Hyperbolic Path Perseverance

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Hyperbolic Path Perseverance
Hyperbolic Path Perseverance

Mysterious Mars has always been shrouded in the mystery of unpredictable events. The path to it is not easy and can present any surprises. A long flight of millions of kilometers of void sometimes ends with not always understandable losses of vehicles. But strange phenomena sometimes occur at the very beginning of the path to the Red Planet. Sit closer and listen: we will tell you a curious story that happened quite recently.

Launch of the Atlas V-541 rocket with the Perseverance rover from the LC 41 launch pad at Cape Canaveral, Florida on July 30, 2020. Photo: NASA

The mystery of the underground apogee

The launch of the Perseverance rover on July 30, 2020 from the US Air Force Base at Cape Canaveral in Florida went on as usual, without foreshadowing anything unexpected. After the first stage, which habitually provided a high suborbital trajectory, a space veteran, the grandfather of Centaur, who has been working at high altitudes for 60 years, joined the work. This space locomotive began to pull out the underground perigee, inherited from the first stage, from deep bowels, from the lower mantle of the Earth. Its steam-powered perigee was lifted from the depths of the earth, at the same rate it was taken out of the atmosphere and left at an altitude of 166 kilometers, closing the trajectory of launching into a low reference orbit.

After a short time, Centaur turned on a second time to accelerate Perseverance for an interplanetary flight to Mars. Due to the increase in speed, the ellipse of the current orbit began to stretch in length, leaving its farthest part farther from the Earth. Now the height of the apogee was growing: at first slowly, then more and more rapidly, constantly accelerating and bringing the cherished moment of the opening of the near-earth orbit closer to the interplanetary trajectory. Data on the rapidly increasing apogee height was displayed in the corner of all monitors displaying the movement of the rocket. They showed how the calculated apogee itself - just a calculated point, not constrained by mass and inertia - was rapidly moving away for millions of kilometers.


And suddenly, before everyone's eyes, an amazing thing happened. Suddenly, telemetry data showed that the height of the apogee became negative and amounted to minus 6378 kilometers - the apogee from deep space, from a distance of 45 million kilometers, suddenly dived into the inner solid iron core of the Earth and remained there.

What the hell is this, worthy of the pen of Nikolai Vasilyevich Gogol? Maybe even here “the cunning devil did not leave his mischiefs”? Or is it a program malfunction, a breakdown of the trajectory measurement and calculation system? Maybe some purely Martian secrets?

The previous launch to Mars in the United States took place a couple of years earlier, on May 5, 2018, and was in many ways unusual. All launches to the Red Planet in the entire history of American astronautics were carried out from Florida. The InSight launch was the first interplanetary launch from Vandenberg Air Force Base in California, the second largest spaceport in the United States, and generally from the Pacific coast of the United States. At the same time, this was the first launch to Mars from a polar reference orbit. Such an unusual start was not chosen at all because of any ballistic gains. On the contrary, there is some loss in launch energy, because in such cases the rotation of the Earth is not used.

Just due to the workload of the Florida launch teams with the existing tight launch schedule, the launch was moved to Vandenberg (although it was still supervised by launch specialists from Florida, the Kennedy Space Center). From this Pacific cosmodrome, they always launch in the direction of the North and South poles of the Earth, into polar and circumpolar orbits, specializing in just such launches. Almost all optical reconnaissance flies in near-polar sun-synchronous orbits, and Vandenberg is not only a cosmodrome, but also the Western Rocket Range. You cannot launch anything from it in the usual eastern direction, because a densely populated continent stretches to the east, along which you cannot throw the worked-out steps.

