Science and Science Fiction: The Moons of Mars in Watchmen

March 28th, 2009

In the movie Watchmen, there is a scene that takes place on Mars and two large, round moons are visible in the sky.   Mars does have two moons, Phobos and Deimos, but they are not large, round moons.   Phobos and Deimos  are tiny, with an approximate diameters of 22km and 13km, respectively, and not exactly round.

Let’s figure out how large the moons should look in the Martian sky.    We can use  an angular size calculator, which is a little easier  today in the age of the internet perhaps than getting the rust off  high school geometry.     There are also simplified versions of the formula we use in astronomy, given that we’re dealing with objects so far away that subtend very small angles.   First, consider our own moon, which is largish in the sky and easily visible with surface features.   The moon’s orbit gives it an average distance of 384,400 km, and it has a diameter of 3,476 km.   From the second link above:

D = linear (physical) diameter
α = angular size in arcseconds
d = distance to object
206,265 = is required (arcseconds per radian)

This can be rearranged and solved for the angular size in arcseconds (1/3600 of a degree), which is then 206265 times the diameter divided by the distance.   For the moon, I get 1865 arcseconds.   Converting that to degrees, you get half a degree, which is coincidently about the same as the angular size of the sun (think about eclipses — the sun has a diameter about 400 times that of the moon, but the moon is about 400 times closer to us than the sun).

So,  now for the angular sizes of  Phobos and Deimos.   I mentioned the  diameters of  22km and 13km.   We need to know how far they are from Mars.   The semi-major axis of their orbits (they’re not quite circular) is 9  377 km and 23  460 km, respectively.   Now we can apply our formula.   The angular size of Phobos in the sky of Mars is then 484 arcseconds, and that of Deimos is 114 arcseconds.

From Mars, Phobos would look about a third the size of our own moon (actually a bit larger than I expected before I did the calculation — their orbital distances are not that large), while Deimos would be less than a quarter the size of Phobos, and less than a tenth the size of the Moon.

They also won’t look nearly as bright.   Sunlight is only about 44% as intense at Mars as compared to the Earth, and Phobos and Deimos are smaller mirrors than the Moon as we’ve seen above.

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