The simpler the words, the more there are. I warned you - don't complain now!

The Earth has an elliptical orbit. An ellipse, unlike a circle, does not have a "radius", but has two "half-axes" of different lengths - a large and a small one. Accordingly, there are two points in the earth's orbit that lie on the major axis and are as far apart as possible compared to any other pair of points in the orbit. Exactly in the middle of the segment between these points, we draw a perpendicular to the plane in which the orbit lies (the plane of the ecliptic). An observer moving along the perpendicular will see the Earth's orbit from a different angle. That is, if we draw rays from the location of the observer to the two previously mentioned points in the Earth's orbit, the angle between the rays will depend on the distance to the ecliptic plane. Very close to the plane, the rays form a very obtuse angle (almost 180°). Very far - very sharp (almost 0°). And there is such a distance at which this angle will be equal to exactly 2 "(two arc seconds; one second is equal to 1 ° / 3600). This is the parsec.

For a stationary alien sitting on the above perpendicular one parsec from the Earth and able to see it somehow (this is rather difficult, since the Earth is not bright enough for such a distant observer), the Earth will change its apparent location slightly due to its orbital movement. The displacement angle between the two extreme visible positions of the Earth will be equal to exactly 2" (we deliberately placed the alien exactly at such a distance in order to obtain such a displacement angle). And relative to some "average" visible location, the Earth will move a maximum of 1" (half of the from 2"). An alien can say that the "annual trigonometric parallax" of the Earth is 1" (one arc second). And call the distance to the Earth "parsec" (PARallax - SEC).

It took a parsec, of course, not for aliens enthusiastically observing the Earth from a perpendicular to the ecliptic, but for earthly astronomers. The stars are so far away from us that their own movement does not lead to a change in position in the sky, even in a year. But they seem to "rotate" in the sky in a circle due to the rotation of the Earth around its axis (one revolution per day). In addition, the stars ADDITIONALLY "move" across the sky due to the movement of the Earth in orbit, although this is hardly noticeable (for complete happiness, the influence of the earth's atmosphere and oscillations of the earth's axis will be added, but, let's say, we took this into account and overcame it). If you try very hard, you can identify and measure this subtle (against the background of the daily "rotation" and other interference) movement and measure the annual trigonometric parallax of the star. And if the star were near the above-described perpendicular to the ecliptic and would have an annual parallax of 1 ", then it is (ta-damm!) Exactly one parsec from us. Indeed, in the reference frame associated with the Earth, it is not the Earth that moves in an elliptical orbit , and the rest of the world for some reason makes a similar movement, but in the opposite direction.Accordingly, for an earthly astronomer who is following the above-described alien (or a star next to him), this is an alien (or a star next to him): 1) why- it rotates around the Earth at a wild speed (with a full revolution in 1 day) and 2) additionally moves in an elliptical orbit (with a full revolution in one year and semi-axes, like the earth's), parallel to the plane of the ecliptic.

The distance to the rest of the stars can also be easily calculated (only geometry with trigonometry and nothing else) in parsecs, if you can measure their annual parallax and (additionally) take into account the position in the sky. The parsec itself is equal (by definition and from trigonometry) to the cotangent of 1 "multiplied by the semi-major axis of the earth's orbit (by the "astronomical unit"). The cotangent of a small angle is equal to one divided by the angle itself in radians. 180 ° is pi radians, 1 ° is pi/180 radians, 1"=1°/3600=pi/(180×3600). Cotangent 1 "is 180 × 3600 / pi≈206.000. Accordingly, the parsec is approximately equal to (a little more than) 206 thousand "astronomical units" (major semiaxes of the earth's orbit). And since we know the parameters of the earth's orbit (including its major semiaxis ), you can already express the parsec itself in other units of distance (meters, light years, etc.) - this is approximately 3.2 light years. The stars closest to us have an annual trigonometric parallax less than (but of the order of) 1 "and, accordingly, are located on greater than (but on the order of) one parsec.

The parsec is a cosmic unit of measure used by astronomers to determine the distance to very distant objects in the universe.