The power of the Atlas V 401 rocket with a large margin was enough to compensate for the energy minus of such a launch. After the launch and the strictly vertical section, the rocket went steeply to the south, over the ocean along the coast of California, in the direction of Antarctica, taking it slightly east of the starting meridian. Having passed over the Channel Islands lying not far from the coast at an altitude of seventy kilometers and without disturbing the famous dwarf mammoths Mammuthus exilis, buried in the Late Pleistocene deposits of these islands, the rocket quickly lifted out of the atmosphere. Once in low polar orbit, the very same space locomotive Centaur, with the standard second start of the engine over Antarctica, put InSight on a flight path to Mars. And at the moment of transition to the interplanetary trajectory, the same amazing picture arose. The telemetry data, now in the upper left corner of the screen, showed a negative apogee altitude of minus 3443.92 miles:


So, this is not an accident, and some paradoxical phenomenon occurs during launches to Mars? But how is it: negative apogee height? What does this mean and how does such data arise? To figure it out, let's start with the basics and take a quick walk through the orbital ballistics garden without diving deep into its thicket, however.

Clash of dissimilar fighters

Let's imagine that in the ring, in a certain space, two fighters come together in a duel. One small, fast and nimble, his trump card is speed. The other is heavy and heavy, like a sumo fighter; its trick is mass. The grip of the "sumo wrestler" is instant, reliable and unrelenting. Only instead of throwing the opponent out of the circle, as in real sumo, he, on the contrary, seeks to keep within the circle. Maybe not exactly a circle, but within the limits of its power. The fast fighter takes in another category - the speed that he has developed, got hold of, got hold of. He will either win or lose to the sumo fighter at the expense of his quickness, sufficient or insufficient. How do you compare them? Can you predict who will win?

In other words, there is a massive gravitating body - and a moving object, a spacecraft. What will be their interaction? The sumo fighter will grab this runner and hold in his grip. Or the runner will avoid the heavyweight and continue running. How do we weigh their capabilities? You can compare them in terms of energy, easily transformable value (in terms of its forms, potential and kinetic) - and therefore a very universal parameter.

The energy of movement of a fast fighter - kinetic energy - is a familiar product: Ek= mV2/ 2. The energy of the grip of the massive, or gravitational energy - Egr = GMm/r, the product of the masses of the fighters by the gravitational constant Gdivided by the distance between them r… The closer, the stronger the heavy sumo wrestler will capture the fast fighter. And it will keep it in orbits around itself, bending them with the force of its grip until it closes, thereby not letting go. And if the quick wins, he will not remain at the mercy of the massive and will leave him to infinity.

What is primary - motion or gravity? The question is meaningless, but gravitation can exist for an infinitely long time without changing the picture in any way. Movement leads to a fight between the fighters; without movement, their meeting is impossible in principle. Comparing the fighters, the first is the energy of the fast movement and the energy of the massive grip is subtracted from it. Both of these energies have a fast body mass m; dividing by it, we obtain for a flying body the energy of its motion per one kilogram of its mass - specific kinetic energy V2/ 2. And the impact of a massive body is determined by the product of its mass by the gravitational constant (GM, this product is called the gravitational parameter, μ, "Mu"), divided by the distance from the center of the gravitational field (simplified - the center of the planet) to the fast body - μ/r… This is the gravitational energy per kilogram of the flying body, that is, the specific gravitational energy.Two specific energies - kinetic and gravitational, per one kilogram of the runner - are the scales that will predetermine the runner's capabilities and the outcome of the meeting between the two fighters. The difference between these specific energies, V2/2 – μ/r, is called the specific orbital energy and is denoted by the symbol e:

e =V2/2 – μ/r

Curves of defeat and victory

Further, the logic is simple: what energy is greater in a kilogram of a flying body, that energy rules; whose reins are stronger, she turns the horse. When the specific gravity energy of a massive body predominates in the runner, its gravitational field does not release the runner, returning the flying body through the closed trajectories: ellipses, ellipses, ellipses. The energy of movement here is less than the energy of gravity in each kilogram of the runner. Subtracting the larger from the smaller, we obtain a negative value of the specific orbital energy e… The fast body is, as it were, in the minus in front of the gravity of the heavy partner and cannot free itself from its gravity.

