Chapter VII. Navigation.
Navigation is the basis of the science of navigation. The navigational method of navigation is to navigate a ship from one place to another in the most advantageous, shortest and safest way. This method solves two problems: how to direct the ship along the chosen path and how to determine its place in the sea based on the elements of the ship’s movement and observations of coastal objects, taking into account the influence of external forces on the ship - wind and current.
To be sure of the safe movement of your ship, you need to know the ship’s place on the map, which determines its position relative to the dangers in a given navigation area.
Navigation deals with the development of the fundamentals of navigation, it studies:
Dimensions and surface of the earth, methods of depiction earth's surface on maps;
Methods for calculating and plotting a ship's path on nautical charts;
Methods for determining the position of a ship at sea by coastal objects.
§ 19. Basic information about navigation.
1. Basic points, circles, lines and planes
Our earth has the shape of a spheroid with a semi-major axis OE equal to 6378 km, and the minor axis OR 6356 km(Fig. 37).
Rice. 37. Determining the coordinates of a point on the earth's surface
In practice, with some assumption, the earth can be considered a ball rotating around an axis occupying a certain position in space.
To determine points on the earth's surface, it is customary to mentally divide it into vertical and horizontal planes that form lines with the earth's surface - meridians and parallels. The ends of the earth's imaginary axis of rotation are called poles - north, or north, and south, or south.
Meridians are large circles passing through both poles. Parallels are small circles on the earth's surface parallel to the equator.
Equator - big circle, the plane of which passes through the center of the earth perpendicular to its axis of rotation.
Both meridians and parallels on the earth’s surface can be imagined in countless numbers. The equator, meridians and parallels form the earth's geographic coordinate grid.
Location of any point A on the earth's surface can be determined by its latitude (f) and longitude (l) .
The latitude of a place is the arc of the meridian from the equator to the parallel of a given place.
Otherwise: the latitude of a place is measured by the central angle between the plane of the equator and the direction from the center of the earth to a given place.
Latitude is measured in degrees from 0 to 90° in the direction from the equator to the poles. When calculating, it is assumed that northern latitude f N has a plus sign, southern latitude f S has a minus sign.
The latitude difference (f 1 - f 2) is the meridian arc enclosed between the parallels of these points (1 and 2).
The longitude of a place is the arc of the equator from the prime meridian to the meridian of a given place. Otherwise: the longitude of a place is measured by the arc of the equator, enclosed between the plane of the prime meridian and the plane of the meridian of a given place.
The difference in longitude (l 1 -l 2) is the arc of the equator, enclosed between the meridians of given points (1 and 2). The prime meridian is the Greenwich meridian. From it, longitude is measured in both directions (east and west) from 0 to 180°. Western longitude is measured on the map to the left of the Greenwich meridian and is taken with a minus sign in calculations; eastern - to the right and has a plus sign. The latitude and longitude of any point on earth are called
geographical coordinates
this point.
2. Division of the true horizon A The mentally imaginary horizontal plane passing through the observer's eye is called the plane of the observer's true horizon, or true horizon (Fig. 38). Let us assume that at the point is the observer's eye, line
ZABC - vertical, HH 1 - the plane of the true horizon, and line P NP S - the axis of rotation of the earth. Of the many vertical planes, only one plane in the drawing will coincide with the axis of rotation of the earth and the point A. The intersection of this vertical plane with the surface of the earth gives on it a great circle P N BEP SQ, called the true meridian of the place, or the meridian of the observer. The plane of the true meridian intersects with the plane of the true horizon and gives the north-south line on the latter NS.
Line
O.W. perpendicular to the line of true north-south is called the line of true east and west (east and west). Thus, the four main points of the true horizon - north, south, east and west - occupy a well-defined position anywhere on earth, except for the poles, thanks to which different directions along the horizon can be determined relative to these points. Directions N (north), S (south),(west) are called the main directions. The entire circumference of the horizon is divided into 360°. perpendicular to the line of true north-south is called the line of true east and west (east and west). Division is made from the point
in a clockwise direction. Intermediate directions between the main directions are called quarter directions and are called NO, SO, SW, NW.
