The upcoming human flight to Mars has shaken up the entire earthly community, becoming the most discussed topic in the last half century. This is truly a significant event in the history of earthly civilization, from which we expect not only the colonization of Mars, but also an evolutionary turn towards “ man of cosmic scale«.

Martian cities - the future of the Fourth Planet

When setting off on a journey along unknown roads, one must also evaluate the danger of the planned enterprise. Space does not like those in a hurry, because it is well known that outer space is not distinguished by the complaisance of a good disposition.

Most of the problems associated with long duration space flights (ignoring radiation effects) are reduced or eliminated by artificial gravity.
Whereas the unfavorable influence of the lack of gravity and the influence of the radiation situation are the biggest obstacles to the development of the Solar system.

NASA, which is actively advancing on the territory of the Red Planet, occupies a leading position in the study of Mars. Elon Musk and Co. are pursuing a similar mission, concentrating serious power on.

But if one wants to go beyond low-Earth orbit, the Moon seems a more obvious choice, since the low effects of gravity can be explored more thoroughly, and within three days of travel from home.

Our closest neighbor is a great place to test technologies for long-term flights in space, isn't it? On the Moon, the designs of manned bases in an alien environment can be thoroughly tested and modified to the maximum.
And one more thing - when working on lunar tasks, spacecraft designs may find more advanced technologies for long-term travel. Do you agree with this?

So why is NASA reluctant to return to the Moon in favor of a human presence on Mars? Why is Space X so persistently ignoring the Moon while rushing to Mars?

However, we are not currently pursuing the goals of a conspiracy theory, allegedly: “they clearly know something about the catastrophe coming to Earth,” so they want to go to the Red Planet. We are simply interested in the question of distant travels.

Weak attraction of artificial gravity.

The concept of artificial gravity is conjured up by footage of giant spinning space station modules, such as in 2001: A Space Odyssey. This looks like the most acceptable solution in terms of long-term space flights. Yes, this is a look at the issue through the eyes of not a specialist, but a potential traveler.

However, creating even primitive structures to obtain artificial gravity is apparently a more difficult task than what NASA or Space X are ready to solve with the current level of technology.

Weightlessness can be both delightful and insidious. On the one hand, this allows astronauts to do things impossible on Earth: for example, moving large equipment with a slight movement of the hand. And, of course, it is of serious interest to scientists: from biology to the material sciences of hydrodynamics.

Prolonged human exposure to weightlessness has been studied for many decades, and the conclusion is alarming - serious consequences for the health of astronauts. The researchers scored, from bone fragility and muscle loss to vision loss.

NASA plans space missions beyond Earth orbit to Mars lasting six to nine months. They are developing ways to eliminate the effects of weightlessness. The confrontation mainly consists of compiling daily hour-long exercises, which is a priority for the agency.

Yes, experts are developing a set of exercises to counteract weightlessness, leaching calcium from the bones. At the same time, no one is experimenting with a countermeasure—the creation of gravity. But this has long been proposed as a means to provide at least partial severity, perhaps sufficient to relieve health problems.

However, surprisingly, artificial gravity is a low priority at NASA and Space X. Perhaps the agencies are not yet ready to fully enter space, and are in too much of a hurry, sending people on an already dangerous journey?

Not a single spacecraft on a Mars mission with a person on board provides rotating structures in one form or another to create the effect of gravity.
Even the giant spacecraft Space X, planned to transport 100 people at once, does not create artificial gravity - but in fact, this is already a habitable station in space.

Experts on the problem of gravity say:

Michael Barratt, a NASA astronaut and physician, explained the agency's reasons for not adopting artificial gravity as a countermeasure against weightlessness: We can keep our bones and muscles healthy, our cardiovascular system healthy, he said during a 2016 conference in September in Long Beach. State of California. We don't need artificial gravity.

The astronaut's view was echoed by NASA executives: Bone loss, muscle loss, vestibular function, these are the kinds of things whose normal functioning we can control through exercise, says Bill Gerstenmaier.

Elon Musk, presenting the Mars mission project, was not concerned with the problem of weightlessness, rejecting the creation of local gravity for the crew of the ships. “I think the substantive issues have been resolved,” says the Space X mastermind.
In passing, there are much more long-term flights to the ISS than the time on the planned trip to Mars.

Technical implementation of artificial gravity.

However, experts were considering options to create gravity. A serious problem is the technical side of the spacecraft project, which implements the idea of ​​artificial gravity, either through a rotating module or by creating some kind of centrifuge.

“We looked at a lot of vehicle designs, trying to provide artificial gravity in different ways. In reality, it just doesn't work, explains Gerstenmaier. This is a significant modernization of the spacecraft. A very big job, while the task is simply to get to Mars.