And if the specific energies of velocity and gravity are equal? Their difference will give zero - the specific orbital energy of the body is zero, e = 0. Nobody wins here: a high-speed body flies off to infinity, but stops there; and the gravitating partner stops the high-speed body, but infinitely far, beyond the limits of its grasp. And he cannot pull him to herself from there. Stalemate situation. And this is the second cosmic speed: a fast body will leave the gravitational field of a heavy one, having gone infinitely far, but the action of this field will eventually stop and cease to be a runner.

What will be the shape of this path of absolute equality? Approaching it with the acceleration of the body, the elliptical trajectory acquires an ever higher and more distant apogee, the highest point of the orbit. And when the apogee rises to infinity, the ellipse will break. The orbit will become an open curve - a parabola.

A parabolic orbit divides all orbits into before and after, dividing the infinity of ellipses and the infinity of hyperbolas, further open trajectories with a predominance of the energy of motion. This is a very fine line, purely calculated; for the surface of a spherical gravitating body, there is only one parabola, in contrast to the countless set of closed ellipses and the same countless set of open hyperbolas. For a parabolic orbit at all its points, the speed is always equal to the second cosmic speed - the speed of escape from the gravitating body. A little less energy - and the flight will close into an ellipse. A little more energy - the flight will go to infinity and continue there.

The spacecraft will overcome gravity with a margin and will fly away from the planet with some residual velocity. And it will not stop in the infinite distance, like on a parabola. Such trajectories are called hyperbolic.

With an increase in the speed of a fast body, all further curves will also be open. The specific energy of motion on them is greater than the specific energy of the gravitational field. The spacecraft will overcome gravity with a margin and will fly away from the planet with some residual velocity. And it will not stop in the infinite distance, like on a parabola. Such trajectories are called hyperbolic. On them, the speed "overrides" gravity, the specific energy of the speed is greater than the specific energy of gravitation, and the specific orbital energy epositive - the runner is in positive territory in front of the gravity of a heavy partner and thus wins him. In addition, a fast body at an infinite distance from the planet retains a residual velocity, called a hyperbolic excess of velocity. At the moment of strange telemetry data, Perseverance entered such a hyperbolic trajectory - on the trajectory of leaving the Earth with a nonzero residual speed, with which it went to the Red Planet.

The situation with the semi-major axis

And we will briefly return to the orbital ballistics garden and take a walk along the path of simple geometry.In an elliptical orbit, the distance between perigee and apogee, the most mutually distant points, forms the major axis of the ellipse (which is elongated in the length of the ellipse; the minor axis and semi-axis will lie across the ellipse). Half of this longest distance in an ellipse is the semi-major axis a… The specific orbital energy of a flying body can be expressed not only in the form of the difference between the kinetic and gravitational specific energies, but also in terms of the gravitational parameter μplanets and the length of the semi-major axis aelliptical orbit of a flying body: e= –Μ/2a… Pay attention to the minus before the fraction.

The specific energy of a body flying along an ellipse is negative (minus, a lack for escape from the planet's gravity) and is equal to e= –Μ/2a… From the same formula, the semi-major axis is equal to a = –Μ/2e… Specific energy negative for the ellipse e together with the minus of the formula gives the positive length of the semi-major axis of the ellipse a.

At a parabola, the apogee recedes to infinity, which means that the length of the major axis and semi-axis becomes infinite. On hyperbolic trajectories, the specific energy has already crossed the parabolic zero and is positive: the body leaves gravity with a margin remaining in the form of a hyperbolic excess of velocity. But for the specific energy of the body to become positive, something in the formula must become negative if there is a minus in front of it.

