Pinpoint Stars

You are here: Nature Science Photography – Natural light – The stars

The light of the stars is not enough to illuminate a landscape as recognizably as the full moon, but the multitude of small dots in the sky can enliven a night shot in an exciting way. But because the terms are so often thrown around, let’s first define what we’re talking about. Stars are in contrast to planets (e.g., the earth) self-luminous objects, i.e., suns. Physical processes within stars cause them to emit various forms of radiation, including visible light.

But how can we make creative use of them? Firstly, just as astronomers use them to draw scientific conclusions, we can represent them as the point sources of light that we ourselves perceive. To avoid confusion, their type of photography, known as Astro- or Deep Sky photography, utilizes large telescopes to explore the universe in depth. But this volume-filling special field shall not be our topic here. Instead, our goal is to focus on creating a well-designed shot using the equipment we already have in our backpacks. A mundane approach? – Perhaps. But such a faithful reflection of our nature is at least as legitimate.

Only self-luminous celestial objects, like our sun, are scientifically correctly called „stars“. All other celestial objects, known as planets, appear to us as bright points in the night sky solely due to their reflection of starlight.

Photographing the stars in the majestic form in which they present themselves to us in a clear night sky is no simple task. After all, our earth rotates inexorably, causing the apparent motion of the sun and all the other celestial bodies in the sky. Therefore, we are „somewhat“ limited as far as the most important parameter of a photograph, the exposure time, is concerned. To determine the measure of this limitation, we need some mathematics.

Preparatory calculations and a little astronomy

The earth rotates around 360° in a 24-hour period. If the camera fails to track this constant movement, the stars consistently appear as arcs or lines, a motif we will explore in the following section. Therefore, the most important question is how long the star track in the finished picture may be at most in order to be still regarded as a sharp point. With this specification, the calculation of the exposure time is an easy matter.

First, determine how large the finished image should be (plan a number too large if you like) and then calculate the magnification scale of the negative/slide/digital image (i.e., a factor of 10 for a 35 mm original and final size of 24×36 cm). Then decide the maximum length of a star trace that you can still tolerate in the finished print (1 mm is usually acceptable) and divide this value by the magnification factor (1 : 10 = 0.1 mm) to determine the largest movement value for the original picture (motion value). We then convert this value to an angular measure to determine the potential movement of the object in the sky during the exposure. To do this, we divide the motion value 0.1 mm by the focal length used, e.g., 200 mm (0.1 : 200 = 0.0005 mm), then determine the arctangent (arctan 0.0005 = 0.0286° – note that your electronic calculator is in a mode where it accepts input in alt degrees DEG for this purpose), and convert the degree value into angular minutes (1 degree = 60 minutes, so 0.0286° x 60 = 1.716 angular minutes). Now we must determine only the time, which the celestial vault needs, in order to move apparently around these 1.716 angle minutes. This apparent movement is 360° in 24 hours or 15° in 1 hour or 1° in 4 minutes or 1′ in 4 seconds. So 1.716 angular minutes are traveled in 1.716 x 4 = 6.864 seconds, and that is the longest possible exposure time to image „sharp stars“ at the underlying values. The time calculated in this way applies to stars at the celestial equator, and this is important because the stars travel through orbits of different distances depending on their angular distance from the celestial equator (declination). For us, this means that depending on the section of the sky, we have star orbits with different radii on the image, and we have to tailor the exposure time to the declination and the focal length used (the fact that longer focal lengths intensify the apparent motion, as we have already learned above in connection with the moon).

Let’s have a look at Figure 42 for explanation. On the basis of the diurnal arcs of the sun, it can be seen that in the depicted position of Central Europe (about 50° North), the sun describes in every season orbits of the same size, which intersect the horizon at a slightly shifted place and which differ only in the size of the part lying above the horizon. North and south of these arcs, we also find orbits that are so small that they are above the horizon at any given time. We refer to the stars in these orbits, which neither rise nor set, as circumpolar stars. The North Star, also known as Polaris, stands out as the most prominent example of this genus. It accurately marks the celestial north pole, hovering only 0.8° away at the start of the 21st century, creating a circle that is barely visible to the unaided eye. In a few hundred years, however, another star will mark the celestial north pole because the earth’s axis is subject to a rotational motion called precession, and so in about 25,800 years it will describe a complete circle in space. Astronomically, circumpolar stars are defined as celestial bodies whose declination is greater than or equal to 90° minus the latitude of the observer, in our case 90°-50° = 40°.

The angular distance of the north and south celestial poles above the horizon, both of which lie in the extension of the earth’s axis of rotation, corresponds to the latitude of the observer, in our example 50°.