Worse, experts say, turning on one section of the spacecraft to maintain gravity could create a new series of problems because astronauts would have to regularly adapt between weightlessness and gravity.

In turn, this can provoke space adaptation syndrome. Astronauts will have to cross zones of weightlessness and gravity several times a day, which can be more problematic than simply staying in zero gravity.

Barrett noted that he and his colleagues have technical concerns about the design of spacecraft that implement artificial gravity. Astronauts are afraid of artificial gravity. Why? We don't like big moving parts.

Vision problems have been reported in some astronauts, which may lead to an overestimation of the importance of artificial gravity. At the same time, the cause of the visual impairment is not known, and there is no guarantee that gravity will be able to eliminate the problem.

There are many ideas about why this happens. One of the factors is rising carbon dioxide levels, experts believe. Thus, the level of carbon dioxide on the ISS is ten times higher than in normal atmospheric conditions on Earth.

— Most likely, the lack of gravity is due to a lack of technology, which simply does not exist to solve the problem today. After all, even Gerstenmaier, being somewhat skeptical about the necessity of gravity, does not completely rule it out.
Yes, as we now understand gravity on spaceships, it is a matter of future technology.

Today, participants in the Mars race are striving to be the first to arrive on Mars and develop at least something suitable for life there.
Humanity needs a feat: weakened by a long flight, on an alien planet, in an atmosphere unsuitable for life, the colonists will build shelters and build life on the Red Planet.
But can anyone tell me why there is such a rush when the attack looks like a flight?

Each of us has ever thought about life outside the Earth, but not everyone knows what role its magnetic field plays in the viability of a body. Scientists' hypothesis that life on Mars is possible has good grounds. What conditions are necessary for this, and what role the magnetic field plays in life support, read below.

Magnetic field of Mars

The magnetic field is a kind of protective shell that rejects all the negative effects of the wind, electrical charges of the Sun or other planets. Not every planet has such a protective field; it is produced by internal thermal and dynamic processes occurring at the center of the core of the cosmic body. Particles of molten metal, while in motion, create an electric current, the presence of which on the planet is involved in the creation of a protective layer.

The magnetic field of Mars clearly exists; it is distributed very weakly and unevenly. This is explained by the immobility of the cooled core relative to the surface. There are places on the planet where the manifestation of the field is several times greater than the force of influence on other parts of the fourth planet. The Mars Global Surveyor magnetometer established the presence of the strongest magnetic field in the southern areas, while on the northern side it was practically not detected by the instrument.

The magnetic field on Mars was previously quite strong; it has a residual nature, preserving the so-called paleomagnetism. This field is not enough to protect against solar radiation or the effects of winds. Thus, the unprotected surface leaves no opportunity for water or other particles to linger.

To the question whether Mars had a magnetic field, and whether it exists now, we can confidently give a positive answer. The presence of a small field on a neighboring planet suggests that it existed earlier, having greater strength than today.

Why did Mars lose its magnetic field?

There is a theory according to which 4 billion years ago the magnetic field of the red planet was quite strong. It was similar to the earth’s and was stably distributed on the surface of its crust.

A collision with a certain large cosmic body, or, as some researchers claim, several large asteroids, influenced the internal dynamic processes of the core. ceased to produce electric currents, as a result of which the field of Mars weakened, its distribution became heterogeneous: it became stronger in some areas, while others remain unprotected. In these places the Sun is two and a half times stronger than on Earth.

How strong is gravity on Mars?

Due to the weak and unevenly distributed magnetic field, gravity on Mars has equally low parameters. To be more precise, compared to the earth's gravity, it is 62% weaker. Therefore, all subjects located here lose their true mass at times.

The force of gravity on Mars depends on several parameters: mass, radius, and density. Despite the fact that the area of ​​Mars is close to that of the Earth, there are large differences in the density and diameters of the planets; the mass of Mars is 89% less than that of Earth.

Having data from two similar planets, scientists calculated the gravitational force of Mars, which is quite different from Earth’s. The force of gravity on Mars is as weak as the magnetic field. Low gravity rearranges the functioning of a living creature. Therefore, a person’s long stay on the Red Plane can have a negative impact on health. If a way is found to overcome the consequences of weak gravity on human health, the time of exploration of other planets will rapidly approach.

In addition to the force of gravity, there is a quantity on the planet itself - the gravitational constant, which shows the force of gravity between the planets. It is calculated relative to two planets, Mars and Earth, Mars and the Sun separately, taking into account the distance between them. This value is fundamental, since the distance between them also depends on the gravitational force of the planets.

Calculation of Martian gravity

To find the force of gravity on Mars, you need to apply the formula:
G = m(Earth) m(Mars) /r2
Here is the gravitational constant, r is the distance from the centers of the Earth and Mars.
Substituting the values, we get
5.97 1024 0.63345 6.67 10-11 /3.488=3.4738849055214
Thus, the value of Martian gravity is 3.4738849055214 N.

