Telescope light gathering power and resolution

Exploring two key properties of telescopes: light-gathering power and resolution. These attributes, determined by the objective's diameter, affect how faint objects can be seen and how well close stars can be resolved. With a focus on practical examples, such as comparing the human eye to an 8-inch telescope, let's outline the significance of telescope design in observing faint stars and double star systems.

The influence of objective diameter on telescope light gathering power and resolution

The objective determines two properties of a telescope uniquely: light gathering power and resolution. Light-gathering power often makes more sense when described in terms of limiting visual magnitude, i.e., how faint you can see shown in the table below (theoretically). Your unaided eye can “theoretically” see stars brighter than sixth magnitude i.e., a limiting visual magnitude of 6. A telescope, because of its larger objective lens diameter, has greater light-gathering power and aids your eye to see a fainter (higher) limiting visual magnitude. You can contrast the light-gathering power of your unaided eye against that of an 8-inch diameter objective (typical of many amateur telescopes) by comparing their collecting areas:

The pupil of your eye has, upon full dark adaptation, a diameter of about 6.3 mm (1/4th of an inch) for a collecting area of 31.7 mm2. An 8-inch diameter objective (196 mm) has a collecting area of about 32,400 mm2. The ratio of the two collecting areas i.e., divide 31.7 into 32,400 to get 1024  means an 8-inch telescope has a collecting area 1024 times bigger than your eye and aids your eye to see 1024 times fainter. A ratio of 1024 times corresponds to a magnitude difference of 7.5, added to the to the limiting magnitude of the unaided eye (6) to get the limiting visual magnitude for a 8-inch diameter telescope of 13.5

Properties of the objective

The last column in relates the diameter of an objective to its resolution; its ability to show two stars as two distinct objects instead of one (think of how a distant car's two headlights appear as one). Objectives focus stars into small blurred disks not into the pinpoints of light they seem. The bigger the objective, the smaller the blur disks and the closer two star images can be and still be seen as two (see above). In As objective diameter goes up, theoretical resolution (the closeness at which two stars are recognizable as two) gets better. The equation for theoretical resolutions for any objective is:

Resolution = 138" / objective diam in millimeters

Resolution is measured in ", otherwise known as arc seconds or 1/3600ths of a degree. Below is a list of double stars (stars that orbit around each other) that progressively have less and less separation (smaller “ of arc distance from each other). Observe each one and sketch it in the space provided. Use progressively higher magnification eyepieces as you work your way down the list starting with 25mm to get the best chance of seeing them resolve. These pairs have been selected to be just about equal magnitudes. For a faint star next to a bright star, like Sirius and its pup, even though they are well separated, right now (about 10”) higher power will be needed to see the pup in the glare of Sirius.

Light gathering power and resolution worksheet

Compare that to the theoretical resolution for your telescope’s objective from the table above