The gravitational parameter cannot be negative: this is the product of the planet's mass by the number, μ = GM, and there is no negative mass. Semi-major axis remains a… In reality, a hyperbola does not have any semi-axis - only an unlimited axis, an infinite straight line, for which the concept of a half is somehow meaningless. As there is no apogee. Its branches go to infinity and do not have a common point there, to which you can postpone the axis and measure the distance. Mathematically, the length of the semi-major axis of the hyperbola is forced to become negative. Directional distances may have sign changes. When the direction of postponement or counting is taken into account, its opposite change must be described in some parameter. Geometrically, this is a 180 degree turn; mathematically, it is a sign change. If the normal semi-major axis of a normal ellipse lies inside the ellipse, then when the sign changes, the negative semi-axis should be deposited in the opposite direction - outward of the curvature. The geometric interpretation of the semi-major axis of the hyperbola is the distance from the perigee of the hyperbola to the point of intersection of its asymptotes, along which the branches of the hyperbola go to infinity. This segment does not lie inside the bend of the curve, as in the ellipse, but outside the hyperbola, in the opposite direction, changing its sign from the respectable interior of the ellipse to the opposite of laying it out.


Moreover, having just "deposited" from the parabola further into the hyperbolic region, the hyperbola has a narrow V-shaped position of these asymptotes, inside which the hyperbola approaches from infinity, unfolds around the center of gravity, passing its perigee (for the sake of familiar sound, we will not say "pericenter" in in the general case, and the perigee is for the usual Earth), and goes back to infinity. Accordingly, the point of intersection of the asymptotes can deviate very far from the perigee of the hyperbola, which lies “inside the narrow beak” of the asymptotes. With almost parallel asymptotes - practically to infinity.

And with a further increase in the flight speed, the hyperbola unfolds with its asymptotes and branches into an increasingly obtuse angle, with an unlimited increase in speed, approaching a straight line. And this is understandable: a body relatively slowly flying along a hyperbola (albeit with a hyperbolic velocity, of course) stays for a long time in the perigee region, where the planet's gravitational grip is strongest and the force bending the trajectory is greatest; the slow speed gives gravity enough time here to work properly on the bend in the path.On the contrary, the faster the speed of the hyperbolic flight around the planet, the less time the body spends in the near-perigee zone, slips it faster and does not allow time to bend its trajectory. Therefore, with a fast flight, the hyperbola is bent less by the gravity of the planet.


The specific energy of the body changes smoothly with an increase in velocity from elliptical to hyperbolic. From negative values ​​of small ellipses, the specific orbital energy of the body gradually decreases with lengthening of the ellipses, small steps approaching the parabolic zero of energy, smoothly passing zero when passing the parabola, and then also smoothly from zero increases on hyperbolic trajectories, already with positive values.

But the length of the semi-major axis behaves differently. As the ellipses stretch, it grows (directly, geometrically), reaching infinity at a parabola. When passing into a hyperbola, the length of the semi-major axis becomes negative (it turns out to be outside the curvature) and is also infinitely large. Decreasing as the hyperbolic velocity continues to grow, the hyperbolic asymptotes "move apart" and the distance between the point of their intersection and the perigee decreases.

Perigee and apogee as a mirror of orbital tasks

It is getting closer to understanding how an apogee with a negative altitude appears in flight data. You just need to pay attention to the particulars of the usual tasks and conditions for launching by start commands.

In closed orbits of artificial earth satellites, apogee and perigee heights are very important, useful and indicative. They define many features of orbital motion, and they, like a mirror, reflect important details of the current ballistic situation or task. For example, the height of the geostationary orbit is undoubtedly an important, key parameter (together with the equally important zero inclination of the orbit). The value of the geostationary altitude must be accurately maintained, and the circular shape of this orbit is characterized by the equality of the heights of the perigee and apogee, that is, their actual absence, when any point of the orbit is both apogee and perigee at the same time. So the circle is expressed by the equality of apogee and perigee.

In another case, it is important to know from what depth to what height the work of the second stage should raise the perigee. Or where and how far the perigee should be lowered into the atmosphere, stopping the orbital motion. For example, if you need to stretch the entrance and make the braking overload by the atmosphere small and easy for the crew, you should not push the perigee into the atmosphere below seventy kilometers. On the approach to such a perigee, the spacecraft will go for a long time almost horizontally in the upper, rarefied layers of the atmosphere - and therefore slow down slowly and for a long time, extinguishing the speed smoothly and without great overload, without accumulating descent energy.

