Space beacons: what good are they in space?
Alexander V. Bagrov («Authors»)
Beacons were invented in ancient times in order to ensure the security of maritime navigation. Until the mid-16th century no way for ship maritime position determination was, and the ships rid by “coastwise trade”: along the shore without leaving it in order to keep the possibility of pilotage. At night the shore was unseen, and then the lights of beacons indicated important shipping places: entrance to the stormproof bay or, conversely, dangerous cliffs.
The position of each beacon was mapped, and sure signs for beacon recognition in daytime (the tower shape) and at night (the colour and duration of flares) were set for each of them. Incidentally, no two beacons are seemingly alike, and each of sea beacons has its own composition of flares alternation!
Nowadays we use the same techniques of “coastwise” space trips like sailors did five centuries ago. Our manned spacecrafts fly very close to the Earth, and their position in space is easily and reliably determined by ground space control services. But time of the Moon and Mars active exploration is not far, and then we will have to use other methods of space navigation. Navigators of spacecrafts will have to determine their exact position in space and astrogate so that to land to the desired position of the Moon or other space body. Unfortunately, analogies of shipping end at that. Sailors could reverse the ship by simple turning of the steering wheel, and then the interaction between steering wheel and water brought about the immediate and desired result. Spacecrafts rest on nothing in space, and they have no wings, no tail blades that we know from construction of cruise missiles and fantastic starship drawings of half century remoteness. Spacecrafts move in the proper sense of celestial mechanics. Trajectory of spacecraft always lies in a plane passing through the center of attraction: in the earth orbits it passes through the Earth’s gravity center, near the Moon it passes through the Moon’s mass center, during interplanetary transfer it passes through the Sun’s center. In order to change the direction of flight, it is necessary to know exactly how the ship’s velocity is oriented relative to the center of attraction, and in what direction it is necessary to change the velocity in order to move into the desired orbit.
All of these issues are solving by the spacecraft position determination in a particular coordinate system. The task is very complex to complete. In space you can’t move in selected direction taking readings of stars! The ship is easy to turn so that a cosmonaut sees the Polaris (or another star) in front of him, but he cannot determine in which direction the spacecraft is moving. That’s why spacecrafts are placed on launch first into the “intermediate” orbit which parameters are determined from ground-based observations, and only then knowledge of exact spacecraft position in orbit and its moving direction allows completion of the spacecraft transferal from intermediate orbit to the calculated one by extra engine firing at the exactly calculated moment for the exactly calculated operating time. Speaking about flying to the Moon and, especially, to distant planets, arrival in the calculated orbit results in some errors. They accumulate in time and require a new high-precision determination of the spacecraft position in space in order to calculate and implement the next phase of trajectory correction. That’s where the greatest difficulties stem.
The spacecraft that fell away from the Earth can’t be seen even by the most powerful telescopes. The celestial mechanics relieves. Spacecraft moves without power after correction, and the plane of its orbit retains its spatial position. The center of attraction position is always known from astronomical observations, the position of the last correction point was calculated from direct measurements of the spacecraft position at the time of its implementation, and it is enough to observe the exact direction to the spacecraft in order to determine the actual orientation of the orbital plane, and additional observations of direction to the spacecraft made at time intervals allow determination of the spacecraft position in its orbit.
How to determine the direction to the distant spacecraft, if it is not seen even through a telescope? To this end, a beacon which would be seen on the Earth should be switched on board of spacecraft. The onboard transmitter that transmit all information from the spacecraft is usually used for this purpose. Modern radiotechnics has reached such high quality that the signals sent even from the borders of the Solar system by the “Pioneer” crafts that have reached them are received on the Earth. But electromagnetic waves of radio-frequency region are long, and in order to measure the direction to space transmitter more accurately, it is necessary to apply the technology of radio interferometry, i.e. to receive its signals simultaneously by space communication antennas located in thousands of miles from one another. Such measurements are very complex and expensive, but they never become impaired and guarantee getting the spacecraft coordinates with the required accuracy.
Indeed, ground services of spacecraft control have the means to measure their trajectory parameters, which is not about the spacecrafts themselves. On-board equipment is not able to determine exact position of the spacecraft yet. High hopes are now put on pulsars: natural beacons of the Universe that flare from a few tens to hundreds of times per second. “Schedule” of pulsar flares is already strongly established by astronomers. If the impulse stages of several pulsars could be measured on board of spacecraft at some moment, then one could determine the spacecraft position at this moment correct to several hundred of meters. It would be great accuracy under flight velocities of tens of kilometers per second! But now it is only plans and hopes for the future.
A higher navigation accuracy than under the interplanetary flights is needed for space bodies landing. Accuracy of few meters is necessary here. Otherwise, you can split upon the planet surface, if we assume it is far enough and you can slow down on time, or vice versa, plunge from the sky, mistakenly believing that the spacecraft was landed to the planet surface and closing down the brake engines. And you can miss the flat level surface and fall onto a steep slope which the spacecraft will not take hold on and fall. It is for this reason that all the moon landings were carried out on the vast plains of the moon seas and oceans.
It would seem that very detailed images of surface, where the boulders and meteorite craters of the size of half a meter are distinguishable, were received under the Moon flyover. Why not use these images in order to land on the Moon at the preselected point? Certainly, it is strived to do. Except it can be done only knowing the coordinates of selected point to the same accuracy as the spacecraft coordinates. To date, the coordinates of the Moon surface details are known to low accuracy of several hundred of meters. Because of this, the planned landing point is determined with an error of 1 … 2 km.