The main and quarter directions have the following values in degrees: Rice. 38.
Observer's true horizon
3. Visible horizon, visible horizon range
The expanse of water visible from a vessel is limited by a circle formed by the apparent intersection of the vault of heaven with the surface of the water. This circle is called the observer's apparent horizon. The range of the visible horizon depends not only on the height of the observer’s eyes above the water surface, but also on the state of the atmosphere. Figure 39.
Object visibility range
The boatmaster should always know how far he can see the horizon in different positions, for example, standing at the helm, on deck, sitting, etc.
The range of the visible horizon is determined by the formula:
d = 2.08 or, approximately, for an observer's eye height of less than 20 m by
formula:
d = 2,
where d is the range of the visible horizon in miles; h is the height of the observer's eye,
m. Example. If the height of the observer's eye is h = 4 m,
then the range of the visible horizon is 4 miles. , The visibility range of the observed object (Fig. 39), or, as it is called, the geographic range D n is the sum of the ranges of the visible horizon With
the height of this object H and the height of the observer’s eye A. , Observer A (Fig. 39), located at a height h, from his ship can see the horizon only at a distance d 1, i.e. to point B of the water surface. ; If we place an observer at point B of the water surface, then he could see lighthouse C located at a distance d 2 from it therefore the observer located at the point :
A,
will see the beacon from a distance equal to D n
D n= d 1+d 2.
m. The visibility range of objects located above the water level can be determined by the formula: If the height of the observer's eye is h = 4 Dn = 2.08(+). h is the height of the observer's eye,
Lighthouse height H = 1b.8 observer's eye height h = 4
Solution.
m. D n = l 2.6 miles, or 23.3 km. The visibility range of an object is also determined approximately using the Struisky nomogram (Fig. 40). By applying a ruler so that one straight line connects the heights corresponding to the observer’s eye and the observed object, the visibility range is obtained on the middle scale. Find the visibility range of an object with an altitude of 26.2 above sea level h is the height of the observer's eye,
m with an observer's eye height above sea level of 4.5
On maps, directions, in navigation manuals, in the descriptions of signs and lights, the visibility range is given for the height of the observer's eye 5 m from the water level. Since on a small boat the observer’s eye is located below 5 If the height of the observer's eye is h = 4 for it, the visibility range will be less than that indicated in manuals or on the map (see Table 1).
m. The map indicates the visibility range of the lighthouse at 16 miles. This means that an observer will see this lighthouse from a distance of 16 miles if his eye is at a height of 5 The visibility range of an object is also determined approximately using the Struisky nomogram (Fig. 40). By applying a ruler so that one straight line connects the heights corresponding to the observer’s eye and the observed object, the visibility range is obtained on the middle scale. above sea level. If the observer's eye is at a height of 3 If the height of the observer's eye is h = 4 then the visibility will correspondingly decrease by the difference in the horizon visibility range for heights 5 and 3 h is the height of the observer's eye, Horizon visibility range for height 5 The visibility range of an object is also determined approximately using the Struisky nomogram (Fig. 40). By applying a ruler so that one straight line connects the heights corresponding to the observer’s eye and the observed object, the visibility range is obtained on the middle scale. equal to 4.7 miles; for height 3 The visibility range of an object is also determined approximately using the Struisky nomogram (Fig. 40). By applying a ruler so that one straight line connects the heights corresponding to the observer’s eye and the observed object, the visibility range is obtained on the middle scale.- 3.6 miles, difference 4.7 - 3.6=1.1 miles.
Consequently, the visibility range of the lighthouse will not be 16 miles, but only 16 - 1.1 = 14.9 miles.
Rice. 40. Struisky's nomogram
Each object has a certain height H (Fig. 11), therefore the visibility range of the object Dp-MR is composed of the range of the visible horizon of the observer De=Mc and the range of the visible horizon of the object Dn=RC:
Rice. eleven.