There may also be an inverse problem - to de-orbit a satellite over a given area so that when it is destroyed in the atmosphere, the remaining unburned fragments do not fly out of the relatively small fall zone. To do this, the satellite should be launched along a steeper entry trajectory, with less "smearing" horizontally: the perigee can be lowered under the Earth's surface by several hundred kilometers - striving for it, the satellite will enter the atmosphere along a steeper trajectory, experience large power and heat loads, it will collapse more strongly and burn more completely, and its surviving parts will fall with a smaller spread. Of course, an ever deeper immersion of the perigee underground will require a larger supply of fuel for the braking impulse; but here such solutions are already chosen that are acceptable in terms of all restrictions, reserves and capabilities.


Etc. Therefore, during launches, it is very convenient to use the apogee and perigee heights as controlled values ​​of movement, good and convenient indicators. Much is clear from them what, where and how it comes out or not, whether the satellite has reached altitude, how it moves with such apogee and perigee. Understandable geometric characteristics, point height, physical, real.Therefore, when displaying orbital flight data, the apogee and perigee altitudes calculated for this motion and the current moment in time are always used. And to calculate the height of the perigee and apogee, separated by the major axis, its half is widely used - the major semiaxis, its length. The higher the apogee, the longer the ellipse, its major longitudinal axis and major semiaxis.

The apogee of not a satellite

However, it is difficult to track one infrequent, but important moment by the height of the apogee - the transition of the closed orbital motion of the vehicle into the hyperbolic one. How to distinguish a very distant apogee from an infinitely distant one? With a large removal of the apogee, its difference with infinity will be small and elusive. The transition of the apparatus to the hyperbola is easier and more correct to track in the context of the specific orbital energy: to watch how the negative specific orbital energy of the satellite smoothly approaches zero, crosses the parabolic zero and then grows into positive values ​​with the transition of the flight to hyperbolic.

But launches to hyperbola - interplanetary - are much less frequent than near-Earth launches. Therefore, the computational model, which displays the current flight data in the form of apogee and perigee heights, remains the same during interplanetary launches - near-Earth. As with most spacecraft launches, the vast majority are artificial satellites of the Earth.

The satellite model of motion is forced to describe by its near-Earth key parameters of motion the flight of an apparatus that ceases to be a satellite.

The computational model of motion for satellites is sharpened for the usual elliptical parameters with an indispensable perigee and apogee. And this satellite model of motion is forced to describe by its near-Earth key parameters of motion the flight of an apparatus that ceases to be a satellite. Therefore, with the transition of motion to hyperbolic, not satellite, the model shows its calculated miracles, purely mathematically calculating - like it or not, how it is laid down - the imaginary apogee at the beginning of the hyperbolic trajectory, as it always does for the usual ellipse. Such calculations are mathematically correct - this is not a typo, not a glitch, not a contradiction - but in hyperbolic motion some of the results of such calculations are already imaginary. Hence, the imaginary apogee of the hyperbola and its negative height appears in the motion data displayed in the corner of the screen.

The attentive reader - or simply an orbital ballistician, for whom certain quantities have long become familiar, like the multiplication table - will see that the distance of 6378 kilometers and 3443.9 nautical miles is the same distance. Moreover, this distance is equal to the average radius of the Earth. That is, the computational model of motion has placed the apogee at the center of our planet. Why exactly in the center is explained by the peculiarities of simplification of the movement model, which would be tiresome to climb into now. And, perhaps, to the question "Why so deep?" - the model of movement with a sly smile would answer that there is simply nowhere deeper …


But these computational incidents have no effect on the real movement of the interplanetary vehicle. Therefore, the resulting negative apogee in a few seconds is simply removed from the telemetry data, and the interplanetary traveler continues his hyperbolic path, which began at these moments, to the applause of the Mission Control Center personnel and wishes him a good journey. And we once again note the outwardly subtle paradox with a negative apogee height, but now as a good friend.


