month the sun is very, very bright, as before, but for the other half of the month the sky is awesomely dark, with the stars, milky way, and a few planets brilliant and unblinking in the inky blackness.  

In summary, one side of the moon is always bathed in the glow of the sun or the earth-shine, and the other side of the moon spends half of each month in inky blackness.  The far side of the moon truly can be considered the "dark side of the moon".

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Astronomical algorithms are a favorite subject on mine. This past month I republished a 2012 edition of Sun Position, my Kindle book that presents two very high accuracy algorithms for calculating exactly where in the sky the sun can be found.

Why should authors keep tabs on their book's Amazon.com sales rank?

I created an automated sales rank notification system several years ago, to help us keep up to speed on our book sales, both for us personally and for other authors published here by Books To Believe In. We wanted to know immediately if there was a sales event, so we could get the feedback needed to help amplify any sales campaigns, publicity, or other current events we, or our authors were doing. We still use this system daily, and it's proven to be a great tool for book marketing.

Here's how it works. My automated system checks Amazon and sends notification emails to us, or to our authors, hourly whenever one or more books were sold during that hour. It is exciting to see which books are selling and theorize on the why’s. We've learned quite a bit about trending topics and other great lessons in marketing and sales, just by observing this activity.

This feedback allows us to directly correlate the publicity work we are doing with our books to their sales. We can tell immediately if a social media campaign is working or if it has failed. We don’t have to wait days, weeks, or months for sales results, we get information in near real time, ready for quick analysis. As it turns out, Twitter campaigns are the most surprising, most effective, and the most fun to watch using this tool.

When we create a virtual launch party for a book, we watch its sales rank go down with each passing hour until it hits a low point, capturing screen grabs of the book’s sales page with every passing hour so we have proof of its low ranking to use in future publicity campaigns. It is a great claim that your book is an ‘Amazon best-seller’, but if you can provide the proof with a screen grab of your low sales rank, your web visitors will know you’re not just blowing hot air.

Our authors go to http://forauthorsonly.com/bookmetrics.php to set up their books with our service, and the process is very easy. (We recently opened up this service to any other book authors who might want it.) Once a sales notification email or text-mail is received, a quick visit to the book's Amazon.com page can show what categories the book might be in the top 100 in. Right below sales rank, Amazon.com lists the top categories the book is in. Again, that is something to publicize through Twitter or Facebook or other publicity programs. It might be hard to be in the top 100 overall on Amazon.com, but frequently a book receiving even a small amount of sales gets in the top 100 of their book’s niche category.  That's valuable marketing leverage!

We are supremely glad we implemented this campaign, because in June of 2010, the sales rank for Secrets to Creating Passive Income suddenly starting dropping towards Number 1 like a rock! We hadn’t done anything substantial with that book for a few weeks, so this surprised us. For almost two weeks, we saw a steady stream of sales of the book and didn’t know what was causing it. We were baffled. Internet searches didn’t yield any answers... Finally, we got an e-mail that explained our new found fame. Our book had been recommended by a national magazine with 1.1 million circulation. We were famous and didn’t know it! If we hadn’t been on alert from these e-mails, we might have completely missed out on being able to play up that magazine’s coverage WHILE it was still on the newsstands. If we had only been aware of a sale’s spike on the monthly check we received from Amazon.com, some 60 days later, we would have completely missed our moment in the sun.

If you are an author, having an automated system act as a watch dog to let you know about sales activity is a tool you should consider taking advantage of. It’s very fun to receive the e-mails, but more importantly, it is powerful to be able to tell in real-time how effective a sales campaign is. It is a tool that will not only notify you of sales, but help you generate more sales too.

Your book is your calling card

The world is changing fast. It used to be that a Phd needed to pay attention to the adage "publish or perish", but in today's world a case can be made that just about all serious business people should get published. There's no need to panic, or feel that this goal is over the top. It's actually quite easy to author a respectable book, because that can include a short Kindle book that's many times easier to write and to publish than were the books of just a few years ago. It's a whole different publishing world out there today!

Instead of handing a prospective employer a resume, how much more powerful is it to hand them a book you wrote? Write the book on a passionate (for you) subject, and the doors to employment in the subject area you are passionate about are much more likely to open. I worked as a solar software engineer back in the 80's, on some of the world's largest solar power fields. Pictures of the photovoltaic trackers I programmed appeared on the covers of Scientific American and Popular Science magazines.