Using formulas (9) and (10), N. N. Struisky compiled a nomogram (Fig. 12), and in MT-63 the table is given. 22-v “Visibility range of objects”, calculated according to formula (9).
Example 11. Find the visibility range of an object with a height above sea level H = 26.5 m (86 ft) when the height of the observer's eye above sea level is e = 4.5 m (1 5 ft).
Lighthouse height H = 1b.8
1. According to the Struisky nomogram (Fig. 12), on the left vertical scale “Height of the observed object” we mark the point corresponding to 26.5 m (86 ft), on the right vertical scale “Height of the observer’s eye” we mark the point corresponding to 4.5 m ( 15 ft); connecting the marked points with a straight line, at the intersection of the latter with the average vertical scale “Visibility range” we get the answer: Dn = 15.1 m.
2. According to MT-63 (Table 22-c). For e = 4.5 m and H = 26.5 m, the value Dn = 15.1 m. The visibility range of lighthouse lights Dk-KR given in navigation manuals and on sea charts is calculated for the height of the observer’s eye equal to 5 m. If the actual height the observer's eye is not equal to 5 m, then the correction A = MS-KS- = De-D5 must be added to the range Dk given in the manuals. The correction is the difference between the distances of the visible horizon from a height of 5 m and is called the correction for the height of the observer’s eye:
As can be seen from formula (11), the correction for the height of the eye of observer A can be positive (when e> 5 m) or negative (when e
So, the visibility range of the beacon light is determined by the formula
Rice. 12.
Example 12. The visibility range of the lighthouse indicated on the map is Dk = 20.0 miles.
From what distance will an observer see the fire, whose eye is at a height of e = 16 m?
Lighthouse height H = 1b.8 1) according to formula (11)
2) according to table. 22-a ME-63 A=De - D5 = 8.3-4.7 = 3.6 miles;
3) according to formula (12) Dp = (20.0+3.6) = 23.6 miles.
Example 13. The visibility range of the lighthouse indicated on the map is Dk = 26 miles.
From what distance will an observer on a boat see the fire (e=2.0 m)
Lighthouse height H = 1b.8 1) according to formula (11)
2) according to table. 22-a MT-63 A=D - D = 2.9 - 4.7 = -1.6 miles;
3) according to formula (12) Dp = 26.0-1.6 = 24.4 miles.
The visibility range of an object, calculated using formulas (9) and (10), is called geographical.
Rice. 13.
Visibility range of the beacon light, or optical range visibility depends on the strength of the light source, the beacon system and the color of the fire. In a properly constructed lighthouse, it usually coincides with its geographical range.
In cloudy weather, the actual visibility range may differ significantly from the geographic or optical range.
IN Lately Research has established that in daytime sailing conditions, the visibility range of objects is more accurately determined by the following formula:
In Fig. Figure 13 shows a nomogram calculated using formula (13). We will explain the use of the nomogram by solving the problem with the conditions of Example 11.
Example 14. Find the visibility range of an object with a height above sea level H = 26.5 m, with the height of the observer’s eye above sea level e = 4.5 m.
Lighthouse height H = 1b.8 1 according to formula (13)
The Earth's surface curves and disappears from view at a distance of 5 kilometers. But our visual acuity allows us to see far beyond the horizon. If the Earth were flat, or if you stood on top of a mountain and looked at a much larger area of the planet than usual, you would be able to see bright lights hundreds of kilometers away. On a dark night, you could even see the flame of a candle located 48 kilometers away.
How far can he see human eye depends on how many particles of light, or photons, are emitted by a distant object. The most distant object visible to the naked eye is the Andromeda Nebula, located at an enormous distance of 2.6 million light years from Earth. The galaxy's one trillion stars emit enough light in total to cause several thousand photons to strike every square centimeter of Earth's surface every second. On a dark night, this amount is enough to activate the retina.
In 1941, vision scientist Selig Hecht and his colleagues at Columbia University made what is still considered a reliable measure of absolute visual threshold—the minimum number of photons that must hit the retina to produce visual awareness. The experiment set the threshold under ideal conditions: the participants' eyes were given time to fully adjust to absolute darkness, the blue-green flash of light acting as a stimulus had a wavelength of 510 nanometers (to which the eyes are most sensitive), and the light was directed at the peripheral edge of the retina , filled with light-sensing rod cells. 