Why is it different on Mars?

The gravity of Mars relative to Earth depends on the size of the planets, their mass, and the distance between their centers. The planet with the most mass exerts the greatest degree of gravitational pull. Thus, the Earth, having the greatest mass, exerts the greatest gravitational force relative to Mars. As the distance between planets increases, the force of gravity between them decreases.

The Earth's gravity, having high rates, is capable of attracting objects with greater force than on Mars. Thus, Earth's gravity, in comparison with Martian gravity, allows one to maintain vital activity and vitality on Earth. While on Mars, low gravity does not hold even water on the surface of the planet.

A comparative analysis of the nature of the gravitational force on Mars relative to the gravitational force of the Earth allows us to answer the question of why there is no such magnetic field on Mars as on Earth.

Despite the similarity of the two planets: area, presence of polar caps, similar inclination of the rotation axis and climate changes, Mars and Earth have significant differences. The pressure on Mars is 99,992.5 millibars lower than the pressure on Earth. The seasonal temperature of Mars is many times lower than on Earth. Thus, in winter the minimum reading was -143 degrees; in summer the surface heats up to 35 degrees Celsius.

Scientists are busy considering the conditions under which life on the fourth from the Sun would be possible. At the moment, research on the Red Planet is not enough to collect data, since the low magnetic field and gravity make it difficult for a person to stay on the planet, or rather expose his body to unwanted changes, which is hardly compatible with life.

On other planets, why it occurs, what it is needed for, as well as its effect on various organisms.

Space

People have dreamed of traveling to the stars since ancient times, starting from the time when the first astronomers examined other planets of our system and their satellites through primitive telescopes, which means, in their opinion, they could be inhabited.

Many centuries have passed since then, but alas, interplanetary flights, and especially flights to other stars, are still impossible. And the only extraterrestrial object that researchers have visited is the Moon. But already at the beginning of the 20th century, scientists knew that the force of gravity on other planets is different from ours. But why? What is it, why does it arise and can it be destructive? We will look at these questions.

A little physics

He also developed a theory according to which any two objects experience a mutual force of attraction. On the scale of space and the Universe as a whole, this phenomenon manifests itself very clearly. The most striking example is our planet and the Moon, which, thanks to gravity, revolves around the Earth. We see the manifestation of gravity in everyday life, we just got used to it and don’t pay attention to it at all. This is the so-called It is because of it that we do not soar in the air, but walk calmly on the ground. It also helps keep our atmosphere from gradually escaping into space. For us it is conventionally 1 G, but what is the force of gravity on other planets?

Mars

Mars is most similar in physical characteristics to our planet. Of course, living there is problematic due to the lack of air and water, but it is located in the so-called habitable zone. True, very conditional. It does not have the terrifying heat like on Venus, centuries-old storms like on Jupiter, and absolute cold like on Titan. And scientists over the last decades have not given up trying to come up with methods for terraforming it, creating conditions suitable for life without spacesuits. However, what is the phenomenon of gravity on Mars? It is 0.38 g from Earth, which is about half as much. This means that on the red planet you can gallop and jump much higher than on Earth, and all the weights will also weigh much less. And this is quite enough to retain not only its current, “frail” and liquid atmosphere, but also a much denser one.

True, it’s too early to talk about terraformation, because first you need to at least just land on it and establish constant and reliable flights. But still, the gravity on Mars is quite suitable for future settlers.

Venus

Another planet closest to us (besides the Moon) is Venus. This is a world with monstrous conditions and an incredibly dense atmosphere, which no one has been able to look beyond for a long time. Its presence, by the way, was discovered by none other than Mikhail Lomonosov.

The atmosphere is responsible for the greenhouse effect and the terrifying average surface temperature of 467 degrees Celsius! Sulfuric acid precipitation constantly falls on the planet and lakes of liquid tin boil. Such an inhospitable gravity is 0.904 G from the earth's, which is almost identical.

It is also a candidate for terraforming, and its surface was first reached by a Soviet research station on August 17, 1970.

Jupiter

Another planet of the solar system. More precisely, a gas giant consisting mainly of hydrogen, which becomes liquid closer to the surface due to the monstrous pressure. According to calculations, by the way, it is quite possible that one day it will flare up in its depths and we will have two suns. But if this happens, then, to put it mildly, it will not happen soon, so there is no need to worry. The gravity on Jupiter is 2.535 g relative to Earth.

Moon

As already mentioned, the only object in our system (other than the Earth) where people have been is the Moon. True, debate still rages over whether those landings were reality or a hoax. However, due to its low mass, the surface gravity is only 0.165 g of Earth's.

