Constellation Globe 26_ Functions and Usage of Constellation Globe

How to calculate the period of revolution of the Earth?

Characteristics of the earth's revolution

Just as the rotation of the earth has its unique regularity, so does the revolution of the earth. These laws are shown in the following aspects: the earth orbit, the angle between the earth orbit plane and the ecliptic, the period of revolution of the earth and the revolution speed of the earth.

The orbit and direction of the earth's revolution

During the revolution of the earth, every point on the route it passes is on the same plane and forms a closed curve. The closed curve that the earth takes in the process of revolution is called earth orbit. If we regard the earth as a particle, then the orbit of the earth actually refers to the orbit of the center of the earth.

Strictly speaking, the center of the earth's revolution is not the center of the sun, but the common center of mass of the earth and the sun. Not only the earth is rotating around this common center of mass, but also the sun is rotating around this point. However, the sun is the central celestial body in the solar system, and the earth is just an ordinary planet in the solar system. The mass of the sun is 330 thousand times that of the earth, and the common center of mass of the sun and the earth is only 450 kilometers away from the center of the sun. Compared with the radius of the sun of about 700 thousand kilometers, this distance is really insignificant, even smaller than the distance between the sun and the earth of 65.438+0.5 billion kilometers. Therefore, it is very close to the actual situation to regard the revolution of the earth as the movement of the earth around the sun (center).

The shape of the earth's orbit is an ellipse close to a perfect circle, and the sun is located at a focal point of the ellipse. An ellipse has a semi-major axis, a semi-minor axis and a semi-focal length, which are denoted by A, B and C respectively, where A is the distance from both ends of the minor axis to the focus (F 1, F2).

There is such a relationship between the semi-focal length and the semi-long axis and the flat short axis:

Namely c2=a2-b2

The ratio c/a of the semi-focal length c to the semi-major axis a is the eccentricity of the ellipse, which is expressed by e, that is, e=c/a,

Eccentricity is a quantitative representation of elliptical shape, and the value of e is greater than 0 and less than 1. The closer the ellipse is to the circle, the smaller the value of e is, that is, it is close to 0; On the contrary, the flatter the ellipse, the greater the e value. It is determined that the semi-major axis A of the earth's orbit is 149600000 km, and the semi-minor axis B is 149580000 km. According to this data, the eccentricity of the earth's orbit is calculated as follows:

It can be seen that the earth's orbit is very close to a circle.

Because the earth's orbit is elliptical, as the earth rotates around the sun, the distance between the sun and the earth is constantly changing. The point on the earth's orbit closest to the sun, that is, the end of the long wheelbase of the elliptical orbit close to the sun, is called the perihelion. In modern times, the date when the earth passes the perihelion is around the beginning of 1 month every year. At this time, the distance between the earth and the sun is about 147 100000 kilometers, which is usually called the nearest distance. The point in the earth's orbit farthest from the sun, that is, the long wheelbase end of the elliptical orbit far from the sun, is called the apohelion. In modern times, the date of the perihelion of the earth is about the beginning of July every year. At this time, the earth is about 152 100000 kilometers away from the sun, which is usually called the distance from the sun. The average value of short distance and long distance is 1 49.6 million kilometers, which is the average distance from the sun to the earth, that is,1astronomical unit.

According to ellipse circumference's calculation formula:

L=2πα( 1-0.25×e2)

According to calculation, the total length of the earth's orbit is 940,000,000 kilometers.

The revolution direction of the earth is consistent with the rotation direction. Seen from the yellow North Pole, it rotates counterclockwise, that is, from west to east. This is consistent with the revolution direction of other planets and most satellites in the solar system.

The anniversary of apparent sports

The revolution of the earth is discovered from the annual apparent movement of the sun. In order to explain the annual apparent motion of the sun, we first analyze the relationship between the moving point and the fixed point.

Assuming that moving point A moves in a circle around fixed point B, then at fixed point B, the trajectory of point A is a circle, and the direction of movement of point A is counterclockwise. In this case, from the driving point A, the motion characteristics of the fixed point B are exactly the same, and the trajectory of the point B is also circular, and the motion direction is also counterclockwise. But the movement of A around B is true, and the movement of B around A is apparent, which is an intuitive reflection of the movement of A around B. ..