According to scientists, in order for the experiment participants to be able to recognize such a flash of light in more than half of the cases, from 54 to 148 photons had to hit the eyeballs. Based on retinal absorption measurements, scientists estimate that on average 10 photons are actually absorbed by the rods of the human retina. Thus, the absorption of 5-14 photons or, respectively, the activation of 5-14 rods indicates to the brain that you are seeing something.
“This is indeed a very small number of chemical reactions,” Hecht and his colleagues noted in a paper about the experiment.
Pay attention to absolute threshold, the brightness of a candle flame and the estimated distance at which a luminous object dims, scientists concluded that a person can discern the faint flicker of a candle flame at a distance of 48 kilometers.
But at what distance can we recognize that an object is more than just a flicker of light? In order for an object to appear spatially extended and not point-like, the light from it must activate at least two adjacent retinal cones—the cells responsible for color vision. Under ideal conditions, an object should lie at an angle of at least 1 arcminute, or one-sixth of a degree, to excite adjacent cones. This angular measure remains the same whether the object is close or far away (the distant object must be much larger to be at the same angle as the near one). The Full Moon lies at an angle of 30 arcminutes, while Venus is barely visible as an extended object at an angle of about 1 arcminute.
Objects the size of a person are distinguishable as extended at a distance of only about 3 kilometers. In comparison at this distance we could clearly distinguish the two
Question No. 10.
Distance of the visible horizon. Object visibility range...
Geographic horizon visibility range
Let the height of the eye of the observer located at the point A" above sea level, equal to e(Fig. 1.15). surface of the Earth in the form of a sphere with radius R
The rays of sight going to A" and tangent to the surface of the water in all directions form a small circle KK", which is called theoretically visible horizon line.
Due to the different density of the atmosphere in height, a ray of light does not propagate rectilinearly, but along a certain curve A"B, which can be approximated by a circle with radius ρ .
The phenomenon of curvature of the visual ray in the Earth's atmosphere is called terrestrial refraction and usually increases the range of the theoretically visible horizon. the observer sees not KK", but the line BB", which is a small circle along which the surface of the water touches the sky. This observer's apparent horizon.
The coefficient of terrestrial refraction is calculated using the formula. Its average value:
Refractive angler determined, as shown in the figure, by the angle between the chord and the tangent to the circle of radiusρ .
The spherical radius A"B is called geographical or geometric range of the visible horizon De. This visibility range does not take into account the transparency of the atmosphere, i.e. it is assumed that the atmosphere is ideal with a transparency coefficient m = 1.
Let us draw the plane of the true horizon H through point A, then vertical angle d between H and the tangent to the visual ray A "B will be called horizon inclination
In the MT-75 Nautical Tables there is a table. 22 “Range of the visible horizon”, calculated using formula (1.19).
Geographic visibility range of objects
Geographic range of visibility of objects at sea Dp, as follows from the previous paragraph, will depend on the value e- height of the observer’s eye, magnitude h- the height of the object and the refractive index X.
The value of Dp is determined by the greatest distance at which the observer will see its top above the horizon line. In professional terminology, there is the concept of range, as well as moments"open" And"closing" a navigational landmark, such as a lighthouse or ship. Calculation of such a range allows the navigator to have additional information about the approximate position of the ship relative to the landmark.
where Dh is the visibility range of the horizon from the height of the object
On marine navigation charts, the geographic visibility range of navigation landmarks is given for the height of the observer's eye e = 5 m and is designated as Dk - the visibility range indicated on the map. In accordance with (1.22), it is calculated as follows:
Accordingly, if e differs from 5 m, then to calculate Dp to the visibility range on the map, an amendment is necessary, which can be calculated as follows:
There is no doubt that Dp depends on the physiological characteristics of the observer’s eye, on visual acuity, expressed in resolution at.