The influence of gravity on living organisms

The force of gravity also has various effects on living beings. Simply put, when other habitable worlds are discovered, we will see that their inhabitants differ greatly from each other depending on the mass of their planets. For example, if the Moon were inhabited, it would be inhabited by very tall and fragile creatures, and vice versa, on a planet with the mass of Jupiter, the inhabitants would be very short, strong and massive. Otherwise, you simply cannot survive on weak limbs in such conditions, no matter how hard you try.

The force of gravity will play an important role in the future colonization of the same Mars. According to the laws of biology, if you don’t use something, it gradually atrophies. Astronauts from the ISS on Earth are greeted with chairs on wheels, since in weightlessness their muscles are used very little, and even regular strength training does not help. So the offspring of colonists on other planets will be at least taller and physically weaker than their ancestors.

So we figured out what the gravity is on other planets.

Let's imagine that we are going on a journey through the solar system. What is the gravity on other planets? On which ones will we be lighter than on Earth, and on which ones will we be heavier?

While we have not yet left the Earth, let's do the following experiment: mentally descend to one of the Earth's poles, and then imagine that we have been transported to the equator. I wonder if our weight has changed?

It is known that the weight of any body is determined by the force of attraction (gravity). It is directly proportional to the mass of the planet and inversely proportional to the square of its radius (we first learned about this from a school physics textbook). Consequently, if our Earth were strictly spherical, then the weight of each object moving along its surface would remain unchanged.

But the Earth is not a ball. It is flattened at the poles and elongated along the equator. The equatorial radius of the Earth is 21 km longer than the polar radius. It turns out that the force of gravity acts on the equator as if from afar. That is why the weight of the same body in different places on the Earth is not the same. Objects should be heaviest at the earth's poles and lightest at the equator. Here they become 1/190 lighter than their weight at the poles. Of course, this change in weight can only be detected using a spring scale. A slight decrease in the weight of objects at the equator also occurs due to the centrifugal force arising from the rotation of the Earth. Thus, the weight of an adult arriving from high polar latitudes to the equator will decrease by a total of about 0.5 kg.

Now it is appropriate to ask: how will the weight of a person traveling through the planets of the solar system change?

Our first space station is Mars. How much will a person weigh on Mars? It is not difficult to make such a calculation. To do this, you need to know the mass and radius of Mars.

As is known, the mass of the “red planet” is 9.31 times less than the mass of the Earth, and its radius is 1.88 times less than the radius of the globe. Therefore, due to the action of the first factor, the gravity on the surface of Mars should be 9.31 times less, and due to the second, 3.53 times greater than ours (1.88 * 1.88 = 3.53 ). Ultimately, it constitutes a little more than 1/3 of the Earth's gravity there (3.53: 9.31 = 0.38). In the same way, you can determine the gravity stress on any celestial body.

Now let’s agree that on Earth an astronaut-traveler weighs exactly 70 kg. Then for other planets we obtain the following weight values ​​(the planets are arranged in ascending order of weight):

Pluto 4.5 Mercury 26.5 Mars 26.5 Saturn 62.7 Uranus 63.4 Venus 63.4 Earth 70.0 Neptune 79.6 Jupiter 161.2
As we can see, the Earth occupies an intermediate position between the giant planets in terms of gravity. On two of them - Saturn and Uranus - the force of gravity is somewhat less than on Earth, and on the other two - Jupiter and Neptune - it is greater. True, for Jupiter and Saturn the weight is given taking into account the action of centrifugal force (they rotate quickly). The latter reduces body weight at the equator by several percent.

It should be noted that for the giant planets the weight values ​​are given at the level of the upper cloud layer, and not at the level of the solid surface, as for the Earth-like planets (Mercury, Venus, Earth, Mars) and Pluto.

On the surface of Venus, a person will be almost 10% lighter than on Earth. But on Mercury and Mars the weight reduction will occur by 2.6 times. As for Pluto, a person on it will be 2.5 times lighter than on the Moon, or 15.5 times lighter than in earthly conditions.

But on the Sun, gravity (attraction) is 28 times stronger than on Earth. A human body would weigh 2 tons there and would be instantly crushed by its own weight. However, before reaching the Sun, everything would turn into hot gas. Another thing is tiny celestial bodies such as the moons of Mars and asteroids. In many of them you can easily resemble... a sparrow!

It is quite clear that a person can travel to other planets only in a special sealed spacesuit equipped with life support devices. The weight of the spacesuit the American astronauts wore on the lunar surface is approximately equal to the weight of an adult. Therefore, the values ​​we have given for the weight of a space traveler on other planets must be at least doubled. Only then will we obtain weight values ​​close to the actual ones.