The characteristics of the earth's revolution around the sun and the apparent motion of the sun seen by observers on the earth are the same as those mentioned above. Although the actual situation is that the earth revolves around the sun, as an observer on the earth, he can only feel the movement of the sun relative to the stars. The trajectory plane of this movement coincides with the orbital plane of the earth, and its direction, speed and period are the same as those of the earth. The motion of the sun relative to the starry sky is a kind of apparent motion, which is called solar annual apparent motion. The annual apparent motion of the sun is actually a reflection of the earth's revolution on the celestial sphere.

The intersection angle between the earth's orbital plane and the equator.

As mentioned earlier, every point in the earth's orbit is on the same plane, and this plane is the earth's orbital plane. The orbital plane of the earth appears as the ecliptic plane on the celestial sphere, which is on the same plane as the annual apparent motion route of the sun.

The earth's rotation and revolution are simultaneous. On the celestial sphere, rotation is represented by celestial axis and celestial equator, and revolution is represented by yellow axis and ecliptic. The celestial equator is on one plane and the ecliptic is on another. The planes of these two concentric circles form an included angle of 23 26', which is called the ecliptic angle.

The existence of the ecliptic angle actually means that the axis of rotation is inclined to the earth's orbital plane during the earth's revolution around the sun. Since the earth axis is perpendicular to the equatorial plane of the celestial sphere, the intersection angle between the earth axis and the earth orbital plane should be 90-23 26', that is, 66 34'. No matter where the earth rotates, this tilt remains the same.

During the revolution of the earth, the spatial orientation of the earth axis has not changed obviously for a long time. At present, the North Pole points to Alpha Star in Ursa minor, that is, near Polaris, which

It is the position of the north pole of the celestial sphere. That is to say, the earth axis moves in parallel during the revolution, so no matter where the earth revolves, the angle between the earth axis and the earth orbit plane is constant, and the angle between yellow and red is also constant.

The existence of the ecliptic angle also shows the deviation between the ecliptic pole and the celestial pole, that is, the yellow north pole (or yellow south pole) and the celestial north pole (or celestial south pole) deviate from 23 26' on the celestial sphere.

Most of the globes we see have an inclined axis of rotation, which is inclined at an angle of 66 34' with the desktop (representing the earth's orbital plane), while the equatorial plane of the globe is at an angle of 23 26' with the desktop, which is an intuitive embodiment of the angle between the yellow and the pond.

Earth revolution and precession period

The time for the earth to revolve around the sun is the period of revolution of the earth. Generally speaking, the revolutionary period is one year. Because the period of the solar annual apparent motion is the same as that of the earth's revolution, the period of the earth's revolution can be measured by the solar annual apparent motion. Observers on the earth observe that the interval between the continuous passage of the sun through a certain point on the ecliptic is one year. Because the selected reference points are different, the length of "year" is also different. The commonly used cycle units are sidereal year, tropic year and perihelion year.

The sidereal year of the earth's rotation is a sidereal year. This periodic unit is obtained with the star as the reference point. In a sidereal year, starting from the center of the sun, the center of the earth takes a star as the background, starts from a certain point, orbits the sun once, and then returns to the same point in the sky; Seen from the center of the earth, the center of the sun starts from a certain point on the ecliptic, is fixed relative to the stars, runs once, and then returns to the same point on the ecliptic. Therefore, from the perspective of the geocentric celestial sphere, the length of a sidereal year is the time interval when the sun center passes the same star twice in succession on the ecliptic.

The sidereal year is obtained with a star as the reference point, so it is the time when the earth rotates 360 degrees, and it is also the real period of the earth's revolution. In days, its length is 365.2564 days, that is, 365 days, 6 hours and 9 minutes 10 second.

The vernal equinox period of the earth's revolution is the Tropic of Cancer. This periodic unit is obtained with vernal equinox as the reference point. In a tropical year, starting from the sun center, the center of the earth has arrived in vernal equinox twice in a row; Seen from the center of the earth, the sun center has reached the vernal equinox twice in a row. From the point of view of the geocentric celestial sphere, the length of a tropic year is the time interval between two consecutive vernal equinoxes, which depends on the ecliptic.

The vernal equinox is the intersection of the ecliptic and the celestial equator. Its position on the ecliptic is not fixed, and it moves 50 ″ .29 to the west every year. In other words, the vernal equinox is a moving point in a year, and its moving direction is from east to west, which is clockwise. The direction of the sun on the ecliptic is from west to east, that is, counterclockwise. These two directions are opposite. Therefore, depending on the center of the sun, the angle taken by the vernal equinox for two consecutive times is not 360, but 360-50.29, that is, 359 59' 9.71,which is the angle of the earth's revolution in a tropic year. Therefore, the tropic year is not the real cycle of the earth's revolution, but only the time required for the earth to rotate at an angle of 359 59' 9 ".71,that is, 365.2422 days, that is, 365 days, 5 hours, 48 minutes and 46 seconds.