The parsec (abbreviated as "parallax second") is a non-systemic unit of measurement used in cosmology to measure distances to particularly distant objects in outer space. This unit performs not only a practical function - it helps to calculate the distance to a particular object in the Universe, but also creates a kind of comfort for astronomers. Judge for yourself, it is much easier to say that the distance from the Sun to the nearest star is 1.3 parsecs than that it is 40.7 trillion kilometers. A person who would regularly operate with numbers with such a huge number of zeros would sooner or later go crazy. Thus, by inventing the parsec, scientists have greatly simplified the computational processes in astronomy.

The parsec is a popular unit of measurement in astrophysics. Fans of this science are well aware that it is equal to 3.2616 light years. Many of them can freely name the distance to one or another distant object in parsecs. But, unfortunately, not everyone understands how this unit of measurement came into being and how to calculate it correctly.

Discovery history

While distances to nearby objects in space can be measured with a radio telescope to within a few centimeters, measuring distances to distant corners of the universe is much more difficult. However, scientists needed to find a way to calculate this value and they decided to use the horizontal parallax method, which is well known in geometry.

The essence of the horizontal parallax method is simple: if you look at a distant object from different places, then against the background of other, more distant objects, it will change its position. Knowing the distance between the places from which observation is carried out, as well as the angle of displacement of the object against the background of distant objects, it is possible to calculate the distance to it by geometric calculations. Astronomers decided to use this axiom; it served as the basis for the discovery of a new unit of measurement - the parsec.

How to determine a parsec

Let's say you're looking at a star and want to determine its distance in parsecs. But for this you need to know what a distance of 1 parsec is. This distance represents the displacement of a celestial body against the background of other, more distant objects by an angle equal to one arc second when the observer moves half the diameter of the earth's orbit.

To some, this definition may seem difficult to understand. In fact, the essence of the definition of a parsec is not so difficult to understand. Returning to our star, the distance in parsecs to which we want to determine, we will have to make two observations of this object from different points in the earth's orbit. This can be done without any space instruments, but simply by waiting for the Earth itself to pass half of its annual path and become on the opposite side of the Sun.

Knowing the length between the points from which the observations were made (it is equal to 1 astronomical unit - the distance of the Earth from the Sun or the radius of the Earth's orbit), as well as the displacement of the star against the background of more distant stars and galaxies, we can calculate the distance to it. If in the observed range the star has shifted by 1 arc second, the distance to it is one parsec, but if it has shifted by half a second, two parsecs. Contrary to conjecture, the smaller the parallax (displacement) of a celestial body, the more parsecs to it.

The name is formed from abbreviations of the words " steam allax" and " sec und" - a parsec is equal to the distance to an object whose annual trigonometric parallax is equal to one arcsecond.

According to an equivalent definition, a parsec is the distance from which a segment one astronomical unit long (virtually equal to the average radius of the earth's orbit), perpendicular to the line of sight, is visible at an angle of one arc second (1″).

1 pc = $\backslash frac(1)(\backslash operatorname(tg)1$} a. e. ≈ $\backslash frac(360\backslash cdot60\backslash cdot60)(2\backslash pi)$ a. e. ≈ 206 264.8 a. e. \u003d 3.0856776 10 16 m \u003d 30.8568 trillion km (petameters) \u003d 3.2616 light years.

Multiple units are also used: kiloparsec (kpc, kpc), megaparsec (Mpc, Mpc), gigaparsec (Gpc, Gpc). Sub-multiples are generally not used, as astronomical units are used instead.

Some distances

• 1 astronomical unit (AU) is approximately 4.848 10 −6 parsecs;
• as of February 13, 2015, the Voyager 1 spacecraft was at a distance of 0.000630 pc (19.4 billion km, or 130 AU) from the Sun, receding at 17.5 microparsecs per year (3, 6 a.u./year);
• Oort cloud diameter ≈0.62 pc;
• the distance from the Sun to the nearest star (Proxima Centauri) is 1.3 parsecs;
• a distance of 10 pc light travels in 32 years 7 months and 6 days;
• the distance from the Sun to the nearest globular cluster, M 4 , is 2.2 kpc;
• the distance from the Sun to the center of our Galaxy is about 8 kpc;
• the diameter of our Galaxy is about 30 kpc;
• distance to the Andromeda nebula - 0.77 Mpc;
• the nearest large cluster of galaxies, the Virgo cluster, is at a distance of 18 Mpc;
• on scales of about 300 Mpc, the Universe is practically homogeneous;
• the distance to the first discovered, brightest and one of the nearest quasars, 3C 273, is 734 Mpc;
• to the horizon of the observable Universe - about 4 Gpc (if we measure the distance traveled by the light registered on Earth), or, if we estimate the modern distance - taking into account the expansion of the Universe (that is, to distant objects that once emitted this radiation) ≈14 Gpc;

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• Article from the Great Soviet Encyclopedia.

An excerpt characterizing the Parsec

Exactly the same phrase about Countess Zubova and the same laugh had already been heard five times in front of strangers by Prince Andrei from his wife.
He quietly entered the room. The princess, plump, ruddy, with work in her hands, sat on an armchair and talked incessantly, sorting through Petersburg memories and even phrases. Prince Andrei came up, stroked her head and asked if she had rested from the journey. She answered and continued the same conversation.
The stroller stood in six at the entrance. It was a dark autumn night outside. The coachman did not see the drawbar of the carriage. People with lanterns bustled about on the porch. The huge house burned with lights through its large windows. In the hall crowded the courtyards, who wanted to say goodbye to the young prince; all the household were standing in the hall: Mikhail Ivanovich, m lle Bourienne, Princess Mary and the princess.
Prince Andrei was called to his father's office, who wanted to say goodbye to him face to face. Everyone was waiting for them to come out.
When Prince Andrei entered the office, the old prince, wearing old man's glasses and in his white coat, in which he received no one except his son, was sitting at the table and writing. He looked back.
– Are you going? And he began to write again.
- I came to say goodbye.
- Kiss here, - he showed his cheek, - thank you, thank you!
- What do you thank me for?
- Because you don’t overstay, you don’t hold on to a woman’s skirt. Service first. Thank you, thank you! And he continued to write, so that the spray flew from the crackling pen. - If you need to say something, say it. These two things I can do together,” he added.
“About my wife… I’m so ashamed that I’m leaving her in your arms…”
- What are you lying? Say what you need.
- When your wife has time to give birth, send to Moscow for an obstetrician ... So that he is here.
The old prince stopped and, as if not understanding, stared with stern eyes at his son.
“I know that no one can help if nature does not help,” said Prince Andrei, apparently embarrassed. “I agree that out of a million cases, one is unfortunate, but this is her fantasy and mine. They told her, she saw it in a dream, and she is afraid.
“Hm ... hm ...” the old prince said to himself, continuing to finish writing. - I will.
He crossed out the signature, suddenly turned quickly to his son and laughed.
- It's bad, isn't it?
- What's wrong, father?
- Wife! said the old prince shortly and significantly.
“I don’t understand,” said Prince Andrei.
“Yes, there’s nothing to do, my friend,” the prince said, “they are all like that, you won’t get married.” Do not be afraid; I won't tell anyone; and you yourself know.
He grabbed his hand with his bony little hand, shook it, looked straight into his son's face with his quick eyes, which seemed to see right through the man, and again laughed his cold laugh.
The son sighed, confessing with this sigh that his father understood him. The old man, continuing to fold and print letters, with his usual speed, grabbed and threw sealing wax, seal and paper.
- What to do? Beautiful! I'll do everything. You be calm,” he said curtly while typing.
Andrey was silent: it was both pleasant and unpleasant for him that his father understood him. The old man got up and handed the letter to his son.
“Listen,” he said, “do not worry about your wife: what can be done will be done.” Now listen: give the letter to Mikhail Ilarionovich. I am writing that he will use you in good places and not keep you as an adjutant for a long time: a bad position! Tell him that I remember him and love him. Yes, write how he will accept you. If it's good, serve. Nikolai Andreich Bolkonsky's son, out of mercy, will not serve anyone. Well, now come here.
He spoke in such a rapid way that he did not finish half of the words, but the son was used to understanding him. He led his son to the bureau, threw back the lid, pulled out a drawer, and took out a notebook covered in his large, long, concise handwriting.
“I must die before you.” Know that here are my notes, to transfer them to the sovereign after my death. Now here - here is a pawn ticket and a letter: this is a prize to the one who writes the history of the Suvorov wars. Submit to the academy. Here are my remarks, after me read for yourself, you will find something useful.