It is often very difficult to explain in words the simplest things or the structure of a particular mechanism. But usually, understanding comes quite easily if you see them with your eyes, or even better, twirl them in your hands. But some things are invisible to our eyes and even being simple are very difficult to understand.
For example, what electric current is - there are many definitions, but none of them describes its mechanism exactly, without ambiguity and uncertainty.
On the other hand, electrical engineering is a fairly well-developed science in which any electrical processes are described in detail using mathematical formulas.
So why not show similar processes using these same formulas and computer graphics.
But today we will consider the action of a simpler process than electricity - the force of gravity. It would seem that there is nothing complicated about it, because the law of universal gravitation is studied at school, but nevertheless... Mathematics describes the process as it takes place under ideal conditions, in some kind of virtual space where there are no restrictions.
In life, everything is usually not so, and the process under consideration is continuously superimposed on many different circumstances, imperceptible or insignificant at first glance.
Knowing the formula and understanding its action are slightly different things.
So, let's take a small step towards understanding the law of gravity. The law itself is simple - the force of gravity is directly proportional to the masses and inversely proportional to the square of the distance between them, but the complexity lies in the unimaginable number of interacting objects.
Yes, we will consider only the force of gravity, so to speak, completely alone, which is of course incorrect, but in this case it is permissible, since this is simply a way to show the invisible.
And yet, the article contains JavaScript code, i.e. all the pictures were actually drawn using Canvas, so the entire article can be taken .

Displaying the capabilities of gravity in the solar system

Within the framework of classical mechanics, gravitational interaction is described by Newton’s law of universal gravitation, which states that the force of gravitational attraction F between two material points of mass m 1 And m 2, separated by distance r, is proportional to both masses and inversely proportional to the square of the distance - that is:

Where G- gravitational constant equal to approximately 6.67384×10 -11 N×m 2 ×kg -2.
But I would like to see a picture of the change in gravity throughout the solar system, and not between two bodies. Therefore, the mass of the second body m 2 let’s take it equal to 1, and simply denote the mass of the first body m. (That is, we imagine objects in the form of a material point - one pixel in size, and we measure the force of attraction relative to another, virtual object, let's call it a “test body”, with a mass of 1 kilogram.) In this case, the formula will look like:

Now, instead of m we substitute the mass of the body of interest, and instead r we go through all the distances from 0 to the value of the orbit of the last planet and get the change in gravitational force depending on the distance.
When applying forces from different objects, we choose the larger one.
Further, we express this power not in numbers, but in the corresponding shades of color. This will give you a clear picture of the distribution of gravity in the solar system. That is, in a physical sense, the shade of color will correspond to the weight of a body weighing 1 kilogram at the corresponding point in the solar system.
It should be noted that:

• The force of gravity is always positive and has no negative values, i.e. mass cannot be negative
• the gravitational force cannot be equal to zero, i.e. an object either exists with some mass or does not exist at all
• the force of gravity can neither be screened nor reflected (like a ray of light with a mirror).

(in fact, these are all the restrictions imposed by physics on mathematics in this matter).
Let's now look at how to display the magnitude of the gravitational force in color.

To show numbers in color, you need to create an array in which the index would be equal to the number, and the value would be the color value in the RGB system.
Here is a color gradient from white to red, then yellow, green, blue, purple and black. In total there were 1786 shades of color.

The number of colors is not that great; they are simply not enough to display the entire spectrum of gravitational forces. Let us limit ourselves to the gravitational forces from the maximum - on the surface of the Sun and the minimum - in the orbit of Saturn. That is, if the force of attraction on the surface of the Sun (270.0 N) is designated by a color located in the table under index 1, then the force of attraction to the Sun in the orbit of Saturn (0.00006 N) will be designated by a color with an index far beyond 1700. So that all the same there will not be enough colors to uniformly express the magnitude of the gravitational force.
In order to clearly see the most interesting places in the displayed forces of attraction, it is necessary that values ​​of the force of attraction less than 1H correspond to large color changes, and from 1H and above, the correspondences are not so interesting - it is clear that the force of attraction, say, of the Earth, differs from the attraction of Mars or Jupiter , yeah, okay. That is, the color will not be proportional to the magnitude of the force of attraction, otherwise we will “lose” the most interesting thing.
To convert the value of the attractive force to the color table index, we use the following formula:

Yes, this is the same hyperbole known since high school, only the square root of the argument was first extracted. (Taken purely from the light, only to reduce the ratio between the largest and smallest values ​​of the force of attraction.)
See how the colors are distributed depending on the attraction of the Sun and planets.


As you can see, on the surface of the Sun, our test body will weigh about 274 N or 27.4 kG, since 1 N = 0.10197162 kgf = 0.1 kgf. And on Jupiter it is almost 26N or 2.6 kgf, on Earth our test body weighs about 9.8N or 0.98kgf.
In principle, all these figures are very, very approximate. For our case this is not very important, we need to turn all these gravity values ​​into their corresponding color values.
So, from the table it is clear that the maximum value of the attractive force is 274N, and the minimum is 0.00006N. That is, they differ by more than 4.5 million times.