The perihelion period of the earth's revolution is perihelion year. This periodic unit is obtained by taking the perihelion of Earth orbit as the reference point. In a perihelion year, the center of the earth (or the apparent sun center) passes through the perihelion of the earth's orbit twice in a row. Because perihelion is a moving point, its moving direction on the ecliptic is from west to east, that is, it is the same as the direction of the earth's revolution (or the direction of the apparent motion of the solar year), and the annual moving amount is11÷÷, so the perihelion year is not the real cycle of the earth's revolution, and the angle of the earth's revolution in a perihelion year is 360+65430.

Only the sidereal year is the real cycle of the earth's revolution. In the following chapters, we will learn that the tropic year is the cycle of the earth's cold and heat, that is, the cycle of the four seasons, which is closely related to human life and production. The tropical year is slightly shorter than the sidereal year, 20 minutes and 24 seconds shorter each year, which is called precession in astronomy.

Why does vernal equinox move westward by 50.29 every year, leading to precession? This is the result of the precession of the earth axis.

The precession of the earth's axis is closely related to the rotation of the earth, the shape of the earth, the existence of the ecliptic angle and the orbital characteristics of the moon around the earth.

The precession of the earth axis is similar to the swing of the gyro shaft around the vertical line. When the tip gyro is tilted, the rotating shaft draws a conical surface around the axis perpendicular to the ground, and the gyro shaft slowly shakes. This is because the gravity of the earth tends to make it fall, and the inertia of the gyro's own rotating motion makes it unable to stay, so it slowly shakes under the action of gravity. This is the precession of the gyro.

The rotation of the earth is like a giant "top", which keeps spinning. Because of inertia, the earth has been spinning. The shape of the earth itself is similar to an ellipsoid, and the equatorial part is convex, that is, there is an equatorial uplift belt. At the same time, due to the existence of the ecliptic angle, the connection between the sun center and the earth center does not often pass through the equatorial uplift belt. Therefore, the attraction of the sun to the earth, especially to the equatorial uplift belt, is unbalanced. In addition, the orbital plane of the moon's revolution around the earth does not coincide with the ecliptic plane and the equatorial plane of the celestial sphere, but forms an angle of 5 9' with the ecliptic plane, that is to say, the connecting line between the center of the earth and the center of the moon does not often pass through the equatorial uplift zone. Therefore, the attraction of the moon to the earth, especially to the equatorial uplift belt, is also unbalanced. According to the law of universal gravitation, f 1 > F2.

This unbalanced gravity of the sun and the moon tries to make the equatorial plane coincide with the orbital plane of the earth and reach a state of balance. However, the inertia of the earth's rotation keeps it tilted. Therefore, the earth swings under the combined action of the unbalanced gravity of the moon and the sun. This kind of swing is characterized by the periodic conical motion of the earth axis with the yellow axis as the axis, and the conical radius is 23 26', which is equal to the intersection angle of yellow and red. This movement of the earth axis is called precession of the earth axis. The precession direction of the earth's axis is from east to west, which is opposite to the revolution direction of the earth's rotation, while the precession direction of the gyro is consistent with the rotation direction.

This is because the gyro tends to "topple" and the earth axis tends to "stand upright".

The precession speed of the earth's axis is very slow, with an annual precession of 50.29 and a precession period of 25,800 years.

Due to the precession of the earth's axis, the tilt direction of the earth's equatorial plane in space has changed, resulting in the corresponding change of the celestial equator, which makes the intersection of the celestial equator and the ecliptic-vernal equinox and the equinox move correspondingly on the ecliptic. The movement direction is from east to west, which is opposite to the revolution direction of the earth, and the annual movement angle is 50 ″ .29. Therefore, the length of a year with spring as the reference point is slightly shorter than that with stars as the reference point, which is the reason for precession.

Due to the precession of the earth's axis, the spatial orientation of the earth's north and south poles has changed, making the celestial pole move around the yellow pole with a period of 25800 years. Therefore, the positions of the celestial north pole and the celestial south pole on the celestial sphere are also moving slowly. Polaris was once the alpha star of Draco in 3000 BC. Currently near Alpha Ursa minor. In 7000 AD, it will be moved to Alpha Star in Cepheus. By the year 14000, