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Saturday, April 13, 2024

How Realistic Is the Celestial Navigation in Moon Knight?

The science in a superhero show doesn’t need to be perfectly accurate to be awesome. Really, one of the reasons we like these shows is because they aren’t realistic. However, that will never stop me from using a show to talk about physics.

Let's look at a scene from Moon Knight, episode 3. If you don’t know anything about Marvel’s newest character from the Disney+ live action series, don’t worry, I can give you a quick intro. Moon Knight is the human avatar of the Egyptian god Khonshu, the god of the moon. This gives him some superpowers, like extra strength and faster healing. But there’s a small problem: The avatar of Khonshu has a dissociative identity disorder. He has at least two different human identities—the mercenary Marc Specter and the businessman Steven Grant.

I won't include any significant spoilers, but still, use some caution if you are waiting to see this episode, which deals with celestial navigation. I’ll start with some very basic but important ideas about navigating with the stars.

How Do You Find Where You Are?

Today, we usually don't need to use the stars to find our way around. I mean, just take out your phone; it has a receiver for the Global Positioning System along with an internet connection to download whatever map you need. But before phones and GPS, people still had to get places. One way to do this was to use objects in the sky. Although it is possible to use the sun and moon (and even the planets) for navigation, I'm going to stick with the stars.

If you look at the stars at night, they appear to move. The stars that you see at 9:00 pm are in a different location by 2:00 in the morning. This is not because the stars actually move; it's because the Earth spins on its axis. Let me draw a super basic example. Suppose you are standing somewhere along Earth’s equator and you look at a star that is directly overhead. If you look again after two hours, it would look like this:

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In fact, all the stars in the sky seem to move together, as if they were part of a fixed sphere that has the same center as Earth’s. We call this the “celestial sphere.” I know it's difficult to visualize, so here's a picture of a celestial sphere model as used in astronomy courses:

In the celestial sphere model, every visible star, and even the ones you can't see, are directly above their own individual points on Earth. You could imagine drawing a line from a particular star down to the surface, so that there would be one-to-one mapping from this star to a single spot on Earth. In celestial navigation, this point is called the "geographical position" of a star. This is, in essence, the key to celestial navigation. If you know the star that is directly above you, then you know your location on Earth. If you don’t have a star directly overhead, you can use multiple stars and some basic geometry to determine where you are.

If the stars were stationary with respect to the surface of the Earth, things would be nice and simple. But remember, the stars seem to move, because the rotation of the Earth makes them appear to move in circles. These circles are centered around the rotation axis of the Earth, which you can imagine as a line that runs through the north and south poles. You can actually see these circles if you create a time-lapse photo of the stars at night. I tried to make my own:

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In the northern hemisphere, there's a star very close to this axis of rotation. We call that the North Star, but its real name is Polaris. If you were at the North Pole, Polaris would be directly overhead. However, as you move further south, Polaris moves closer to the horizon. At the equator, it would appear exactly at the horizon. This means that we can use the angular distance between the horizon and Polaris as our latitude on the Earth's surface. As an example, the latitude at the north pole is 90 degrees and in Chicago it would be 41.9 degrees.

That takes care of latitude, but what about longitude? This is a bit trickier. Since the stars are constantly moving, you need to know the location of a star at different times. That means you actually need to know the time. You really need a clock—a really accurate one—to figure out your longitude.

How Much Do the Stars’ Apparent Positions Change?

Let's review some important astronomy information: The Earth spins on its axis roughly once a day. It also orbits the sun once a year. In turn, the sun, along with all the other stuff in the solar system, moves in an orbit around the galactic center of our galaxy, the Milky Way. (Although our galaxy is also moving, that doesn't matter for celestial navigation. Pretty much everything that you see in the sky is in our galaxy.)

Since all this stuff is moving, do the stars change their position relative to each other—in other words, do they move on the celestial sphere? The answer is yes, but not very much. Each star is in its own orbit around the galactic center, and it's possible that they are interacting with nearby stars.

A star moving straight towards or away from the Earth wouldn't change its position (but it could change its brightness). The change in position depends on if that star moves in a direction perpendicular to our line of sight. We call this the proper motion. This proper motion would indeed change the shape of constellations in the sky, since different stars have different motions. But the change would be super tiny. In fact, you would probably never notice anything different in the shape of constellations over the course of your lifetime.

Stars also change their position in the sky because of parallax. Here is a quick demonstration of parallax that you can try at home: Hold your thumb out in front of your face at arm's length and close your left eye. Now line your thumb up so that it’s pointing at something far away. Next, close your left eye and open your right eye. Did you notice anything? Your thumb should be lined up at a different location and no longer pointing to the same object. This is parallax—the change in the apparent position of objects due to a change in viewing location, in this case from switching from viewing with one eye to the other.

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Our planet also changes positions. In six months, the Earth will go from one side of the sun to the other. This is a change in distance of almost 300 million kilometers, and it's enough to cause a noticeable apparent position change for some of the nearest stars. In fact, parallax is an important tool for measuring the distance to these stars. (Here are the other ways to measure stellar distances.)

So, yes, constellations change—but not that much.

Finding Your Longitude

Here’s how to find your longitude with a clock and a star chart. Let’s start with the star chart. Suppose there is a star on that chart that will always be directly above a point in Greenwich, England, at 4 am local time, which we would call Greenwich Mean Time. (I didn’t pick Greenwich at random. The prime meridian, or the 0 degree longitude line, runs right through the Royal Observatory Greenwich, so it’s good for measurements.)

Now let’s imagine that you are in another location and trying to figure out where you are by using that same star. You will need to know what time it is when that star appears directly overhead at your location. Hence the clock.

Checking the time reveals that, where you are, that star appears directly overhead at 1 am, instead of 4 am—three hours earlier than Greenwich. That means you are three out of 24 hours to the west of Geenwich. If you want to convert that to degrees, it would be (3/24) × 360 = 45 degrees. That would put you on a longitude line that runs through Greenland and Brazil. (Things can get a bit more complicated than this, since you likely wouldn’t have a star directly overhead, but you get the idea.)

Next, if you are in the northern hemisphere, you can use the North Star to calculate your latitude and determine your exact location on the planet, which is where those latitude and longitude lines cross. Hopefully, it’s not in the middle of the Atlantic Ocean.

What’s Wrong with Moon Knight?

Now it's time to talk about Moon Knight. (Some spoilers ahead.) In episode 3, Moon Knight, the earthly avatar of Khonshu, has teamed up with Marc’s wife, Layla. They are trying to find the tomb of the Egyptian god Ammit. If Ammit is freed, she will do some bad stuff to the human race, so they really want to get there first. They put together parts of a burial shroud to form an ancient star chart, and want to use this to find the location of the tomb, which is just like celestial navigation.

But there is a problem: This map was made 2,000 years ago, so the arrangement of the constellations is wrong. The stars have since moved to new positions. Since Moon Knight is the avatar of Khonshu, he uses his powers to move the stars in the sky back into the pattern shown when the map was created. Problem solved. Moon Knight and Layla are able to get to Ammit's tomb.

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Hopefully you can tell what's wrong with this scene: A map of the stars doesn't tell you the location of a spot on the Earth—at least not without a precise time.

Let's say that the map came with a time and date. If this time was off by just one second, which seems very plausible over the course of 2,000 years, that would lead to a longitude error of 0.004 degrees. At the latitude of Egypt, this would be a distance of 386 meters. That might be a small enough error to still find the tomb, but that doesn't even include the 27 leap seconds that have been added since 1972. (A leap second is a small adjustment to our clocks to take into account the non-integer number of days in a year. It's the same concept as the extra day in a leap year.)

Fine, but what's right about this scene? There are two things. First, the ancient Egyptians did indeed create star charts. However, these were probably used as a way to mark the dates of different religious events. They could also be used for the souls of the dead to find their way to the heavens.

The second thing that's correct is that the star chart would show slightly different constellation shapes compared to today's sky, due to the proper motion of stars. But you don't even need to be an Egyptian god to see what the stars looked like 2,000 years ago. You just need the internet. Personally, I like the web version of Stellarium, a free planetarium software that lets you change your viewing location and the date and time.

OK, so this episode of Moon Knight isn't scientifically perfect. Honestly, that's not a big deal, as it's still a great episode. But if you do want to change it, I have some ideas.

Option 1: An episode needs to give the characters an item to collect and a puzzle to solve. It can't be too complicated or too easy. And the star chart is a good puzzle, so you could improve the episode just by making the situation more accurate. Instead of having Khonshu change the sky to what it looked like 2,000 years ago, he could use his power to find the exact date and time that corresponds to the star chart. Then Layla could use her iPad to do real celestial navigation and find the location of the tomb (while telling Moon Knight about how they need to factor leap seconds into their calculations.)

Option 2: Toss out the star map all together. Instead, use a solar eclipse. Khonshu is the Egyptian god of the moon, and a solar eclipse occurs when the moon comes between the Earth and the sun. This casts a moving shadow along a portion of the Earth's surface. Because the moon's orbit is not a perfect circle, the size of this shadow varies with each eclipse. The width of the track of the shadow can be as wide as 267 kilometers (166 miles), but it can technically be any size smaller than that. The same is true for the time duration; an eclipse can last several minutes or just a few seconds.

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So, here is the plan. Moon Knight and Layla still find a burial shroud with some type of puzzle on it. They decode the puzzle and find that the location of Ammit’s tomb is the same as the location where the shadow from a specific solar eclipse fell, lasting just a fraction of a second. Now they can either use some means of calculating the location of this eclipse path or they could use the power of Khonshu. Either way, they can find the tomb.

Alternatively, they could know the date of a larger eclipse, but also know that it crosses some geological formation, like a river or mountain range. The intersection between the eclipse’s shadow and the river (or other geological formation) would give the tomb's location.

Both of these would give you a more scientifically accurate episode of Moon Knight—and they’d still be just as fun.


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