What Phobos tells us about our Moonby Matthew R. Francis 

Eclipses can be terrifying to people, even to those who know they can do no harm. The Sun’s light is dimmed or snuffed out when the Moon passes between it and Earth. The full Moon slowly diminishes only — in the case of a total eclipse — to reappear with an eerie red-orange tint. It’s no wonder eclipses are associated with doom in mythology, and why the early development of astronomy was often devoted to predicting eclipses.

The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the LORD come. — Joel 2:31

A major reason solar eclipses in particular seem frightening is because the Sun and the Moon appear to be nearly the same size in the sky. The Moon’s orbit around Earth is slightly tilted compared with Earth’s orbit around the Sun, so on most passes, it never passes directly between us and the Sun. However, when it does, the closeness of apparent size is enough that the Moon can sometimes appear to cover the Sun entirely — or nearly so.

The situation is different on Mars. Our neighbor planet has two moons: Phobos and Deimos, which are tiny compared to Earth’s Moon. Whereas the Moon’s diameter is a little more than a quarter of Earth’s diameter, Phobos is a potato-shaped lump of rock and ice only 27 kilometers across its longest side, and Deimos is about half that size. While the Moon is massive enough to churn Earth’s oceans and atmosphere as it orbits (which are the tides), Phobos and Deimos barely affect Mars … though the reverse isn’t true, as we’ll see shortly. Due to their shapes and compositions, Mars’ moons may be captured asteroids. However, the shape of their orbits and the weird density of Phobos indicates they may have formed from fragments blasted off Mars during the early history of the Solar System.

(Phobos and Deimos were the personifications of fear and terror in Greek mythology, who accompanied Ares or Mars, the god of war, into battle. They sometimes took the form of dogs, so when Shakespeare wrote “Cry havoc! and let slip the dogs of war”, he may have been referring to Phobos and Deimos. I was an English minor in college.)

Despite its small size, Phobos still can cause eclipses of the Sun, though never total eclipses. The images here, taken by the Mars Curiosity rover, show an annular eclipse, an event when the moon passes fully between Mars and the Sun, but doesn’t block all its light. So, if Phobos is so tiny, how can it cause eclipses? If the Moon is so small, how can it cause eclipses of the Sun?

The answer is perspective. If you hold your thumb close to your eye, you can block that eye’s entire field of view; if you hold that same thumb out at arm’s length, it blocks far less. In fact, at arm’s length, it appears to be nearly the same size as the full Moon and Sun in the sky. To put it simply, a small object can appear relatively larger if it’s close. The reasons can be seen using simple geometry.

Imagine a weird Solar System in which the Sun has only 3 times the diameter of the Moon. Since the average distance between the Earth and Sun is 1 astronomical unit (AU), let’s call the distance from Earth to the Moon “1 Moon unit” (MU), and the diameter of the Moon “1 zappa”. As the figure on the left shows, we can draw a triangle with Earth at one vertex and the Moon as the base. The apparent size of the Moon is the angle at the vertex where we are. (The size of Earth is irrelevant, since what matters is actually the size of a human eye—which is obviously far too small to worry about!) In this toy Solar System, the Sun is 3 zappas in diameter, so all we need to do to make it appear the size of the Moon is to add to the triangle without changing its angle. When the triangle is big enough that the Sun fits in the base, that’s the distance it needs to be from Earth—and that number is precisely 3 MU.

Similarly, if the Sun were 20 times bigger than the Moon, than it must be 20 times farther away to appear the same size. In the real Solar System, the Sun is 412 times the size of the Moon (412 zappas in diameter), and it is 395 times farther away from Earth (395 MU) on average, with a bit of variation due to the eccentricities of orbit. Therefore, the Sun generally appears very slightly larger than the Moon in the sky, but the difference in appearance is small enough to be insignificant most of the time.

So what about Mars and Phobos? Since Mars orbits about 1.5 times as far from the Sun as Earth does, the Sun appears about 2/3 as big in Martian sky. Phobos is only about 0.007 zappas on its longest side, which would make it virtually invisible if it orbited at one MU. However, its orbit is only 0.02 MU in size — which is barely above the top of Mars’ atmosphere, and smaller than Earth’s radius. That closeness makes Phobos appear to be about half the width of the Sun in the sky when everything is lined up.

The small orbit also will lead to doom in the future. Mars exerts a larger force on Phobos’ near side than its far side, which slows the moon down as it orbits. This difference is known as the tidal force, and (as you’d guess) it’s also responsible for the tides on Earth. However, for Phobos it’s a feedback process: the closer the moon gets, the stronger the tidal force, which slows it down more and brings it into lower orbits. Eventually the tidal force may be strong enough to pull the moon into pieces. (That was the fate of an icy moonlet orbiting Saturn — resulting in the planet’s beautiful rings.) We don’t know exactly when that destruction will be, partly because astronomers aren’t entirely sure what Phobos’ internal structure is.

Tidal forces acting on Earth’s Moon, in contrast, cause it to move slowly away from Earth, but at a rate of about 3 millimeters per year — not enough to make a noticeable difference in its apparent size over human history. That also tells us that the similarity in size between Sun and full Moon is a remarkable coincidence and nothing more.

The contrast between Phobos and the Moon helps us think about our own history and mythology. If Earth was orbited by a different kind of Moon, how would our planet be different? How would our culture be different? If eclipses were more common, or not as dramatic, would astronomy have been slower to develop in ancient times? How would our myths and religious tales differ? Phobos, a potato-shaped satellite named for the mythological personification of fear, shows us another world under another moon — and another perspective on our own Earth.

[Portions of this article appeared at Galileo’s Pendulum.]