It is also clear that all the planets turned out to be almost the same color. But this does not matter, the important thing is that the boundaries of the planets’ attraction will be clearly visible, since the attractive forces of small values ​​change color quite well.
Of course, the accuracy is not great, but we just need to get a general idea of ​​the gravitational forces in the Solar System.
Now let’s “arrange” the planets in places corresponding to their distance from the Sun. To do this, you need to attach some kind of distance scale to the resulting color gradient. The curvature of the orbits, I think, can be ignored.
But as always, the cosmic scale, in the literal sense of these words, does not allow us to see the whole picture. Let's see, Saturn is located approximately 1430 million kilometers from the Sun, the index corresponding to the color of its orbit is 1738. That is. it turns out in one pixel (if we take on this scale one shade of color is equal to one pixel) approximately 822.8 thousand kilometers. And the radius of the Earth is approximately 6371 kilometers, i.e. diameter is 12,742 kilometers, about 65 times smaller than one pixel. Here's how to maintain proportions.
We'll go the other way. Since we are interested in the gravity of circumplanetary space, we will take the planets separately and color them and the space around them with a color corresponding to the gravitational forces from them and the Sun. For example, take Mercury - the radius of the planet is 2.4 thousand km. and equate it to a circle with a diameter of 48 pixels, i.e. One pixel will be 100 km. Then Venus and Earth will be 121 and 127 pixels, respectively. Quite convenient sizes.
So, we make a picture 600 by 600 pixels in size, determine the value of the force of attraction to the Sun in the orbit of Mercury plus/minus 30,000 km (so that the planet turns out to be in the center of the picture) and paint the background with a gradient of color shades corresponding to these forces.
At the same time, to simplify the task, we paint not with arcs of the corresponding radius, but with straight, vertical lines. (Roughly speaking, our "Sun" will be "square" and will always be on the left side.)
To ensure that the background color does not show through the image of the planet and the zone of attraction to the planet, we determine the radius of the circle corresponding to the zone where the attraction to the planet is greater than the attraction to the Sun and paint it white.
Then in the center of the picture we place a circle corresponding to the diameter of Mercury on a scale (48 pixels) and fill it with a color corresponding to the force of attraction to the planet on its surface.
Next, we paint from the planet with a gradient in accordance with the change in the force of attraction to it and at the same time constantly compare the color of each point in the layer of attraction to Mercury with a point with the same coordinates, but in the layer of attraction to the Sun. When these values ​​become equal, we make this pixel black and stop further painting.
Thus, we obtain a certain form of visible change in the gravitational force of the planet and the Sun with a clear black boundary between them.
(I wanted to do exactly this, but... it didn’t work out, I couldn’t make a pixel-by-pixel comparison of two image layers.)

In terms of distance, 600 pixels are equal to 60 thousand kilometers (i.e., one pixel is 100 km).
The force of attraction to the Sun in the orbit of Mercury and near it varies only within a small range, which in our case is indicated by one shade of color.


So, Mercury and the force of gravity in the vicinity of the planet.
It should be immediately noted that the eight subtle rays are defects from drawing circles in Canvas. They have nothing to do with the issue under discussion and should simply be ignored.
The dimensions of the square are 600 by 600 pixels, i.e. this space is 60 thousand kilometers. The radius of Mercury is 24 pixels - 2.4 thousand km. The radius of the attraction zone is 23.7 thousand km.
The circle in the center, which is almost white, is the planet itself and its color corresponds to the weight of our kilogram test body on the surface of the planet - about 373 grams. The thin blue circle shows the boundary between the surface of the planet and the zone in which the gravitational force toward the planet exceeds the gravitational force toward the Sun.
Then the color gradually changes, becomes more and more red (i.e. the weight of the test body decreases) and finally becomes equal to the color corresponding to the force of attraction to the Sun in a given place, i.e. in Mercury's orbit. The boundary between the zone where the force of attraction to the planet exceeds the force of gravity to the Sun is also marked with a blue circle.
As you can see, there is nothing supernatural.
But in life the picture is somewhat different. For example, in this and all other images, the Sun is on the left, which means, in fact, the planet’s gravitational region should be slightly “flattened” on the left and elongated on the right. And in the image there is a circle.
Of course, the best option would be a pixel-by-pixel comparison of the area of ​​attraction to the Sun and the area of ​​attraction to the planet and selecting (displaying) the larger of them. But neither I, as the author of this article, nor JavaScript are capable of such feats. Working with multidimensional arrays is not a priority for this language, but its work can be shown in almost any browser, which solved the issue of application.
And in the case of Mercury, and all the other planets of the terrestrial group, the change in the force of attraction to the Sun is not so great as to display it with the available set of color shades. But when considering Jupiter and Saturn, the change in the force of gravity towards the Sun is very noticeable.