High accuracy of position determination on the Earth is provided by astronomical observations. Coordinates of “astronomical points” were measured correct to centimeter; the system of geodetic coordinates is based on them. Coordinates of all other points on our planet are defined in this coordinate system, and, certainly, the accuracy of their determination cannot be higher than the accuracy of the measured astronomical points coordinates.
There are no astronomical points on the Moon. Lunar (“selenodetic”) coordinates are determined by the ground-based astronomical observations. Besides the fact that you can determine the coordinates only within the bounds of the apparent Moon surface in such a manner (and it always faces the Earth by one side and its reverse side is not available for terrestrial observations!), accuracy of lunar coordinate assignment is determined by limited capacity of telescope observations through the Earth’s atmosphere. The smallest detail of the lunar features that is discernible through the telescope has a size of about one kilometer. Therefore, the whole system of selenodetic coordinates has accuracy of kilometer in the center of lunar disk, and several times worse accuracy is at its edges. Improvement of the accuracy of coordinate system is not easy, and one of the main difficulties of this problem is the absence of such items, which size would be smaller than the desired value of the coordinate system errors, on the Moon. For example, a point on the Moon with zero latitude and zero longitude is central peak top of the crater Mjolnir-A. And what is the “top”? You can make a very detailed image of the central peak, but what point of dozens of detail in the image can be considered as “top”?
We proposed a simple and very reliable method for determining a reference point: you need to place beacon on the Moon. Modern semiconductor lasers (they did not exist at the beginning of space age) can shine continuously for several years, while consuming very little power. Laser diode of power of 7W emits enough light to make it easy to see it not only from lunar orbit, but even from the Earth through telescope. An upcoming Russian mission to the Moon provides delivery of such a laser beacon onto lunar surface to the region near the southern pole. Any satellite in polar orbit, which is equipped with a camera for surveying the lunar surface will easily notice a beacon light, which will be several times brighter than the surrounding surface. Turning around the Moon, the satellite will not only take pictures of the lunar surface, which it flies above, but also have some pictures of the lunar beacon.
Since the Moon’s satellite turns around the Moon’s center of mass in the proper sense of celestial mechanics, and the plane of its orbit always passes through the center of the Moon, spatial coordinates of the satellite can be determined in a coordinate system centered at the Moon’s center of mass. Orientation of the satellite is always measured by its star sensors, so it is quite simple to select on each image the surface point located on the line between the satellite and the center of the Moon. It turns out that coordinates of each point may be obtained for each such in the same coordinate system which the position of the satellite was measured in! You only need to decide where to place the origin of this coordinate system.
The scientific paper “Building a the global positioning system for uninhabited planets”  provides a mathematical justification of possibility not only of lunar surface details determination relative to the light beacon coordinates, but also a complete determination of the lunar satellite orbital parameters. The used technique is called “geodesic equalization” in the higher geodesy because it takes into account all the measurement errors, ranging from errors in determining the onboard camera orientation and to the satellite orbit variations caused by irregularities in gravitational field of the Moon.
The size of laser beacon luminous element is several millimeters. Luminescence center position could be determined correct to 1 mm and to even higher precision. And to such precision you can define the whole system of selenodetic coordinates! This is not necessary just yet. The Russian mission to the Moon will provide coordinate measurement accuracy of 6 meters. The station landing will be determined to such precision. If the ordinary computation scheme of “ballistic trajectory” was used for this purpose, the error in determining the landing would range from 1 to 2 km. That’s what a light beacon for astronautics! As a result of prepared mission accomplishment we will get a much more accurate way to determine on board moon crafts flight trajectory than using ground-based measurements that can provide predictable descent of space base in difficult mountainous areas correct to several meters.
The “salt” of our proposed method is that we do not need use of astronomical points for carrying out the precise coordinate measurements. They will be replaced by the optical beacons and their position measurement will be implemented on board of the spacecraft. Because it does not matter where the beacon is and how many of them work on the Moon’s surface, the exact coordinates will be measured for each of them. It gave us the right to consider the described method the “global positioning”. But unlike the existing global positioning systems, the proposed version will run on the same satellite, and will not depend on the ground system of permanently operationing astronomical points.
Even more impressive may be the use of our method for measuring the Earth’s beacons coordinates. If the onboard direction light indicator will have an accuracy of 0.001 arcsec (e.g. interferometer), the accuracy of the beacons positions can enter the submillimeter level of accuracy. Since this accuracy is achieved under a single measurement in the split seconds, it is possible to investigate crustal deformation as earthquake precursors, and to study the drift and deformation of continental plateaus. So light beacons may be useful not only in space, but also on the Earth.
Finally, the installation of beacons on the spacecrafts can make them “seen” through the ground-based telescopes, and improve much navigational support of interplanetary missions. Optical beacons are very useful in space and the time when both all the spacecrafts and landing stations will be equipped with them is not far.
 Alexander M. Shirenin, Elena M. Mazurova, Alexander V. Bagrov.Building the global positioning system for uninhabited planets and natural satellites. Space Colonization Journal, Vol. 15, 2014. URL: http://jour.space/volume/vol5/ (in English).
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