On hyperbolic trajectoriesnot only interplanetary launches take place, but also flyby of planets during the so-called perturbation, or gravitational, maneuvers. In this case, the speed of the spacecraft relative to the planet at the beginning of the flyby is equal to the speed after its completion, only the trajectory bends and the direction of motion changes.But relative to the Sun, in the heliocentric frame of reference, after flying around the planet, the magnitude of the vehicle's velocity also changes: it receives a velocity increment, positive or negative. Accordingly, the apparatus changes its orbit around the Sun. In a new orbit, it can move faster, fly away from the star, or, conversely, slowing down, approach the inner region of the solar system and its planets. Gravitational maneuvers based on hyperbolic flyby are used very widely. They can be carried out many times in one flight; for example, in the program of the Parker solar probe - seven gravitational deceleration maneuvers near Venus, of which he has already performed three (the first two near the inner, to the Sun, day side of Venus; the third time - a month ago, for the first time outside it, on the night side), and four stay ahead.

What is the trajectory of Perseverance now? Hyperbolic? No. Its trajectory was hyperbolic only relative to the Earth in its vicinity, during its departure. In relation to the Sun, Perseverance moves in an elliptical orbit, being a companion of the star; its motion is a revolution around the sun, and it is now doing part of a revolution. The spacecraft will also approach Mars with a hyperbolic velocity relative to the planet, from which it will begin to enter the atmosphere.

Center of the gravitational field, the center of the Earth - what exactly is the center of the Earth? The earth's surface has a complex shape that cannot be described analytically, that is, precisely with the help of mathematical formulas. For a surface of complex shape, the center will not be an equidistant point, like a ball; what is the center of such a surface? If we talk about the center of the Earth's gravitational field - similarly, the real gravitational field has a rather complex, "uneven" structure. In this case, the geometric center of the surface of our planet, no matter how it is determined, does not have to coincide with the center of the gravitational field (also no matter how it is defined). The different density of the underlying rocks in different regions, even with an ideal ball of the Earth, creates irregularities in the gravitational field that do not coincide with the features of the surface. Which of these centers - geometric or gravitational field - to choose for reference? What are the satellites around? For the center of revolution in orbital ballistics, a separate concept is used - the barycenter. All low-mass satellites revolve around the planet's barycenter. The name is derived from the Greek word βαρύς (“baris”) - “heaviness”. From the same word, the name of bariteriums originated - the first large and really heavy, weighing a couple of tons, Eocene proboscis. From the point of view of the distribution of masses over the volume of the Earth, the barycenter is its center of mass. We can say that this is a point that replaces the entire planet in its movement and interaction with other bodies. Therefore, the movement of a satellite around a real planet is simplified as its revolution around the barycenter of the Earth.

Sun-synchronous orbits- a class of orbits in which under each point of the orbit on the Earth there is always one and the same local solar time. That is, at a specific sub-satellite point, the angular position of the Sun above the local horizon is always approximately the same. This means virtually unchanged lighting conditions at each sub-satellite point. For example, it is always the same length of the shadow cast by an object over which a satellite passes in such an orbit. Changing the length of the shadow means only one thing - changing the height of the object. With the same lighting, it is easier to register changes on the ground. Therefore, they like to launch optical reconnaissance satellites into sun-synchronous orbits. Although there are other tasks: for example, ballistic provision of eternal illumination of a LEO satellite. So that he never goes into the shadows, continuously receiving power for powerful consumption - perhaps for constant radar observation and the operation of on-board emitting devices.To do this, the device is launched into a sun-synchronous orbit, passing everywhere over the twilight zone of the Earth's surface. In such an orbit, the satellite does not enter the shadow of the planet, always circling across the sun's ray, around it, and the entire revolution remains illuminated. For sun-synchronous orbits, the launch is not carried out strictly to the North Pole, but a little to the west, about eight to ten degrees, providing an orbital inclination of about 98-100 °. And the orbital altitude is formed in the range of 600-1000 kilometers. For such launches, Vandenberg Air Force Base in California is great because the launch paths from here run north and south across the ocean.

