Crater/Dome Illusion

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Vesper Shines in the Evening Sky

5256732620_130024e956_bAny clear night through early March, look to the western sky shortly after it gets dark. You can’t miss that extremely bright “star.” Some have mistaken it for the landing lights of an incoming plane, and in the past it has even been reported as a UFO. It is very bright, and for folks who do not ordinarily look at the sky, it may seem unnatural. But it is very natural.

To the ancient Romans, this brilliant star-like object was “Vesper” when it shone in the evening sky as it does now. When seen in the morning sky, it was called “Lucifer,” the bearer of light.* To us, it is the planet Venus.

Venus is the third brightest astronomical object in the sky, after the Sun and Moon. It outshines all other planets and stars. Under the right conditions, it can even cast a shades. In fact, it is so bright that experienced observers can actually see it in broad daylight.

You really can’t miss Venus if you look in the right direction (West) and the right time (around an hour after sunset). Look soon, though, because its orbit causes it to oscillate from one side of the Sun to the other. Right now it is on the eastern side, meaning that it trails the Sun and remains for a short while after sunset in the western sky. But by late March it will be too close to the Sun to be seen, set to emerge in the predawn eastern sky in early April.

Venus is the closest planet to Earth, beating out Mars by about 10 million miles when each are at their closest points (about 25 million miles for Venus and 35 million miles for Mars). But the actual distance changes all the time. For example, on February 15, 2017, Venus is about 40.5 million miles from Earth. Mars, which currently appears nearby in the sky, is at about 181 million miles away at the same time!

Even when they are at nearly the same distance, Venus outshines Mars because it is covered by bright white clouds. And always being closer to the Sun, the reflected light is brighter.

[The image used here is by Tavis Jacobs and used under Creative Commons licensing. It shows a predawn view of Venus above Haleakala in Hawaii, on November 23, 2010. Although at a different location and time, it represents well its appearance in the western sky after sunset right now. The main difference is that you will not see the bright star above and to the right of Venus. That is Spica, one of the brightest stars in our sky. Right now, the planet Mars is nearby (slightly above and to the left of Venus), but much fainter and somewhat difficult to see unless the conditions are right.]

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How’s Your Altitude (and Azimuth)?

geograph-3960153-by-JaggeryAstronomers use several different coordinate systems to specify the location of objects in the heavens. Some are useful for use with small telescopes, but can be hard to visualize. The oldest and simplest, called Altitude and Azimuth, is no longer generally used by professional astronomers except in some very specific applications. However, because it is easier to visualize, it is the system used for my courses.

Azimuth is all about what direction (“cardinal point direction”) you are facing when you observe something. Analogies for azimuth usually compare it to a compass or clock face. Imagine that you have a large compass, maybe 10 or 15 feet across, laid out on the ground and aligned to North. The compass needle points North and the dial is turned properly to align the compass dial with the needle. Now imagine that you can stand right at the very center of the compass. If you align yourself with the North side of the needle, you will be facing North. In azimuth, we call that 0 degrees North, or more usually, just 0 degrees azimuth.

Then if you turn one quarter turn to the right (“clockwise”), you will be facing East. A one-quarter turn in a circle is 90 degrees, so we call this “90 degrees azimuth.” (As an aside, we say that the sun rises in the East, but only a couple of times during the year will it be exactly at 90 degrees azimuth as it rises. Here in Colorado it runs from about 60 degrees azimuth on the first day of summer to about 120 degrees azimuth on the first day of winter.)

Another quarter turn (90 degrees), brings you to due South. Now from North, that is 90 plus 90 or 180 degrees, so we are at 180 degrees azimuth.

Keep in mind that there are many intermediate values. For example, you could face 40 degrees or 55 degrees or 135 degrees 160 degrees and so on. I will expect your estimates to be reasonably accurate to the nearest 5 degrees, so something like 87.3978 degrees is simply beyond anyone’s ability to estimate just with the eye, and if I were to see an estimate like that, I would know that it did not come from this method.

OK, from due South, another quarter turn brings us due West, which is 90+90+90 or 270 degrees azimuth.

