One of the problems in launching a satellite into space is the problem of immediate navigation - that is, the problem of finding the position and direction of a satellite hovering somewhere above the sky in real time. The stars could be the solution
Eran Galili, Galileo
"Big Brother, his eye is open" - this is what George Orwell wrote in his book "1984", and today it seems that over 3,000 satellites orbiting our planet are fulfilling his words. But launching a satellite is not a matter of so-and-so - the harsh conditions prevailing in space and the enormous resources needed to get the satellites there impose two heavy constraints on space engineers: first, satellite components must be as durable as possible to withstand the conditions of extreme temperatures, strong magnetic fields and radiation which prevail in space, but at the same time, the components must also be as light and small as possible - each additional kilogram in the weight of a satellite adds tens of thousands of dollars to the price of sending it into orbit.
Photographing stars is not as simple a task as it seems: asteroids and even space debris may hide certain stars from the satellite. The satellite may also "detect" them as "new" stars
Even from an algorithmic point of view, designing a satellite is not an easy endeavor: the satellite's control system must deal with many problems independently, without the help of humans on Earth. One of the main problems is the problem of immediate navigation - that is, the problem of finding the position and direction of a satellite hovering somewhere above the sky in real time.
Since the navigation problem is a very basic and important problem, there are many systems that deal with it. However, the more accurate information is needed - the more expensive the system becomes, both financially, and in terms of volume and weight - resources are limited, especially in satellites.
There are satellites that require extremely precise location data - photography satellites. As the photography technology improves and the cameras improve and can photograph smaller and smaller objects, the more careful the navigation must be - an inaccuracy of a fraction of a degree in the direction of a photographic satellite may cause it to completely miss its target, and instead of a secret military base to photograph two goats and a capricorn. Systems that provide the level of accuracy required for photography satellites are heavy, large and expensive.
The solution lies in the stars
This problem can be solved in a creative way: instead of buying an expensive, large, and heavy component, we will use an expensive, large, and heavy component that is already on every photography satellite, whatever it is: the camera. But instead of photographing bases and goats on Earth, we will rotate the satellite 180 degrees - and photograph the stars.
The relative position of the Earth, the nearby stars, and the distant stars causes the nearby stars to "move" in the sky during the year
If the satellite can identify the stars in its field of vision, it will be able to calculate its direction - similar to a sailor in the ocean, but much more precisely (because the sailors who navigated by the stars did not have microprocessors. Today sailors navigate using the GPS satellites, and the satellites -GPS navigate using the stars). In fact, many sophisticated navigation systems are based on the principle of star detection, but they use a dedicated component called a star tracker.
If so, to navigate our photography satellite we only need to identify stars from a photograph taken from its camera. Sounds simple - but in fact it is not. The method of navigation with the help of the stars, and especially with a normal camera, has to overcome several obstacles.
The obstacles of the star system
First, the camera with which the satellite is equipped is indeed very suitable for photographing objects on the surface of the earth, but the stars are a completely different matter. Photographing stars sounds simple at first thought - they are just white dots on a black background - but quite a few obstacles stand in our way. First, asteroids, dust clouds, disabled satellites, and even space debris may hide certain stars from the satellite, or, alternatively, it may mistakenly "detect" them as "new" stars. On top of that, the satellite, the Earth around it is a sphere and the stars themselves move incessantly in complex orbits, causing a change in their position as the satellite "sees" them.
There is, therefore, a need to integrate filters into the software capable of differentiating between the main and secondary celestial bodies, and ordering with maximum precision where stars appear (or, more precisely, where their centers appear) - but this is only the beginning.
Here is the place to make a basic distinction between two different points of view - the input space, which is the positions of the stars as seen by the satellite, and the catalog space, which is the positions of the stars as they appear in our database, or catalog - that is, as seen by an observer standing (apparently) in the center of a sphere -Haaretz, on January 1.1.2000, 12, at 1.1.2000 noon, according to Greenwich time (see the description of the database below). Since no satellite is in the center of the Earth on 8 (at least not in the last XNUMX years...), the two spaces may be completely different.
The aspiration of the algorithm2 (the word "algorithm" denotes an orderly method consisting of a sequence of predefined actions. For example, the algorithm "boil water, pour coffee powder into a cup, pour the water into the cup, add sugar or milk and stir" is an algorithm for making coffee) is Identify the stars in the input space and match them to their appearances in the catalog space.
The differences between the different points of view can be not small at all - see picture 1, differences in the position of Barnard's star in the last twenty years. (Bernard's Star, about 6 light-years away from our Sun, is the fourth nearest star to us. However, because it is a red dwarf de la massa star, its light intensity is very weak and cannot be seen with the naked eye.) (See image above to the left)
Several physical phenomena are responsible for the differences in the apparent position of stars. Since each star may move in a different way from other stars, if we do not consider these phenomena, we will not be able to adapt the input space to the catalog space. Therefore, our algorithms must take into account astronomical factors that have a non-negligible effect on the position of the stars.
Parallax
Parallax is a difference in the apparent position of near objects relative to some distant background, as a result of changing the position of the observer. In our case, the objects are relatively close stars, and the background is very distant stars, whose position in the sky does not change (at least not as a result of refraction!).
The first to measure parallax of celestial bodies was Friedrich Bessel, in 1838. Bessel used it to calculate the distance between the Earth and the Cygni-61 star, in a way that will be described later.
As you can see in the picture, the relative position of the Earth, the nearby stars and the distant stars causes the nearby stars to "move" in the sky during the year. The parallax angle, θ, which determines the extent of the movement of the observed star in the sky, depends on the distance of the star from the observer on Earth, and can be calculated using the trigonometric formula below (you can prove the formula by looking at the tangent of the vertex angle to θ in the figure):
Imagine you are in the car, while outside it is raining (but there is no wind!). When the car is stationary (the left square in the picture), the rain outside the window falls vertically - from top to bottom. But when the car is moving, the rain seems to fall at an angle, and the higher the speed of the car, the sharper the angle of the rain; This is because the speed of the car increases in the direction perpendicular to the direction of the movement of the rain. The same happens with light rays, when the observer has a velocity perpendicular to their direction.
We do not notice the aberration of light in everyday life because the speed of light is about ten million times greater than the speed of our cars, but the Earth moves at a much higher speed - about 1/10,000 of the speed of light. Therefore, there is a deviation in the direction of the light rays from the stars to the Earth, and therefore also in the apparent position of the stars.
Self movement
Aberration and parallax are also known as non-self motions, because they are caused by the motion of the earth and the observer, and not by the motion of the stars themselves; The stars usually appear in fixed constellations. However, accurate measurements at intervals of many years have shown that the stars do move independently of each other, but due to the huge distance between them and between them and us, the movement is very small and can be calculated in a simple way, except in extreme cases, caused by unusual speeds or orbits in relation to the sun (such as Barnard's star, pictured above). This motion is called proper motion.
In the second part of the article: What are the data needed for the satellite so that it can "look" for the stars in the right place, and how do you identify the stars?
