How images are made
Angular Resolution: Why Hubble Cannot See the Apollo Lunar Landers
Size alone does not decide what a telescope can see, and neither does distance. The angle between them does.
Two questions about Hubble come up again and again. Can it photograph the Apollo landers left on the Moon? And why are its pictures of Pluto so blurry, when it can produce a portrait of the Whirlpool Galaxy roughly 100 million pixels in size, even though that galaxy is unimaginably farther away? Both have the same answer, and it depends on neither size nor distance alone. It depends on the angle an object covers in the sky.
Above the blur of the atmosphere
Every telescope on the ground looks up through Earth's atmosphere, which shimmers and blurs fine detail. A side-by-side comparison of star-forming regions in the Whirlpool Galaxy, one from the WIYN telescope at Kitt Peak in Arizona and one from Hubble, shows the difference at once: the ground-based view softens the clusters into glowing patches, while Hubble separates them into knots and individual bright stars. Hubble orbits above the atmosphere and avoids that problem.
Even without the atmosphere, though, every telescope has a limit. Hubble has the highest resolution of any visible-light telescope, but there is still a long list of things it cannot make out.
Reading a road sign
Driving toward a sign on a highway is a good everyday model. Far away, only the sign's shape and color register. Closer in, it becomes clear that there is lettering, but the words cannot be read. Eventually the words snap into focus.
Nothing about the sign has changed. What changed is the angle the letters cover in the driver's view. An object of a given size subtends a smaller angle the farther away it is, and that angular size is what decides whether it can be seen in detail.
The observer's side of the equation is angular resolution, the smallest angle at which two points, or two details within an object, can still be told apart. Angles are measured in degrees, 360 to a circle; each degree divides into 60 arcminutes and each arcminute into 60 arcseconds. The human eye resolves about 1 arcminute. Letters on a sign become readable when they span a few times that, a few arcminutes.
Hubble's limit in arcseconds
Hubble's angular resolution is about one-twentieth of an arcsecond, 0.05 arcseconds, roughly 1,200 times finer than the eye. Anything that covers a smaller angle than that stays an unresolved point, like a sign too small and too far away to read even with the best eyesight.
Start with the Moon. At its average distance of 384,400 kilometers, 0.05 arcseconds corresponds to about 93 meters (101 yards), roughly the length of a football field. To show up as more than a smudge, an object on the Moon would have to be several football fields across. The Apollo landers are much smaller than a football field, far below that limit.
Hubble did photograph the Apollo 17 landing region in 2005, as part of a study of minerals on the lunar surface. The image shows the valley, its craters and its ridges. The landing site itself has to be marked with a symbol, because nothing left there by the astronauts is big enough to appear. The lunar module hardware was later photographed from close range by NASA's Lunar Reconnaissance Orbiter, which is covered in Why the Apollo Photos Can't Be Faked.
Why Pluto is only a few pixels wide
Pluto, at the closest point of its orbit, is about 30 times farther from the Sun than Earth, around 4.5 billion kilometers. At that distance 0.05 arcseconds spans just over 1,000 kilometers. Pluto is a little less than 2,400 kilometers across, so a standard Hubble camera captures it in barely more than two resolution elements. The surprise is that Hubble managed any surface detail at all.
The 1996 views above stretch to roughly 15 pixels across Pluto's disk because they came from the Faint Object Camera, part of Hubble from 1990 to 2002, when it was removed during Servicing Mission 3B. In its high-resolution mode the camera offered about seven times the resolution of Hubble's standard cameras. The trade-off was a very small field of view and sensitivity limited to green through ultraviolet light, so it suited small, faint targets like Pluto and could never have produced a picture like the Whirlpool Galaxy.
Why the Whirlpool fills 10,000 pixels
The Whirlpool Galaxy is far larger and far more distant than Pluto, and the comparison comes down to which factor wins. The galaxy is about 60,000 light-years across, medium-sized next to the Milky Way's 100,000. That is around 250 trillion times Pluto's diameter. Taking its distance as about 23 million light-years, it is roughly 50 billion times farther away than Pluto.
Size beats distance by a factor of 250 trillion divided by 50 billion, which is 5,000. If Pluto spans about two resolution elements, the Whirlpool should span about 5,000 times two, or around 10,000. The real mosaic is 11,477 by 7,965 pixels, very close to the estimate.
At the galaxy's distance, Hubble's resolution corresponds to more than 5 light-years, a coarse grain by any everyday standard. But since the galaxy is roughly 10,000 times larger than that, it is beautifully resolved. How the camera's field of view, a separate quantity from resolution, determines how many pointings a target needs is discussed in Fields of View.
The rule in one line
Physical size matters and distance matters, but neither decides on its own. Their combination, the angular size, set against the telescope's angular resolution, tells what can and cannot be seen. By that measure Hubble has no chance with the lunar landers, barely makes out Pluto, and shows the Whirlpool in exquisite detail.
Questions readers ask
Can Hubble see the flags or landers on the Moon?
No. Hubble's resolution of about 0.05 arcseconds corresponds to roughly 93 meters at the Moon's distance. The landers and flags are much smaller than a football field, so they fall far below what Hubble can separate. Orbiting spacecraft close to the Moon have photographed them instead.
What is angular resolution?
It is the smallest angle between two points that an instrument can still distinguish as separate. The human eye manages about 1 arcminute. Hubble reaches about 0.05 arcseconds, around 1,200 times finer, and it works above Earth's blurring atmosphere.
Why are Hubble images of Pluto blurry?
Pluto is small and very far away, so it covers a tiny angle in the sky. A standard Hubble camera spans it with only about two resolution elements. The 1996 Faint Object Camera images do better, with about 15 pixels across, thanks to that camera's special high-resolution mode.
How many pixels is the Hubble image of the Whirlpool Galaxy?
The full mosaic released in 2005 measures 11,477 by 7,965 pixels, close to 100 million in total. That fits a simple estimate based on the galaxy's size and distance compared with Pluto's, which predicts about 10,000 resolution elements across.