Angle resolution- this is the smallest angle at which two objects are distinguished by the eye as separate, i.e. in our task it is the ability to distinguish between an object and the horizon line.
Let's look at Fig. 1.18. Let us write down the formal equality
Due to the resolution of the object, an object will be visible only if its angular dimensions are no less than at, i.e. it will have a height above the horizon line of at least SS". Obviously, y should reduce the range, calculated using formulas (1.22). Then
The segment CC" actually reduces the height of object A.
Assuming that in ∆A"CC" angles C and C" are close to 90°, we find
If we want to get Dp y in miles, and SS" in meters, then the formula for calculating the visibility range of an object, taking into account the resolution of the human eye, must be reduced to the form
The influence of hydrometeorological factors on the visibility range of the horizon, objects and lights
The visibility range can be interpreted as an a priori range without taking into account the current transparency of the atmosphere, as well as the contrast of the object and background.
Optical visibility range- this is the range of visibility, depending on the ability of the human eye to distinguish an object by its brightness against a certain background, or, as they say, to distinguish a certain contrast.
Daytime optical visibility range depends on the contrast between the observed object and the background of the area. Daytime optical visibility range represents the greatest distance at which the apparent contrast between the object and the background becomes equal to the threshold contrast.
Night optical visibility range this is the maximum visibility range of the fire at a given time, determined by the intensity of the light and the current meteorological visibility.
Contrast K can be defined as follows:
Where Vf is the background brightness; Bp is the brightness of the object.
The minimum value of K is called threshold of contrast sensitivity of the eye and equals on average 0.02 for daytime conditions and objects with angular dimensions of about 0.5°.
Part of the luminous flux from lighthouse lights is absorbed by particles in the air, resulting in a weakening of the light intensity. This is characterized by the atmospheric transparency coefficient
Where I0 - luminous intensity of the source; /1 - luminous intensity at a certain distance from the source, taken as unity.
TO 
the atmospheric transparency coefficient is always less than unity, which means geographical range- this is the theoretical maximum, which in real conditions the visibility range does not reach, with the exception of anomalous cases.
Assessment of atmospheric transparency in points can be made using a visibility scale from table 51 MT-75 depending on the state of the atmosphere: rain, fog, snow, haze, etc.
Thus, the concept arises meteorological visibility range, which depends on the transparency of the atmosphere.
Nominal visibility range fire is called the optical visibility range with a meteorological visibility range of 10 miles (ד = 0.74).
The term is recommended by the International Association of Lighthouse Authorities (IALA) and is used abroad. Domestic maps and navigation manuals indicate the standard visibility range (if it is less than the geographical one).
Standard visibility range- this is the optical range with meteorological visibility of 13.5 miles (ד = 0.80).
The navigation manuals “Lights” and “Lights and Signs” contain a table of horizon visibility range, a nomogram of object visibility and a nomogram of optical visibility range. The nomogram can be entered by luminous intensity in candelas, by nominal (standard) range and by meteorological visibility, resulting in the optical range of visibility of the fire (Fig. 1.19).
The navigator must experimentally accumulate information about the opening ranges of specific lights and signs in the navigation area in various weather conditions.
Talks about amazing properties our vision - from the ability to see distant galaxies to the ability to capture seemingly invisible light waves.
Look around the room you are in - what do you see? Walls, windows, colorful objects - all this seems so familiar and taken for granted. It's easy to forget that we see the world around us only thanks to photons - light particles reflected from objects and striking the retina.
There are approximately 126 million light-sensitive cells in the retina of each of our eyes. The brain deciphers the information received from these cells about the direction and energy of photons falling on them and turns it into a variety of shapes, colors and intensity of illumination of surrounding objects.
U human vision has its limits. So, we are not able to see the radio waves emitted electronic devices, the smallest bacteria cannot be seen with the naked eye.
Thanks to advances in physics and biology, the limits of natural vision can be determined. "Every object we see has a certain 'threshold' below which we stop recognizing them," says Michael Landy, a professor of psychology and neurobiology at New York University.