For their calculations, astronomers use special units of measurement that are not always clear to ordinary people. It is understandable, because if cosmic distances were measured in kilometers, then the number of zeros would ripple in the eyes. Therefore, to measure cosmic distances, it is customary to use much larger quantities: an astronomical unit, a light year, and a parsec.

Quite often used to indicate distances within our own solar system. If you can still express it in kilometers (384,000 km), then the closest way to Pluto is about 4,250 million km, and this will already be difficult to understand. For such distances, it is time to use the astronomical unit (AU), equal to the average distance from the earth's surface to the Sun. In other words, 1 a.u. corresponds to the length of the semi-major axis of the orbit of our Earth (150 million km.). Now, if you write that the shortest distance to Pluto is 28 AU, and the longest path can be 50 AU, this is much easier to imagine.

The next largest is the light year. Although the word “year” is present, you should not think that it is about time. One light year is 63,240 AU. This is the path that a ray of light travels in 1 year. Astronomers have calculated that it takes more than 10 billion years for a beam of light to reach us from the farthest corners of the universe. To imagine this gigantic distance, let's write it down in kilometers: 950000000000000000000000. Ninety-five billion trillion habitual kilometers.

The fact that light does not propagate instantly, but at a certain speed, scientists began to guess since 1676. It was at this time that a Danish astronomer named Ole Roemer noticed that the eclipses of one of Jupiter's moons began to be delayed, and this happened precisely when the Earth was heading in its orbit towards the opposite side of the Sun, the opposite of where Jupiter was. Some time passed, the Earth began to return back, and the eclipses again began to approach the previous schedule.

Thus, about 17 minutes of time difference was noted. From this observation, it was concluded that it took 17 minutes for light to travel a distance the length of the diameter of the Earth's orbit. Since the diameter of the orbit was proved to be approximately 186 million miles (now this constant is 939,120,000 km), it turned out that a beam of light traveled at a speed of about 186,000 miles per second.

Already in our time, thanks to Professor Albert Michelson, who set out to determine as accurately as possible what a light year is, using a different method, the final result was obtained: 186,284 miles in 1 second (about 300 km / s). Now, if we calculate the number of seconds in a year and multiply by this number, we get that a light year is 5,880,000,000,000 miles long, which corresponds to 9,460,730,472,580.8 km.

For practical purposes, astronomers often use the unit of distance known as the parsec. It is equal to the displacement of the star against the background of other celestial bodies by 1 "" when the observer is displaced by 1 radius

"- a parsec is equal to the distance to an object whose annual trigonometric parallax is equal to one arc second.

According to an equivalent definition, a parsec is the distance from which a segment one astronomical unit long (virtually equal to the average radius of the earth's orbit), perpendicular to the line of sight, is visible at an angle of one arc second (1″).

1 pc = texvc not found; See math/README for setup help.): \frac(1)(\operatorname(tg)1"") a. e. ≈ Unable to parse expression (executable file texvc not found; See math/README for setup help.): \frac(360\cdot60\cdot60)(2\pi) a. e. ≈ 206 264.8 a. e. \u003d 3.0856776 10 16 m \u003d 30.8568 trillion km (petameters) \u003d 3.2616 light years.

Multiple units are also used: kiloparsec (kpc, kpc), megaparsec (Mpc, Mpc), gigaparsec (Gpc, Gpc). Sub-multiples are generally not used, as astronomical units are used instead.