As our last turn, another quarter turn of the circle or 90 degrees, brings to 360 degrees azimuth back to due North. Now, a circle has only 360 degrees, so by convention we don’t refer to it as being 360 degrees azimuth, but 0 degrees azimuth. Every time you come back around to North, it reverts to 0 degrees azimuth.

So what does this mean? When we specify the position of something in the sky, we need four bits of information. Azimuth or distance along the horizon is one of them. Let’ say that you go out some night to observe the Moon, you will be turned a certain number of degrees away from North. Let’s say that when you are facing the Moon, the point on the horizon that is directly beneath the Moon is where you want to estimate the azimuth. If that was halfway between due East and due South, it would be 135 degrees azimuth (90+45 = 135).

Now the Moon at this point is not directly on the horizon, but up in the sky, so we have to specify how far. That’s what we call “altitude.” (Sometimes it is also called “elevation.”) while azimuth counts 360 degrees clockwise from the North, altitude counts degrees from the horizon (0 degrees) to the point directly overhead, the zenith (90 degrees). You can’t go higher than directly overhead, so altitude cannot exceed 90 degrees. Let’s say that you estimate that the Moon is one third of the way from the horizon to the zenith. That’s one third of 90, or 30 degrees. So at this time, the Moon is at 30 degrees altitude, 135 degrees azimuth.

But that is not all. Notice that I mentioned “at this time”? The third piece of information that you must include in a position estimate is time. Why? At a particular time on a particular day, the Moon rises. Then (very) roughly 6 hours later it is in the southern sky. And roughly 6 hours after that, it is setting somewhere in the western sky. The Moon, the Sun, planets and stars all move across the sky constantly, so a position at 8:35 pm will not be valid at 9 pm. So you have to supply the time as well as altitude and azimuth.

So if you made your estimation of the position of the Moon at 8:35 pm on April 22, 2018, the description would be:

April 22, 2018, 8:35 pm, 30 degrees altitude, 135 degrees azimuth

Oh, wait. Sorry, we’re not quite there yet. Actually, “there” is important. You have to specify your location on Earth. That’s because the sky, and the position of things in it, vary according to your location on Earth. The positions of the Sun, Moon, planets stars are different for say, Quito, Ecuador is different from Denver. Normally for your class I would assume that you make your observation in the Denver area, but since I have students in faraway places, you do have to specify your location. So, finally, the correct description of your observation of the Moon would be:

Location: Denver, Colorado (you could use GPS coordinates, but they are not necessary for this activity.)
Date: April 22, 2018
Altitude: 30 degrees
Azimuth: 135 degrees

Obviously you would not always have to state it quite like that. It could be formatted differently (as in a table), but this is the complete description.

Image used under Creative Commons Licence

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Lies will not make “America Great Again”

Snap 2017-01-07 at 10.56.48

It is clear that all politicians lie or distort the truth to some extent, but it also is oh so obvious that Trump simply has no shame and no conscience. So many lies and complete fabrications just to get people to vote for him. When I was a child — back in the 50s that so many people today allude to when they think about a “great” America — I was taught that lying was wrong and that distorting the truth was the same as lying. I learned in Church that Christianity was devoted to the Truth and that “…ye shall know the truth, and the truth shall make you free.” (John 8:32)

It seems that today many have forgotten this, and that many in later generations never learned it. Today more than ever, people accept the lies that confirm what they want to be true, or perhaps just what the manipulators what us to believe. The real truth, contrary as it may seem to the trumped up and racist vision of a “great” America, is ignored, denied, distorted and even vilified. And to make it worse, we tend to get all our “news” from outlets that are nothing more than propaganda factories. The real news, from sources that aspire to the old-fashioned idea of unbiased journalistic integrity, are maligned and denounced as biased in favor of the “other side.”

I wish we could go back to a time when we had more confidence in our public figures. It was so long ago I do not remember much directly, but I have warm and fuzzy feelings for the 50s. And I always kind of liked Ike. I feel comfortable that he did not tell such major lies and that he truly had the best interests of the American people at heart. Of course, this is mostly after the fact, as I was in gradeschool then. But that was a time when, in my mind at least, America seemed happier.

