1 Introduction

Consider two simple facts, and the inescapable conclusion:

1. A constellation such as Orion rises by crossing the horizon, travels across the sky, then sets by crossing the horizon.¹ You can see this for yourself.²
2. There is such a thing as longitude. Suppose Orion is straddling the horizon in Atlanta at 9:00 pm EST, as shown in figure ‍1. At that time it will still be far above the horizon in Los Angeles. It won’t look like figure ‍1 until 9:00 pm PST, which is 3 hours later.

Figure ‍1: Orion Straddling The Horizon

Those two observed facts tell us the earth cannot possibly be flat. Here’s the reasoning:

Figure ‍2: Left: Star above red horizon and below blue horizon.  ‍ Right: Horizon same for everybody

2 Sequencing and Witnessing

Let’s look at how Orion moves.

Figure ‍3: Bellatrix 15^∘ Above the Horizon

We start with figure ‍3. Orion is in the center. The star Bellatrix is 15 degrees above the horizon. The star Betelgeuse is 7½ degrees higher. Let’s call this the 8:00 situation.³

Figure ‍4: Bellatrix 10^∘ Above the Horizon

Figure ‍4 shows the 8:20 situation. Bellatrix is now only 10 degrees above the horizon. Once again Betelgeuse is 7½ degrees higher.

Figure ‍5: Bellatrix 5^∘ Above the Horizon

Figure ‍5 shows the 8:40 situation. Bellatrix is now only 5 degrees above the horizon. Unsurprisingly, Betelgeuse is 7½ degrees higher.

Figure ‍6: Bellatrix Just Barely Above the Horizon

Figure ‍6 shows the 9:00 situation. Bellatrix is just barely above the horizon. Unsurprisingly, Betelgeuse is 7½ degrees higher.

Figure ‍7: Bellatrix Just 5^∘ Below the Horizon

Figure ‍6 shows the 9:00 situation, which is the punch line. Bellatrix is not visible, because it is below the horizon. Even so, we know exactly where it is, because Betelgeuse is visible 2½ degrees above the horizon, and Bellatrix is 7½ degrees below that, as always.

Let’s be clear: The stars we can see bear witness to the stars we can’t see.

Note: The diagrams in this section correspond to a viewpoint on the equator.

The reason for calling attention to constellations is discussed in appendix ‍A.

3 Video

Here’s a video of Orion setting across the western horizon.

In the video, the viewpoint is at 28^∘ south latitude, so the geometry is a little different from the diagram. The stars are still moving across the sky at a rate of 1 degree every 4 minutes; the only difference is that they are moving along a slight diagonal. In any case, the punch line is the same: The constellation sets by crossing the horizon. The stars we see bear witness to the stars we can’t see.

4 Stars are Well Behaved

Don’t try to tell me that the stars aren’t really below the horizon, and only appear to be so due to distortion. There is always "some" small distortion, but it so small that it is undetectable in the video. It is utterly irrelevant to this discussion. The fact is, the stars move across the sky like clockwork. The constellations maintain their size and shape as the rise, cross the sky, and set.

Actually it’s ironic to say that the stars move like clockwork. For thousands of years, if you wanted to check the accuracy of your clock, you checked it against the stars, which are far more accurate than any manmade clock ever made, until ultra-fancy atomic clocks came on the scene in the 1950s.

It cracks me up when some flatnik asks "Where are the stars?". The answer is, they’re in the sky. You should take a look some time. Watch the stars as they set below the horizon.

"Where are the stars?" You’ve got to be kidding. We know where the stars are. The Hipparcos catalog contains position data for roughly 118,000 stars, including all the stars you can see with the unaided eye, or even a modest-sized telescope. In nearly all cases the position is known very accurately, better than a millionth of a degree, a million times more accurately than you could judge by eye. Spare me the atmospheric blah refraction blah fisheye blah blah. We know where the stars are. https://www.cosmos.esa.int/web/hipparcos/catalogue-summary

*   A The Value of Constellations

Constellations are artificial and arbitrary and in some sense imaginary, but they serve a very real purpose: They are a way of visualizing and remembering the geometrical relationships among the stars. The stars and their relationships are entirely real.

Here’s why I recommend observing constellations rather than isolated stars, the sun, or the moon, especially for beginners:

1. Strength in numbers: There are hundreds of stars visible to the naked eye, and thousands of geometric relationships. In contrast, there’s only one moon. Remember the punch line: The stars you can see bear witness to the stars you can’t see.
2. Simplicity: You can go stargazing with minimal preparation. A few optional hints are discussed in stargazing.
3. Size: Orion is huge compared to the sun or moon. That means you can easily observe it, and easily understand what you’re seeing. Orion takes more than half an hour to completely cross the horizon. In contrast, the moon takes only a couple of minutes.

   It is perfectly OK to watch the moon rise or set; it’s just harder to draw conclusions from what you see. Any phase of the moon will do, provided it’s not too close to new.

   In each of the diagrams in section ‍2, near the lower-left corner there is a small magenta square. It is half a degree on a side. The disk of the sun or moon would fit snugly in that square. You can see that it’s really tiny compared to Orion. Therefore you might want to use a telescope, or a camera with a long lens, with a tripod. You have to take care with the timing and aiming. It also helps to take a series of pictures, with timestamps. That’s because the punch line is the same: The pictures of what you can see bear witness to what you can’t see.
4. Don’t mess with the sun unless you are sure you know what you are doing. You can do permanent damage to your eyes. You can do permanent damage to your telescope.

*   A Stargazing

Here are a few simple suggestions that may enhance your stargazing experience.

• Acquire a copy of H.A. Rey’s book The Stars – a new way to see them
• Also acquire a red light, so you can read the star charts while preserving your night vision. You can buy such things, or put a red filter over an ordinary flashlight, or just use your phone. Here is a web page that you can display on your phone that turns the screen red (reference ‍4.
• If you live in a place with too much pollution, you should go on a field qtrip. It will do you good. There are known good dark-sky stargazing sites within a 90 minute drive of every major city in the US. You can find them by googling. You could leave at 5 PM, drive for a while, stargaze for a couple of hours, and still be home by 10 PM.

*   B Southern Sequence

Figure ‍8: Bellatrix Above the Horizon

Figure ‍9: Bellatrix Nearer the Horizon

Figure ‍10: Bellatrix Even Nearer the Horizon

Figure ‍11: Bellatrix Just Barely Above the Horizon

Figure ‍12: Bellatrix Just 5^∘ Below the Horizon

*   Notes and References

1.

Provied you are at a reasonable latitude, not too near the poles.

2.

Provided it’s not too cloudy or too polluted.

3.

The actual local time at which astronomical events will be observed depends on the date, and on where you are situated relative to the timezone boundaries.

4.

Here is a web page that turns your screen red. It’s not an app; it’s just an HTML web page that’s all red. Save the page to your phone using the "offline reading" feature, so you can use it even in places where you don’t have internet connectivity.

It’s not very bright, but for stargazing you don’t need it to be very bright.

Double-click or swipe the screen to turn it on and off.

av8n.com/astro/red-screen.html