Venus

Actually, everything is the same as that of the previous planet, only the size of Venus and its mass are much larger, and the force of attraction to the Sun in the planet’s orbit is less (the color is darker, or rather, more red), and the planet has a larger mass, so the color of the planet’s disk is more light.
In order for a planet with a zone of attraction of a test body weighing 1 kg to fit in a 600 by 600 pixel picture, we reduce the scale by 10 times. Now there are 1 thousand kilometers in one pixel.

Earth+Moon

To show the Earth and the Moon, changing the scale by 10 times (as in the case of Venus) is not enough; you need to increase the size of the picture (the radius of the Moon’s orbit is 384.467 thousand km). The image will be 800 by 800 pixels in size. The scale is 1 thousand kilometers in one pixel (we understand well that the error of the picture will increase even more).


The picture clearly shows that the zones of attraction of the Moon and the Earth are separated by a zone of attraction to the Sun. That is, the Earth and the Moon are a system of two equivalent planets with different masses.

Mars with Phobos and Deimos

The scale is 1 thousand kilometers in one pixel. Those. like Venus, and the Earth and the Moon. Remember that distances are proportional, and the display of gravity is nonlinear.


Now, you can immediately see the fundamental difference between Mars and its satellites and the Earth and the Moon. If the Earth and the Moon are a system of two planets and, despite their different sizes and masses, act as equal partners, then the satellites of Mars are in the zone of the gravitational force of Mars.
The planet itself and its satellites were practically “lost.” The white circle is the orbit of the distant satellite - Deimos. Let's zoom in 10 times for better viewing. There are 100 kilometers in one pixel.


These “creepy” rays from Canvas spoil the picture quite badly.
The sizes of Phobos and Deimos are disproportionately increased by 50 times, otherwise they are completely invisible. The color of the surfaces of these satellites is also not logical. In fact, the force of gravity on the surfaces of these planets is less than the force of gravity towards Mars in their orbits.
That is, everything is “blown away” from the surfaces of Phobos and Deimos by the gravity of Mars. Therefore, the color of their surfaces should be equal to the color in their orbits, but only to make it easier to see, the disks of the satellites are colored in the color of the force of gravity in the absence of the force of gravity towards Mars.
These satellites should simply be monolithic. In addition, since there is no gravitational force on the surface, it means they could not have formed in this form, that is, both Phobos and Deimos were previously parts of some other, larger object. Well, or, at least, they were in a different place, with less gravity than in the gravitational zone of Mars.
For example, here Phobos. The scale is 100 meters in one pixel.
The surface of the satellite is indicated by a blue circle, and the gravitational force of the entire mass of the satellite is indicated by a white circle.
(In fact, the shape of the small celestial bodies Phobos, Deimos, etc. is far from spherical)
The color of the circle in the center corresponds to the gravitational force of the satellite's mass. The closer to the surface of the planet, the weaker the force of gravity.
(Here again there is an inaccuracy. In fact, the white circle is the boundary where the force of attraction to the planet becomes equal to the force of attraction to Mars in the orbit of Phobos.
That is, the color outside this white circle should be the same as the color outside the blue circle indicating the surface of the satellite. But the color transition shown should be inside the white circle. But then nothing will be visible at all.)
It looks like a cross-sectional drawing of the planet.
The integrity of the planet is determined only by the strength of the material from which Phobos is composed. With less strength, Mars would have rings like Saturn, from the destruction of satellites.


And it seems that the collapse of space objects is not such an exceptional event. Even the Hubble Space Telescope “detected” a similar case.

The disintegration of asteroid P/2013 R3, which is located at a distance of more than 480 million kilometers from the Sun (in the asteroid belt, further than Ceres). The diameter of the four largest fragments of the asteroid reaches 200 meters, their total mass is about 200 thousand tons.
And this Deimos. Everything is the same as Phobos. The scale is 100 meters in one pixel. Only the planet is smaller and, accordingly, lighter, and is also located further from Mars and the force of attraction to Mars is less here (the background of the picture is darker, i.e., more red).

Ceres

Well, Ceres is nothing special, except for the coloring. The force of attraction to the Sun is less here, so the color is appropriate. The scale is 100 kilometers in one pixel (the same as in the picture with Mercury).
The small blue circle is the surface of Ceres, and the large blue circle is the boundary where the force of gravity on the planet becomes equal to the force on the Sun.

Jupiter

Jupiter is very large. Here is a picture measuring 800 by 800 pixels. The scale is 100 thousand kilometers in one pixel. This is to show the planet's entire gravitational region. The planet itself is a small dot in the center. Satellites are not shown.
Only the orbit (outer circle in white) of the farthest satellite, S/2003 J 2, is shown.


