Hubble's Universe Unfiltered

  • March 16, 2017

    Angular Resolution and What Hubble Can't See

    by Frank Summers

    The crisp, stunning images from the Hubble Space Telescope are a wonder to behold. As one can see in the image comparison accompanying this article, Hubble's views are significantly higher resolution than similar images obtained by ground-based observatories. (To really appreciate it, click on the image and examine the full resolution version.)

    Terrestrial telescopes must look through Earth's atmosphere, which blurs the view and limits their resolution. Orbiting above Earth's atmosphere, Hubble avoids that problem and can get a clearer view of the universe. However, Hubble still has limitations.

    While Hubble provides the highest resolution of any visible-light telescope, that resolution has a limit. There are many things in the universe that Hubble can't resolve, and the public is constantly curious about that boundary.

    One question that we often hear is whether Hubble can see the lunar landers left behind by the Apollo missions (short answer: no). We also get questions asking why Hubble has such poor views of nearby Pluto, when it can get almost 100 million pixels of the much more distant Whirlpool Galaxy. To answer questions like these fully, one must delve into a combination of size and distance called “angular resolution”.

     

    Reading the Signs

    Let's start with an example from everyday life. When driving along a highway, one can often see signs far in the distance down the road. At first, only the shape and color of the sign are recognizable. Then, one can tell that there is writing on the sign, but it is not possible to make out the words. Eventually, the words become clear enough to read.

     

    The signs on the near bridge are readable, while those on the far bridge are not.

     

    The physical sizes of the sign and its lettering do not change. The major change is the distance between the observer and the sign. At a large distance, the sign covers a very small angle in one’s field of view and cannot be read. When close, it covers a large enough angle to be readable. We say that an object “subtends” an angle that depends on its size and distance from the observer. That "angular size” is the important characteristic of the object in this scenario.

    For the observer, the important characteristic is called “angular resolution”. The angular resolution is a measure of the smallest angle at which the observer can distinguish between two objects (or details within an object). As you probably know, there are 360 degrees of arc in a circle. For measuring small angles, we divide each degree into 60 arcminutes, and each arcminute into 60 arcseconds. The angular resolution of the human eye is about 1 arcminute.

    The result is that, for the sign along the highway, the words become readable when the letters have an angular size that is several times larger than the angular resolution of the human eye. Hence, the angular size of the letters needs to be several arcminutes.

     

    Hubble's Angle on the Universe

    These same ideas apply to observations with the Hubble Space Telescope. Hubble has an angular resolution of about 1/20th of an arcsecond. That is a very small angle, but things in the universe can be very, very far away. Objects whose angular size is less than this value are not resolved by Hubble. They are like a cosmic highway sign that is too small and too distant for even Hubble to read.

     

    A comparison of the relative angular size, as seen from Earth, for the Moon, four planets, and two Hubble images.

    For scale, the Moon is about half a degree in angular size.

     

    Let's address that query asking whether Hubble can see the Apollo landers on the Moon. To be seen by Hubble, an object would need to subtend an angle greater than 0.05 arcseconds. The Moon is, on average, about 384,400 km away. At that distance, 0.05 arcseconds is equal to a size of 93 meters (101 yards), or the length of a football field.  An object on the Moon must be a few football fields in size, or Hubble cannot resolve it. The Apollo landers are much smaller than a football field, and too small for Hubble to see.

    Now, what about the images of Pluto and the Whirlpool Galaxy?

     

    Hubble images of Pluto (left) and the Whirlpool Galaxy (right).

    Note: these images are at wildly different physical and angular scales.

     

    At its closest point to the Sun, Pluto is about 30 times farther from the Sun than Earth, which is a distance of about 4.5 billion km. At that distance, an angular resolution of 0.05 arcseconds corresponds to a physical size of just over 1,000 km. Pluto's diameter is a little less than 2,400 km, making it a little more than 2 pixels in a standard Hubble image. The image above shows about 15 pixels across the diameter of Pluto. One should not be asking why the resolution is so bad, but, instead, why the resolution is so good!

    The extra resolution in the Pluto image is from the Faint Object Camera (FOC), which was part of Hubble's instruments from 1990 to 2002. (It was removed during Servicing Mission 3B.) Designed to see small, faint objects like Pluto, the FOC instrument had a high-resolution mode that provided 7 times the resolution of the standard Hubble cameras. The limitation of FOC was that it could provide such resolution over a very small field of view, and at shorter wavelengths (green to ultraviolet). As such, FOC was not suited to general purpose imaging, and could not take images like the one of the Whirlpool Galaxy above.

    The Whirlpool Galaxy is not only much, much bigger than Pluto, but also much, much farther away. Let's see how the size and distance factors play out in terms of angular resolution.

    The Whirlpool is about 60,000 light-years across, making it medium-sized compared to the 100,000 light-year diameter of our Milky Way. At that size, the galaxy is around 250 trillion times larger than Pluto. The galaxy's distance is about 23 million light-years, or about 50 billion times more distant than Pluto. The size difference (250 trillion) is larger than the distance difference (50 billion) by a factor of 5,000. Therefore, Hubble should get around 5,000 x 2 = 10,000 pixels across an image of the Whirlpool. The full resolution of the above image is 11,477 pixels by 7,965 pixels.

    Hubble's angular resolution at the distance of the Whirlpool Galaxy corresponds to a large physical distance: over 5 light-years. However, the galaxy is roughly 10,000 times larger than that, and is extremely well-resolved.

    Physical size of the object is important, but only part of the story. Distance to the object is also a factor, but not enough for the full calculation. The combination of physical size and distance, as expressed by angular size and angular resolution, is the important criterion for determining how well Hubble, other telescopes, or even the human eye will be able to see an object. Using these measures, one can tell that Hubble has no hope of seeing the lunar landers, will just barely discern Pluto, and can view the Whirlpool Galaxy in gorgeous detail. I hope we can now consider these questions resolved.