Low reference orbit. Low is about 180-200 kilometers. In the United States, an altitude of 185 km is often adopted - the round number of a 100-mile orbit. Often, in a low reference orbit, they do not make a full turn - only a part. Because they are already leaving it for further business: in the case of only temporary placement on it, the orbit is the reference one. And if nothing happens further, it's just a low orbit. In English, it is customary to say "parking orbit" - parking orbit. The device is left on it, like a car parked on the site. A low reference orbit is needed in order to calmly travel along it to the desired point above the Earth, where to perform a given action, an impulse to transfer to another orbit. For optimality, it is often done after half a turn, on the other side of the Earth - they get there in the reference orbit, quickly and conveniently. The stay on it is short, so the deceleration by the remnants of the atmosphere is generally already significant (you will not find satellites with a working orbit of 200 kilometers - they are falling too quickly), and in general it is not scary - it will change the altitude insignificantly in a short time.

Suborbital trajectories Earth orbits with underground perigee are called. If the body enters the earth, the perigee of its orbit was underground, and the body moved towards it. The suborbital ellipse has two parts: one real part - the body moves along it; the second is underground. And so this is an ordinary Keplerian ellipse, regardless of the fact that it has an underground part. It only says that there will be no full turnover. The place of intersection of the descending part of the ellipse with the Earth's surface will become the point of impact, in reality, of course, the area of ​​impact. All ballistic missiles travel along suborbital trajectories. In fact, the entire combat ballistics of missiles, from operational-tactical to intercontinental ones, is combat suborbital ballistics. It has worked out and developed a huge number of all kinds of special questions. Many numerical values ​​of motion parameters are secret. In the suborbital combat movement, features are added related to the reliability of the combat mission, combat features of the movement. For example, possible maneuvering in the active phase, carried out as part of the complication of intercepting an accelerating ballistic missile by enemy anti-missile weapons. This requires a greater thrust-to-weight ratio and special logic for constructing such maneuvers. Compared to the combat area, the suborbital trajectory of the space launch at the first stage is in many ways simpler. This is a typical, only energetically optimized elimination stage. Although there are unexpected ballistic incidents on it. But about them another time.

Destruction in the atmosphere has a peculiarity in terms of space and suborbital vehicles. The satellites enter very gently, the picture of their destruction is rather extended. Apart from them, there are two types of purely suborbital vehicles - combat ones. These are warheads designed to overcome all atmospheric loads, and disengagement stages, or combat stages, that fly behind the warheads and enter the atmosphere at about the same places. The latter are in no way adapted for entering the atmosphere; their design contains only resistance to starting overloads and precise work in space.The stages of disengagement usually enter half a minute later than the last warheads - and although with rather gentle angles of inclination of the trajectory, they are still steeper than the orbital intruders. At a steeper entrance, rapidly growing aerodynamic forces heat up and break the combat stage - then again, then fragments, many times. Sometimes on the ground, after the pieces fall out, details of the destruction of the structure by a hypersonic flow are visible. With what a rift on the edges of Aeolus destroyed the affairs of Vulcan, the stream broke the special alloy. Visually, the destruction of the battle stages looks like the flight of an unusually large orange-red star, usually with a long streak of fire, like a torch. Around the brightly glowing main "comet", several times close flashes of white light are seen, similar to the flashes of a camera or electric welding - these are fragments of magnesium alloys burned out. Gradually blushing with fire, the step stretches out into a flat strip of orange coals of decelerating fragments, quickly cooled by the frost of the lower stratosphere to invisibility. At night, a green glowing trail remains in the sky, dimming and extinguishing in half a minute - you can see the glow of the recombination of impact ionization of the air of the stage when everything was on fire. The destruction of the step is best seen from the farthest distance during winter anticyclones with clear calm nights, medium frosts and dense dry air. In severe frosts, frost haze accumulating in the surface layer often interferes, blurring the details to indistinctness, as well as refraction on air inhomogeneities.

Mammoths … about them another time.

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