Jupiter has 67 moons. The largest are Io, Europa, Ganymede and Callisto.
The farthest satellite, S/2003 J 2, orbits Jupiter at an average distance of 29,541,000 km. Its diameter is about 2 km, its mass is about 1.5 × 10 13 kg. As you can see, it goes far beyond the planet’s sphere of gravity. This can be explained by errors in the calculations (after all, quite a lot of averaging, rounding and discarding of some details were done).
Although there is a way to calculate the limit of Jupiter's gravitational influence, determined by the Hill sphere, the radius of which is determined by the formula

where a jupiter and m jupiter are the semimajor axis of the ellipse and the mass of Jupiter, and M sun is the mass of the Sun. This gives a rounded radius of 52 million km. S/2003 J 2 is moving away in an eccentric orbit to a distance of up to 36 million km from Jupiter
Jupiter also has a ring system of 4 main components: a thick inner torus of particles known as the “halo ring”; relatively bright and thin “Main Ring”; and two wide and weak outer rings - known as "web rings", named after the material of the satellites - that form them: Amalthea and Thebes.
A halo ring with an inner radius of 92,000 and an outer of 122,500 kilometers.
Main ring 122500-129000 km.
Arachnoid ring of Amalthea 129000-182000 km.
Spider ring of Thebes 129000-226000 km.
Let's enlarge the picture 200 times, there are 500 kilometers in one pixel.
Here are the rings of Jupiter. The thin circle is the surface of the planet. Next come the boundaries of the rings - the inner boundary of the halo ring, the outer boundary of the halo ring and also the inner boundary of the main ring, etc.
The small circle in the upper left corner is the area where the gravitational force of Jupiter's moon Io becomes equal to the gravitational force of Jupiter in Io's orbit. The satellite itself is simply not visible at this scale.


In principle, large planets with satellites need to be considered separately, since the difference in the values ​​of gravitational forces is very large, as are the dimensions of the planet’s gravitational region. As a result, all interesting details are simply lost. But looking at a picture with a radial gradient doesn’t make much sense.

Saturn

Picture size 800 by 800 pixels. The scale is 100 thousand kilometers in one pixel. The planet itself is a small dot in the center. Satellites are not shown.
The change in the force of attraction towards the Sun is clearly visible (remember that the Sun is on the left).


Saturn has 62 known satellites. The largest of them are Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus.
The farthest satellite is Fornjot (temporary designation S/2004 S 8). Also referred to as Saturn XLII. The average radius of the satellite is about 3 kilometers, mass 2.6 × 10 14 kg, semi-major axis 25,146,000 km.
Rings on planets appear only at a considerable distance from the Sun. The first such planet is Jupiter. Having a mass and size larger than Saturn's, its rings are not as impressive as Saturn's rings. That is, the size and mass of the planet for the formation of rings are less important than the distance from the Sun.
But look further, a pair of rings surrounds the asteroid Chariklo (10199 Chariklo) (asteroid diameter is about 250 kilometers), which orbits the Sun between Saturn and Uranus.

Wikipedia about the asteroid Chariklo
The ring system consists of a dense inner ring 7 km wide and an outer ring 3 km wide. The distance between the rings is about 9 km. The radii of the rings are 396 and 405 km, respectively. Chariklo is the smallest object whose rings have been discovered.
However, the force of gravity has only an indirect relation to the rings.
In fact, rings appear from the destruction of satellites, which consist of material of insufficient strength, i.e. not stone monoliths like Phobos or Deimos, but pieces of rock, ice, dust and other space debris frozen into one whole.
So the planet drags him away with its gravity. Such a satellite, which does not have its own gravity (or rather, has a force of its own gravity less than the force of attraction to the planet in its orbit) flies in orbit, leaving behind a trail of destroyed material. This is how a ring is formed. Further, under the influence of gravity towards the planet, this fragmentary material approaches the planet. That is, the ring expands.
At some level, the force of gravity becomes strong enough that the falling speed of these debris increases, and the ring disappears.

Afterword

The purpose of publishing this article is that perhaps someone with programming knowledge will be interested in this topic and make a better model of gravitational forces in the Solar System (yes, three-dimensional, with animation.
Or maybe he will even make it so that the orbits are not fixed, but are also calculated - this is also possible, the orbit will be a place where the force of gravity will be compensated by the centrifugal force.
It will turn out almost like in life, like a real solar system. (This is where it will be possible to create a space shooter, with all the subtleties of space navigation in the asteroid belt. Taking into account the forces acting according to real physical laws, and not among hand-drawn graphics.)
And this will be an excellent physics textbook that will be interesting to study.
P.S. The author of the article is an ordinary person:
not a physicist
not an astronomer
not a programmer
does not have higher education.