Therefore, stars near the celestial equator move on a larger orbit than those farther away, necessitating a greater apparent motion in a given time. So, strictly speaking, we must also take this factor into account when calculating the exposure time as follows (set your calculator to the correct mode; the angle argument is entered in Alt degrees DEG):

Formula 1

T = The maximum exposure time
L = The length of the longest tolerable star movement in mm
E = The degree of enlargement of the original image
F = The focal length of the lens used in mm
D = The angular distance of the star from the celestial equator, the 
declination, in degrees

If, as is often the case, you do not know the exact value of D, you can safely do without the division by the cosine of D or proceed according to the first method and then obtain the maximum permissible exposure time for a star at the celestial equator. Since the movement of the objects in this area of the sky (declination 0°) is, as said, the largest, I would advise to always make the calculation in this way in order to be „on the safe side“ for the large part of the sky captured with a wide-angle lens with the resulting shorter exposure time. The table gives some hints concerning the exposure time for still stars in relation to focal length and declination:

Focal lenght	Stars near the celestial equator	Stars at approx. 45° declination	Stars near the celestial pole
18 mm	45 sec	60 sec	120 sec
28 mm	25 sec	40 sec	90 sec
50 mm	12 sec	20 sec	45 sec
100 mm	5 sec	7 sec	16 sec

Longer exposure times, which nevertheless should image the stars point-like, require the camera to follow the earth’s rotation. You can either place the camera directly on an electrically driven sled or mount it on an appropriately equipped telescope (equatorial mount) to achieve this. You can build a simpler version of these platforms yourself. For this purpose, a screw pushes apart two wooden plates connected by a hinge, allowing them to follow the earth’s movement when the entire structure aligns precisely with one of the celestial poles. Such a device allows for exposure times of 10 to 15 minutes without the stars leaving streak marks. You can find instructions for these devices, also known as „Barndoor Tracker“ or „Scotch Mount,“ on the web by searching for these terms.

Have you noticed anything up to this point? – Right. There is no mention of the aperture setting or the film speed. Hard to believe, eh, but up to here these settings are not relevant yet because they are not related to the fixation of the stars against the rotation of the earth. These settings primarily determine the brightness of the stars in the final image. The larger the aperture and the more sensitive the film, the brighter the image of the stars and the more faint stars are imaged.

The Greek astronomer Hipparchus noted more than 2000 years ago that the stars differ in their apparent brightness, seemingly due to their varying distances. According to his perception, he divided the points in the sky into magnitude classes (mag) and called the brightest stars „1st magnitude stars“ and the faintest ones, which he (and also we) could just see with the naked eye, „6th magnitude stars“. The refinement of this brightness classification continued over the centuries. For instance, the telescope’s invention necessitated extending the scale beyond the 6th magnitude, as even the initial modest instruments could detect fainter stars. Modern large telescopes can observe the faintest stars with a brightness of the 30th magnitude class. These instruments also led to the realization that the brightest stars in the sky and some planets are brighter than 1st magnitude, which is why the 0th, -1st -2nd etc. magnitude was introduced. The brightest star in the night sky is Sirius, with -1.46 mag. Jupiter and Mars can reach -2.8 mag under favorable conditions, and Venus can reach -4.4 mag. The full moon makes it to -12.7 mag and the sun reaches -26.8 mag. The exact measuring methods of the 20th century brought moreover the realization that the magnitude class is not an arbitrary unit. It was found out that two stars A and B, whose brightness differs by exactly one magnitude, differ in their radiation intensity by a factor of 2,512. If star A is two magnitudes brighter than star B, their radiant intensities differ by a factor of 2.512 x 2.512 = 6.310.

But since stars are point light sources whose light does not spread out with increasing length of the focal length, the f-number actually plays a minor role in contrast to the extended objects of our everyday life. What truly matters is their effective diameter, which is determined by the ratio to the focal length:

Formula 2

d = Effective diameter of the aperture
f = Focal length
k = Aperture number

For example, a 1:2.8/28 mm lens has a maximum effective aperture of only 10 mm (28 : 2.8), while a 1:2.8/135 mm lens has a maximum effective aperture of 48.2 mm (138 : 2.8). A shorter focal length must therefore be faster or be used together with higher-sensitivity film in order to achieve the same imaging performance with respect to the brightness of the stars as optics with a longer focal length.

Practically, this means that we have to a) use film sensitivities of at least ISO 400 and, in any case, work with an open aperture (the more sensitive, the brighter the imaged objects. Material with ISO 3,200 still shows quite fine nebulae) and b) that, provided all other variables remain the same, doubling the sensitivity or opening the aperture by 1 stop allows us to image stars that are about 1 magnitude fainter.

Then there is the effect that brighter stars appear larger on a photo than fainter ones. This is no imagination but has solid reasons. First of all, even the heaviest and most stable tripod always transmits a certain amount of vibration, which moves the point of light somewhat around the central point. Secondly, the earth’s atmosphere scatters the light, preventing it from striking the same point on the image carrier, resulting in a slight enlargement. And third, the light also vagabonds around within the sensitive layer of the film, exposing silver nuclei that are slightly off. This phenomenon, known as halation, is largely, but not entirely, prevented by special protective layers.

Next Startrails

Main Natural light

Previous Equipment and shooting technique

If you found this post useful and want to support the continuation of my writing without intrusive advertising, please consider supporting. Your assistance goes towards helping make the content on this website even better. If you’d like to make a one-time ‘tip’ and buy me a coffee, I have a Ko-Fi page. Your support means a lot. Thank you!