Sadly, Trump is no Ike. We can’t go back to the 50s, but we can make America greater by making politicians responsible for their lies and distortions. It won’t be by sitting back and buying into the deception and lies. Something I read recently said that “nice people made the best Nazis” because they did not resist, they did not complain, they just let it happen because they were afraid. I do not think we are in that same situation, but there is a remarkable amount of fear and hatred in this country right now. If we let it continue, America will be “great” only for the rich and powerful. We all have an obligation to find the truth, and not just guzzle down the snake oil that feeds our often distorted idea of how things should be. Please, wake up America.

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“Landing” on a comet

Rosetta_at_Comet_Poster_landscape_node_full_image_2On Friday, September 30, 2016, the Rosetta space probe will crash land on a comet. It is not the first time a mission has landed on a small solar system body. In fact, 15 years ago, on February 12, 2001, NASA spacecraft NEAR*, touched down on the surface of asteroid EROS. It was not originally intended to land, but controllers decided to take it down to get closer and closer images of the surface, knowing that contact with the spacecraft would soon be lost anyway. It sent back photos from as close as a few meters from the surface, but contact was lost on touchdown.

Philae_close-up_node_full_image_2Then just two years ago in 2014, a small probe called Philae, a lander from the very same  Rosetta mission, scheduled to contact the the comet on Friday, “soft” landed on the surface of a comet for the first time. In this case, Philae was designed and intended to land, which it did, although with complications. Photos and other data were received, but contact was spotty and was lost permanently a few months later.

Now, this week, the Rosetta mothership itself also will touch down on comet (67P/Churyumov–Gerasimenko), although like the NEAR-Shoemaker probe, it was never designed nor intended to do so. It will take photos and readings on the way down, but all contact is expected to be lost with first contact with the surface of the comet. It may be more accurate to refer to the “landing” as a controlled impact.

67PChuryumovGerasimenkoToo far and faint to be seen in Earth-telescopes, the comet and spacecraft are passing through the area of sky between Spica and Gamma Virginis in the constellation Virgo. (For northern observers, this area of sky sets very shortly after sunset.) The comet and probe will be roughly 719 million kilometers (447 million miles) at the time of spacecraft impact.

The “collision manoeuvre” will begin at  20:50 GMT on Thursday, September 29. That’s 2:50 pm MDT or 4:50 pm EDT. The slow descent will take about 14 hours, with the expected cometary contact within 20 minutes of 10:40 GMT on Friday. This is 4:40 am MDT or 6:40 am EDT.  You can follow this online here:'at_region

The cometary nucleus is approximately 4.3 by 4.1 km (2.7 by 2.5 mi) in size, and composed primarily of dust-covered ice. 67P/Churyumov–Gerasimenko is a short period comet, reaching its closest point to the Sun every 6.45 years, although never getting bright enough to be seen without a telescope. In fact, in its current orbit it never gets as close to the Sun as the Earth, and is essentially just a cometary nucleus without a visible coma or tail. Its orbit has been significantly altered by the gravity of Jupiter, but it likely originated much farther out in the Kuiper Belt.

(All images courtesy of the European Space Agency, ESA)

* Near Earth Asteroid Rendezvous, later rechristened NEAR-Shoemaker in honor of pioneering Earth-space science Eugene Shoemaker

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The Equinox: When day and night are not equal

Let’s try this again…. this was originally posted on September 20, 2012, but it is completely valid today with slight changes to the date and time.

A lot of people know that on the Equinox, every location on Earth is supposed to get 12 hours of daylight. In fact, the term “Equinox” means “equal night,” signifying that the period of night should equal the period of daytime, and since the day is 24 hours long, we should have 12 hours of each. This year, the September Equinox occurs at exactly at 8:21 a.m. MDT on Thursday, September 22 (2016). At that moment, Autumn or Fall begins for the Earth’s Northern Hemisphere. [Note that I avoid calling it the “Autumnal Equinox” simply because that is true only for half of the Earth. In the other half, the Southern Hemisphere, the same event marks the transition from Winter to Spring.]

MWSnap150 2012-09-20, 09_47_30So it might be expected that September 22 would have exactly (or almost) 12 hours of possible sunshine and 12 hours of night. But it doesn’t. A simple check of sunrise and sunset times will show that there are more than exactly 12 hours on that date. In Denver, the Sun rises at 6:48 a.m. and sets at 6:56 p.m., with each time rounded to the nearest minute. This yields 12 hours and 8 minutes.