Some distances

• 1 astronomical unit (AU) is approximately 4.848 10 −6 parsecs;
• as of February 13, 2015, the Voyager 1 spacecraft was at a distance of 0.000630 pc (19.4 billion km, or 130 AU) from the Sun, receding at 17.5 microparsecs per year (3, 6 a.u./year);
• Oort cloud diameter ≈0.62 pc;
• the distance from the Sun to the nearest star (Proxima Centauri) is 1.3 parsecs;
• a distance of 10 pc light travels in 32 years 7 months and 6 days;
• the distance from the Sun to the nearest globular cluster, M 4 , is 2.2 kpc;
• the distance from the Sun to the center of our Galaxy is about 8 kpc;
• the diameter of our Galaxy is about 30 kpc;
• distance to the Andromeda nebula - 0.77 Mpc;
• the nearest large cluster of galaxies, the Virgo cluster, is at a distance of 18 Mpc;
• on scales of about 300 Mpc, the Universe is practically homogeneous;
• the distance to the first discovered, brightest and one of the nearest quasars, 3C 273, is 734 Mpc;
• to the horizon of the observable Universe - about 4 Gpc (if we measure the distance traveled by the light registered on Earth), or, if we estimate the modern distance - taking into account the expansion of the Universe (that is, to distant objects that once emitted this radiation) ≈14 Gpc;

see also

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Notes

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• Article from the Great Soviet Encyclopedia.

An excerpt characterizing the Parsec

“Well, then I’ll wait for her,” the pleased little girl confidently declared. “And we’ll all be together again, right, papa?” You want your mother to be with us again, right? ..
Her huge gray eyes shone like stars, in the hope that her beloved mother would one day also be here, in her new world, not even realizing that this HER current world for mom would be nothing more and nothing less than just death. ...
And, as it turned out, the baby didn’t have to wait long... Her beloved mother reappeared... She was very sad and a little bewildered, but she held herself much better than her wildly frightened father, who now, to my sincere joy, little by little came to his senses.
The interesting thing is that during my communication with such a huge number of dead entities, I could almost say with certainty that women accepted the “shock of death” much more confidently and calmly than did men. At that time I still could not understand the reasons for this curious observation, but I knew for sure that it was so. Perhaps they endured deeper and harder the pain of guilt for the children they left in the “living” world, or for the pain that their death brought to relatives and friends. But it was precisely the fear of death that most of them (unlike men) almost completely lacked. Could this be explained to some extent by the fact that they themselves gave the most valuable thing that was on our earth - human life? Unfortunately, I didn't have an answer to that question...
- Mommy, mommy! And they said that you would not come for a long time! And you are already here! I knew you wouldn't leave us! squealed little Katya, choking with delight. “Now we are all together again and now everything will be fine!”
And how sad it was to watch how all this sweet friendly family tried to save their little daughter and sister from the realization that it was not at all so good that they were all together again, and that none of them, unfortunately, there was no longer the slightest chance for their remaining unlived life ... And that each of them would sincerely prefer that at least one of their family would remain alive ... And little Katya still muttered something innocently and happily , rejoicing that again they are all one family and again completely “everything is fine” ...
Mom smiled sadly, trying to show that she was also glad and happy ... and her soul, like a wounded bird, screamed about her unfortunate babies who had lived so little ...
Suddenly, she seemed to “separate” her husband and herself from the children with some kind of transparent “wall” and, looking straight at him, gently touched his cheek.
“Valery, please look at me,” the woman said quietly. – What are we going to do?.. It’s death, isn’t it?
He raised his big gray eyes to her, in which such mortal anguish lapped, that now instead of him I wanted to howl like a wolf, because it was almost impossible to take all this into my soul ...
- How could this happen? .. Why should they? .. - again asked Valeria's wife. - What do we do now, tell me?
But he could not answer her, much less offer something. He was simply dead, and, unfortunately, he did not know anything about what happens “after”, just like all the other people who lived in that “dark” time, when everyone and everyone was literally driven in with the hardest “hammer of lies” into the head that “after” there is nothing more and that human life ends at this mournful and terrible moment of physical death ...
- Dad, mom, where are we going now? the girl asked cheerfully. It seemed that now, when everyone was assembled, she was completely happy again and was ready to continue her life even in such an unfamiliar existence for her.
- Oh, mommy, and my pen went through the bench !!! But how can I sit down now? .. - the little girl was surprised.
But mother didn’t have time to answer, when suddenly, right above them, the air sparkled with all the colors of the rainbow and began to thicken, turning into an amazingly beautiful blue channel, very similar to the one I saw during my unsuccessful “bathing” in our river. The channel sparkled and shimmered with thousands of stars, and more and more densely enveloped the dumbfounded family.