How Do Telescopes Work, and How Fast Does the View Slip Away?

A telescope works by collecting light across an aperture far wider than the human pupil, bringing it to a focus with a lens or a curved mirror, and handing the focused image to an eyepiece that magnifies it. Three numbers decide what the instrument can do: aperture diameter, which sets how much light arrives and how fine a detail can be separated; focal length, which divided by the eyepiece focal length gives the magnification; and focal ratio, focal length over aperture, which fixes how bright the beam leaving the eyepiece will be. NASA's Space Place page states the first rule in one line: "The bigger the mirrors or lenses, the more light the telescope can gather." Collecting area grows with the square of diameter, so a 130 mm mirror gathers 345 times the light of a 7 mm dark-adapted pupil.

The number that catches first-time buyers is printed on no box. NASA's Earth fact sheet gives the sidereal rotation period as 23.9345 hours: 86,164 seconds for a full turn of 1,296,000 arcseconds, so 15.04 arcseconds of sky slide past every second. At 90x in an entry-level refractor, that carries Jupiter from the center of the field to the edge in 66 seconds.

Aperture sets the ceiling, and two authorities disagree on where it sits

Light grasp is settled arithmetic. A 130 mm mirror has 3.45 times the area of a 70 mm objective lens, so it delivers 3.45 times the photons per second from the same star.

Resolution is where the sources part company. The Dawes limit, which William Rutter Dawes derived in the 1860s from double stars he could actually split, gives the finest separable angle as 116 divided by aperture in millimeters. The Rayleigh criterion, derived from diffraction physics rather than eyepiece work, gives 138. The 19 percent gap is how much of a dip between two merged star images each man accepted: about 4 percent for Dawes, 22 for Rayleigh. On a 130 mm mirror that is 0.89 arcseconds against 1.06. Retailers quote the flattering figure; Astronomics lists the Heritage 130 at "0.89 arcseconds."

The spec sheets check out against each other. Astronomics puts the Heritage 130's limiting magnitude at 13.05, Celestron's own page the AstroMaster 70AZ at 11.7. That gap of 1.35 magnitudes is a light ratio of 3.47 on the scale N. R. Pogson standardized in 1856. The aperture areas differ by 3.45: two manufacturers, working independently, reproduced the same constant to within one percent.

Magnification is a division, and the divisor has a hidden cost

Magnification is telescope focal length divided by eyepiece focal length, the formula Sky & Telescope prints in its guide for telescope owners. The Heritage 130's 650 mm tube gives 26x with its supplied 25 mm eyepiece; the AstroMaster 70AZ's 900 mm gives 45x with its 20 mm, the figure Celestron lists on the product page.

Pushing the divisor down has a limit, and the sources disagree on where it falls. Celestron advertises a highest useful magnification of 165x for the 70 mm tube. The workshop rule of 50x per inch of aperture, or 2x per millimeter, caps it at 140x. Equipment writers report a third ceiling over both: on an average night the atmosphere holds useful power near 200x to 250x whatever the aperture, with better conditions on fewer than one night in ten.

The cost shows up in the exit pupil, the width of the beam leaving the eyepiece, which equals eyepiece focal length divided by focal ratio. The Heritage 130 at f/5 with its 25 mm eyepiece produces 5.0 mm. The AstroMaster at f/13 with its 20 mm produces 1.56 mm, and with the 10 mm just 0.78 mm. Any beam wider than the observer's own pupil is wasted, and pupils shrink with age. Bradley and four colleagues at Texas Tech University Health Sciences Center measured 263 people with a NeurOptics pupillometer, publishing mean dark-adapted diameters in the Journal of Refractive Surgery in 2010: 7.33 mm at 20 to 29, 6.15 mm at 40 to 49, and 4.85 mm at 80.

What slips back, and how fast

True field of view is apparent field divided by magnification. Eyepiece makers publish apparent field by design: about 50 degrees for a Plössl, 40 for the simpler Kellners bundled with starter kits, 82 for a Tele Vue Nagler. Convert the true field to arcseconds, divide by 15.04, and the answer is how long an object near the celestial equator stays in view with no drive running, the condition of every manual mount.

| Setup | Power | True field | Center to edge | Full crossing | |---|---|---|---|---| | Heritage 130, 25 mm eyepiece | 26x | 1.92° | 3 min 50 s | 7 min 40 s | | AstroMaster 70AZ, 20 mm eyepiece | 45x | 1.11° | 2 min 13 s | 4 min 26 s | | Heritage 130, 10 mm eyepiece | 65x | 0.77° | 1 min 32 s | 3 min 04 s | | AstroMaster 70AZ, 10 mm eyepiece | 90x | 0.56° | 66 s | 2 min 13 s | | AstroMaster 70AZ at its rated 165x | 165x | 0.30° | 36 s | 72 s |

Figures assume a 50-degree apparent field; narrower Kellners cut every time above by a fifth.

The Moon makes the rate concrete. JPL's Horizons data, reproduced in the Lunar Fact Sheet, puts its mean apparent diameter at 1,868 arcseconds, or 31′08″, ranging from 29′24″ at apogee to 33′33″ at perigee. At 15.04 arcseconds per second, the Moon travels its own width across the sky in 124 seconds.

The rate falls with the cosine of declination, so a target 60 degrees north of the celestial equator crawls at half the equatorial pace and Polaris barely stirs. Everywhere else, a planet at 165x needs nudging back to center before the eye has finished dark-adapting to it.

Anyone can run the number before buying:

1. Divide telescope focal length by eyepiece focal length for magnification.
2. Divide the eyepiece's apparent field by that magnification for true field in degrees.
3. Multiply true field by 3,600 and divide by 15.04 for the seconds an equatorial target needs to cross it.