In reality, no day has exactly 12 hours of sunshine. In Denver, the day that most closely matches this is September 25 this year. (It changes a bit from year to year, due mostly to the Leap Year cycle). Rounded to the nearest minute, the Sun rises at 6:51 a.m. and sets at 6:51 p.m. on September 25th in Denver. Much the same is true for other cities. (See link below.)

So are astronomers, who normally are very accurate, wrong on this one? Is the Equinox really on the 25th this year?

No, the astronomers are correct. The Equinox occurs at  8:21 a.m. MDT on Thursday, September 22 (2016).  Astronomy is an observational science, but in this case, observations can be misleading. The times of sunrise and sunset are given for the apparent rise and set times. In other words, given clear skies and an unobstructed horizon, the times given are those that the Sun would be seen to rise and set. The key word here is “apparent.”

The fact is that the Sun appears to rise a few minutes before it actually crosses the eastern horizon, and stays in the sky a few minutes after it has, in fact, disappeared below the western horizon.

The reason lies with the Earth’s atmosphere, which bends the sunlight around the horizon. It is somewhat like peering around the corner with a periscope. The atmosphere bends the Sun’s light around the horizon slightly, such that the Sun appears in the East a couple of minutes before it actually rises. In the evening the reverse happens – the Sun’s light is bent around the horizon to cause the Sun to remain visible for a few minutes after it has really dipped below the western horizon.

This is known as refraction, a fancy way of saying bending, due to the atmosphere. It is the same effect that causes a pencil stuck in a glass of water to appear offset slightly. Truth is, when you sight along the horizon, you are looking through much more atmosphere then when you look high in the sky. Because of this, the refractive effect is much greater near the horizon, even allowing objects that are technically just beyond the horizon to appear.

Thus on the day of the Equinox the theoretical period of sunlight is 12 hours, but because of this refraction or bending of sunlight around the horizon, the apparent day is longer.

However, at this time of year the days are getting shorter. So a few days later, when the theoretical period of sunshine should be significantly less than 12 hours, the lengthening due to refraction brings it up to 12 hours even (or almost).

So the Equinox occurs on the 22nd, but the day with 12 hours of sunshine comes 3 days later. (Again, this can vary a bit with geographic location…. for example, in Houston it is on the 26th). In the Spring, the opposite effect occurs. As days get longer, the observed equinox comes a few days before the official Equinox.

(If you are not lucky enough to live in Denver, you can compute the rise and set times for your location from this US Naval Observatory page:

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Think that you are “bad” at math?


You are not bad at math

Are you one of those people who tell yourself that you are “bad” at math? Does just the thought of numbers cause you to seize up and maybe start foaming at the mouth?

Relax. You are not bad at math. You have just talked yourself into the belief. Teachers and others may have let you believe it, or may even have encouraged this self-defeating behavior. I do not know why. It’s kind of ridiculous. I’ve even had students seem almost proud of their self-proclaimed ignorance of math (and science). The truly sad thing is simply that anyone would want to think like that.

Apparently there are primary and secondary school teachers and even college instructors who undermine students’ confidence in their math abilities by claiming and displaying their own hatred and contempt for math. This is amazing and very disturbing. If you have ever had such a teacher, I am here to tell you that they were wrong. Math is not some horrible invention of the devil. Instead it is one of the greatest accomplishments of humankind.

Personally, I’m not “bad” at math. I am certainly not a “whiz” at it either, but basic math is simple, easy and oh, so useful. Every adult American — every adult anywhere — should be able to perform simple addition, subtraction, multiplication and division in their heads. I can, and so can you.

You are not “bad” at math. You have talked yourself into the belief. It is a self-fulfilling prophecy. Certainly you can do the math I require for my classes. I don’t require much, and I won’t require anything more than you can handle. But if you continually tell yourself that you can’t, then your mind will accept that assessment and make sure that you get the wrong answers or just give up in despair. That is too bad, because you are better than that. You are smarter than that.

I do not intend to turn this into a pep talk, but I do want to point out this fact and drive it home:

You are not bad at math

Want more? Check out this article from the Washington Post: “Stop telling kids you’re bad at math. You are spreading math anxiety ‘like a virus.’”

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