 I felt very fortunate to land that job back then. Recently, my book titled "Sun Position" was released on Amazon, in both Kindle and paperback versions. What a tremendous "calling card" or "resume" this could be if I were to decide to apply for a solar engineering position today. (I'm quite happy working on my LucidBrake invention right now, thank you, although I'd be glad to entertain contract or consulting work.)

  If you speak as part of your professional life, having a book to sell at the back of the room is a proven way to increase your cash flow.

If you're looking for employment in a highly technical or professional position, having a book can move you to the front of the line.

If you're simply looking for a way to increase your visibility and credibilty in a professional role, having a book is the ticket.

There are many, many more options today for getting published fast, efficiently, cost-effectively, and in a way that you can have more control over than was possible in the past. There's a lot to learn, but lots of people are finding it easier and more beneficial than ever before. For getting started, I suggest checking out the economical online video lessons, or the all-day intensive seminars provided by EJ Thornton at Books To Believe In. She really knows her stuff, and her information will likely save you thousands of dollars when you hire editors, graphics artists, printers, and other service providers.

Microsoft and manhole covers

Many years ago, when I was visiting in the Microsoft Press offices, a discussion of strange employment questions came up. I had heard a story that Microsoft often asked interviewees if they knew why manhole covers were always round. It sounds silly, but there is important logic to round manhole covers - they're round so they can't slip through the hole in the street and cause real problems when they fall into the manhole.

Supposedly they asked this question to see how well people could think outside the box, and of course, programmers who could think outside the box were more desirable to Microsoft. I've never been asked this question about manhole covers by Microsoft or anyone else, but for several years now I've had my own unique answer ready to go. (Microsoft Press published quite a few of my books though, so I'm sure not complaining.)

You see, the standard answer is wrong! There are an infinity of manhole cover shapes that won't fall down the hole. Let me explain.

A circle has a constant diameter, no matter which way you turn it. A square lid, on the other hand, can be rotated such that its width is less than its corner-to-corner distance, allowing it to slip through the square hole in the street.  The theory is that any planar shape other than a circle will have some distance across it that is less that some other distance across it, so it can be turned to slip through its own hole.  But consider the shield shape shown here.

This shape is formed by striking three intersecting arcs with their centers at the corners of an equilateral triangle. The distance from any corner to any point on the far edge is constant, just like the diameters of a circle are all constant.  There is no way to turn this figure such that it can slip through a slot based on its shape, again just like with a circle.

What's more, instead of three equally spaced points to define the corners, we can use 5. Or 7. Or any odd number of points.  Here's what the 5 pointed shield figure looks like.

There are an infinity of figures we can form this way, although they quickly approach the shape of a circle as the number of points increases.

Pulling numbers into a range

In my recently published book, Sun Position, there are several astronomical calculations that result in angles well outside the range of 0 to 360 degrees. For example, there's a rather complicated formula for the mean longitude of the earth, or the number of degrees of angular travel for the earth as it orbits the sun, accurate for past, present, and future moments in time. The angle is calculated by a polynomial that returns a number that increases approximately by 360 for every year added to the input value. As a result, the angular position of the earth in its orbit around the sun is calculated as so many thousands of degrees, a number that's hard to work with.

The most straightforward way to convert this angle to something more usable is to repeatedly subtract 360 degrees until the result is brought into the range 0 to 360, although this is computationally inefficient. A better approach, and the one used most often, is to divide the large angle by 360, take the integer part of the result and subtract that number times 360 from the original value.

This technique works pretty good to bring large angles into the range 0 to 360, but sometimes, as in the case of an elevation angle, the range -180 to +180 is more appropriate. Also, in some calculations the angles are in radians instead of degrees, so ranges of 0 to 2*PI or -PI to +PI are more appropriate.

So, I decided to create a flexible function that could handle all these cases with ease. Here's the result, in Visual Basic syntax. It works very well...


Public Function Range(ByVal x As Double, ByVal rMin As Double, ByVal rMax As Double) As Double
   Dim delta As Double = rMax - rMin
   Return (((x - rMin) Mod delta) + delta) Mod delta + rMin
End Function


To use this function, pass it the number to be processed, the low end of the desired range, and the high end of the range. It works well with negative numbers, radians, degrees, or other number ranges. Here are a few examples...

Range(1234.56789, 0, 360) = 154.56789
Range(-456.7, -180, 180) = -96.7
Range(1234.56789, -3.1415926, 3.1415926) = 3.0635908
Range(1234.56789, 0, 1) = 0.56789