Let's first consider this threshold in terms of our ability to distinguish colors - perhaps the very first ability that comes to mind in relation to vision.
Illustration copyright SPL Image caption Cones are responsible for color perception, and rods help us see shades of gray in low light.Our ability to distinguish, e.g. purple from magenta is related to the wavelength of photons striking the retina. There are two types of light-sensitive cells in the retina - rods and cones. Cones are responsible for color perception (so-called day vision), and rods allow us to see shades of gray in low light - for example, at night (night vision).
The human eye has three types of cones and a corresponding number of types of opsins, each of which is particularly sensitive to photons with a specific range of light wavelengths.
S-type cones are sensitive to the violet-blue, short-wavelength portion of the visible spectrum; M-type cones are responsible for green-yellow (medium wavelength), and L-type cones are responsible for yellow-red (long wavelength).
All of these waves, as well as their combinations, allow us to see the full range of colors of the rainbow. "All sources visible to humans"lights, with the exception of some artificial ones (such as a refractive prism or laser), emit a mixture of wavelengths of different lengths," says Landy.
Illustration copyright Thinkstock Image caption Not the entire spectrum is good for our eyes...Of all the photons existing in nature, our cones are capable of detecting only those characterized by wavelengths in a very narrow range (usually from 380 to 720 nanometers) - this is called the visible radiation spectrum. Below this range are the infrared and radio spectra - the wavelengths of the latter's low-energy photons vary from millimeters to several kilometers.
On the other side of the visible wavelength range is the ultraviolet spectrum, followed by X-rays, and then the gamma ray spectrum with photons whose wavelengths are less than trillionths of a meter.
Although most of us have limited vision in the visible spectrum, people with aphakia - the absence of a lens in the eye (resulting surgical operation with cataracts or, less commonly, due to birth defect) - are able to see ultraviolet waves.
In a healthy eye, the lens blocks ultraviolet waves, but in its absence, a person is able to perceive waves up to about 300 nanometers in length as blue-white color.
A 2014 study notes that, in some sense, we can all see infrared photons. If two such photons almost simultaneously hit the same retinal cell, their energy can be summed up, turning invisible waves length, say, 1000 nanometers in visible wave 500 nanometers long (most of us perceive waves of this length as a cool green color).
How many colors do we see?
In the eye healthy person three types of cones, each of which is capable of distinguishing about 100 different shades of color. For this reason, most researchers estimate the number of colors we can distinguish at about a million. However, color perception is very subjective and individual.
Jameson knows what he's talking about. She studies the vision of tetrachromats - people with truly superhuman abilities to distinguish colors. Tetrachromacy is rare and occurs in most cases in women. As a result of a genetic mutation, they have an additional, fourth type of cone, which allows them, according to rough estimates, to see up to 100 million colors. (In people suffering color blindness, or dichromats, there are only two types of cones - they distinguish no more than 10,000 colors.)
How many photons do we need to see a light source?
In general, cones require much more light than chopsticks. For this reason, in low light, our ability to distinguish colors decreases, and rods are taken to work, providing black and white vision.
Under ideal laboratory conditions, in areas of the retina where rods are largely absent, cones can be activated by just a few photons. However, the wands do an even better job of registering even the dimmest light.
Illustration copyright SPL Image caption After eye surgery, some people gain the ability to see ultraviolet radiationAs experiments first conducted in the 1940s show, one quantum of light is enough for our eyes to see it. "A person can see a single photon," says Brian Wandell, a professor of psychology and electrical engineering at Stanford University. "It just doesn't make sense for the retina to be more sensitive."
In 1941, researchers from Columbia University conducted an experiment - they took subjects into a dark room and gave their eyes a certain time to adapt. The rods require several minutes to achieve full sensitivity; This is why when we turn off the lights in a room, we lose the ability to see anything for a while.
A flashing blue-green light was then directed at the subjects' faces. With a probability higher than ordinary chance, the experiment participants recorded a flash of light when only 54 photons hit the retina.