Mirrors instead of lenses, and the second thing that slips

Light in a reflector enters an open tube, strikes a concave primary mirror at the bottom, converges back up the tube and meets a small flat secondary set at 45 degrees, which diverts it out the side wall to the eyepiece. Sky-Watcher's Heritage 130 uses a 130 mm borosilicate parabolic primary at f/5.

NASA's Space Place gives the reason mirrors won: they are "lighter, and they are easier than lenses to make perfectly smooth," and a lens thick enough to be powerful starts absorbing the light passing through it. The same page names the trade: mirrors invert the image, and correcting that costs another surface.

What a retailer rarely mentions is alignment. Two mirrors held apart in an open tube drift out of collimation with handling, and a mirror warmer than the night air sends convection currents up its own light path. Sky-Watcher states that the Heritage's retractable truss holds collimation through the collapse cycle, a claim about that mechanism rather than reflectors generally. A refractor's sealed cell has nothing to align, offset by the false color a cheap achromat puts around bright objects.

A 70 mm refractor and a 130 mm tabletop Dobsonian at the same counter

Celestron lists the AstroMaster 70AZ at $199.95, Sky-Watcher the Heritage 130 at $305.00, which specialist dealers routinely discount below $250.

| Property | Dark-adapted eye | AstroMaster 70AZ | Heritage 130 | |---|---|---|---| | Aperture | about 7 mm | 70 mm | 130 mm | | Light collected, eye = 1 | 1 | 100 | 345 | | Focal length | n/a | 900 mm | 650 mm | | Focal ratio | n/a | f/13 | f/5 | | Finest detail | about 60″ (retinal limit) | 1.66″ (Dawes) | 0.89″ (Dawes) | | Faintest star | magnitude 6 | 11.7 | 13.05 | | Widest exit pupil | 7 mm | 1.56 mm | 5.0 mm | | List price | n/a | $199.95 | $305.00 |

The refractor's long f/13 tube reaches high power with cheap eyepieces and needs no alignment. The Dobsonian collects 3.45 times more light, splits nearly twice as fine, reaches 1.35 magnitudes deeper, and at 26x gives a 5 mm exit pupil that still fits a middle-aged eye, which is why it reaches galaxies and nebulae rather than only the Solar System. It weighs 20 pounds assembled against 10.8 for the Celestron kit, and needs a table.

How far a telescope sees is a question about angles, not distance

Nothing in a telescope reaches out. Aperture buys two things: photons enough to cross the eye's detection threshold, and a diffraction pattern small enough to separate two nearby angles. A galaxy millions of light-years off is visible because it is enormous and bright; a flagpole 384,400 km away is not.

Phil Plait, a professional astronomer who writes The Universe column for Scientific American, sets the scale: "At its best, Hubble's resolution is about 0.05 arcsecond—a very tiny angle!" At lunar distance, he notes, "Hubble's resolution surprisingly limits it to resolving objects no smaller than about 90 meters across." The Smithsonian's National Air and Space Museum records the Apollo lunar flags as 3 by 5 feet of nylon. A 5-foot span at 384,400 km subtends 0.0008 arcseconds. Splitting it would take an aperture of 142 meters by the Dawes rule and 169 by Rayleigh's. The largest ground telescopes under construction are 39 meters.

The atmosphere sets the real ceiling long before the optics do. Seeing, the blur imposed by air turbulence, runs 2 to 4 arcseconds at ordinary low-elevation backyard sites and reaches medians of 0.6 to 0.8 arcseconds only at professional mountaintops. On a 3-arcsecond night anything above 39 mm of aperture is already sky-limited: the 70 mm and the 130 mm hit the same wall, and the larger one merely gathers more light behind it. William H. Pickering of Harvard College Observatory built the 1-to-10 scale still used to log the condition, publishing it in Astronomische Nachrichten in 1892: a rating of 1 means the star image bloats to about 13 arcseconds, a 10 that the diffraction rings sit still.

Questions people actually ask

How does a telescope work simply?

A telescope gathers light over a wide lens or mirror and focuses it into a small, bright image that an eyepiece magnifies. Aperture sets how much light and detail arrive; telescope focal length divided by eyepiece focal length sets magnification. A 130 mm mirror collects 345 times the eye's light.

Why cannot we see the flag on the Moon with a telescope?

The Apollo flags measure 3 by 5 feet, per Smithsonian records, and at 384,400 km a 5-foot span covers 0.0008 arcseconds. Resolving that needs an aperture near 142 meters under the Dawes rule, 169 under Rayleigh's. Hubble's 2.4 m mirror resolves about 90 meters at the Moon.

Can you actually see planets with a telescope?

Yes. Jupiter's disk spans 44 to 50 arcseconds at opposition and Saturn's globe 16 to 21, both far coarser than the 1.66-arcsecond Dawes limit of a 70 mm refractor. At 90x a small telescope shows Jupiter's cloud belts, its four bright moons and Saturn's rings.

How are telescopes able to see so far?

Distance is not what limits them; angle and brightness are. A telescope collects hundreds of times more photons than the pupil, lifting faint objects above the eye's detection threshold, and separates finer angles than the eye's 60-arcsecond limit. Distant galaxies are visible because they are vast and luminous.

How do optical telescopes work?

Optical telescopes bend or bounce visible light to a focus. A refractor uses an objective lens; a reflector uses a concave primary mirror. Both form a real image at the focal plane, which the eyepiece magnifies. NASA's Space Place notes that mirrors are easier than lenses to make perfectly smooth.

How does a reflecting telescope work?

Light enters an open tube, strikes a concave primary mirror at the bottom, and converges back up the tube, where a small flat secondary angled at 45 degrees sends it out the side to the eyepiece. Sky-Watcher's Heritage 130 uses a 130 mm parabolic primary at f/5.