Phobos Annular Eclipse

NASA’s Perseverance rover was in the right place at the right time to capture this amazing video. It shows Phobos, the larger and closer of Mars’ two moons, passing in front of the Sun in what is called an annular eclipse. This occurred on April 2, 2022.

It wasn’t the first Phobos eclipse recorded by a Mars rover. Spirit and Opportunity captured the first photos in 2004. Curiosity was the first to capture video in 2019. But Perseverance, using its Mastcam-Z imaging system, recorded the highest magnification and highest frame-rate video to date.

Several interesting features are visible in this frame from the video:

The indentation near the bottom is Stickney Crater, named for Chloe Angeline Stickney Hall, wife of Asaph Hal, discoverer of Phobos. Here’s a non-silhouetted view with Stickney Crater at 5 o’clock:

Mt. Indeterminate is just barely visible in the shadows near the top. That’s not its official name, but I wanted make a point: When a moon is irregular in shape it’s difficult to decide what qualifies as a mountain. Is it really a “protrusion” or is it undisturbed surface surrounded by indentations? That’s why, on worlds like this, the IAU names the largest craters but rarely names mountains.

Additional Content for the Mathematically Inclined:

The eclipse recorded by Perseverance lasted only 38 seconds. On Earth, eclipses can last over 7 minutes. There’s several reasons for this disparity …

First, the Sun looks smaller from Mars. On Earth, the Sun’s apparent angular diameter is 0.5°. From Mars, 78 million kilometers farther from the Sun, it appears only 0.35° in diameter.

Second, Phobos is about 157 times smaller than our Moon. It measures only 27 × 22 × 18 km. Using its average diameter of 22.7 km, when passing overhead at an altitude of 5966 km its angular diameter is roughly 0.22°. By comparison, our Moon orbits at an altitude of 378,000 km and has an angular diameter of 0.5°.

So with an orbital circumference of 360°, and an orbital period of 2.76×104 s, Phobos will have an angular speed of: ω = 360° / 2.76×104 s = 0.013°/s (as viewed from the center of its orbit).

We can use ω to calculate the expected duration of an eclipse. Eclipse duration is usually defined as the time between first contact and last contact, so we add the angular diameters of the Sun and Phobos and divide by the angular speed:

ΔT = θ/ω = (0.35° + 0.22°) / 0.013°/s = 44 s

In the video Phobos doesn’t track across the Sun’s full diameter, so the eclipse duration is less than 44 s.

There’s an additional factor that affects the duration of a Phobos eclipse: elevation above the horizon. We used ω = 0.013°/s in our calculation, but that value is for observations from the center of Mars. Seen from the surface, its speed would change as it moves through the sky. Nonetheless, this geometric simplification provides a quick approximation for ΔT.

When observing from the surface, the distance between Phobos and the observer changes significantly. When near the horizon Phobos is 50% farther away (compared to when overhead), so it appears to move more slowly. When near the horizon Phobos also appears 50% smaller (compared to overhead). Finally, its motion near the horizon is not perpendicular to the line of sight (as it is when overhead), so some of it’s motion is toward the observer reducing its apparent speed. All these factors affect the duration of an eclipse.

We see this illusory speed change even more so with the ISS. It orbits with near-constant speed (7.3 km/s) at a much lower altitude than Phobos — 400 km compared to 5966 km. Next time you go out to spot the ISS note how when it first appears low in the sky it moves slowly. Then, as it climbs to its highest elevation, it appears to speed up. Beyond that it appears to slow down.

Next Week in Sky Lights ⇒ Phobos Speed Illusion

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Q&A: Phobos Speed Illusion