Not all photons reaching the retina are detected by light-sensitive cells. Taking this into account, scientists have come to the conclusion that just five photons activating five different rods in the retina are enough for a person to see a flash.
Smallest and most distant visible objects
The following fact may surprise you: our ability to see an object does not depend at all on its physical size or distance, but on whether at least a few photons emitted by it will hit our retina.
“The only thing the eye needs to see something is a certain amount of light emitted or reflected by the object,” says Landy. “It all comes down to the number of photons that reach the retina. No matter how small the light source, even if it exists for a fraction of a second, we can still see it if it emits enough photons."
Illustration copyright Thinkstock Image caption The eye only needs a small number of photons to see light.Psychology textbooks often contain the statement that on a cloudless, dark night, a candle flame can be seen from a distance of up to 48 km. In reality, our retina is constantly bombarded by photons, so that a single quantum of light emitted from a great distance is simply lost against their background.
To get an idea of how far we can see, let's look at the night sky, dotted with stars. The size of the stars is enormous; many of those we see with the naked eye reach millions of kilometers in diameter.
However, even the stars closest to us are located at a distance of over 38 trillion kilometers from Earth, so they visible dimensions so small that our eyes are unable to distinguish them.
On the other hand, we still observe stars in the form of bright point sources of light, since the photons emitted by them overcome the gigantic distances separating us and land on our retina.
Illustration copyright Thinkstock Image caption Visual acuity decreases as the distance to the object increasesAll individual visible stars in the night sky are located in our galaxy, the Milky Way. The most distant object from us that a person can see with the naked eye is located outside the Milky Way and is itself a star cluster - this is the Andromeda Nebula, located at a distance of 2.5 million light years, or 37 quintillion km, from the Sun. (Some people claim that on particularly dark nights sharp vision allows them to see the Triangulum Galaxy, located at a distance of about 3 million light years, but let this statement remain on their conscience.)
The Andromeda nebula contains one trillion stars. Due to the great distance, all these luminaries merge for us into a barely visible speck of light. Moreover, the size of the Andromeda Nebula is colossal. Even at such a gigantic distance, its angular size is six times the diameter full moon. However, so few photons from this galaxy reach us that it is barely visible in the night sky.
Visual acuity limit
Why are we unable to see individual stars in the Andromeda Nebula? The fact is that resolution, or visual acuity, has its limitations. (Visual acuity refers to the ability to distinguish elements such as a point or line as separate objects that do not blend into adjacent objects or the background.)
In fact, visual acuity can be described in the same way as the resolution of a computer monitor - in the minimum size of pixels that we are still able to distinguish as individual points.
Illustration copyright SPL Image caption Quite bright objects can be seen at a distance of several light yearsLimitations in visual acuity depend on several factors, such as the distance between the individual cones and rods of the retina. An equally important role is played by the optical characteristics of the eyeball, due to which not every photon hits the light-sensitive cell.
In theory, research shows that our visual acuity is limited to the ability to distinguish about 120 pixels per angular degree (a unit of angular measurement).
A practical illustration of the limits of human visual acuity can be an object located at arm's length, the size of a fingernail, with 60 horizontal and 60 vertical lines of alternate white and black colors applied to it, forming a semblance of a chessboard. “Apparently, this is the smallest pattern that the human eye can still discern,” says Landy.
The tables used by ophthalmologists to test visual acuity are based on this principle. The most famous table in Russia, Sivtsev, consists of rows of black capital letters on a white background, the font size of which becomes smaller with each row.
A person’s visual acuity is determined by the size of the font at which he ceases to clearly see the outlines of letters and begins to confuse them.
Illustration copyright Thinkstock Image caption Visual acuity charts use black letters on a white backgroundIt is the limit of visual acuity that explains the fact that we are not able to see with the naked eye biological cell, the dimensions of which are only a few micrometers.
But there is no need to grieve over this. The ability to distinguish a million colors, capture single photons and see galaxies several quintillion kilometers away is quite a good result, considering that our vision is provided by a pair of jelly-like balls in the eye sockets, connected to a 1.5 kg porous mass in the skull.
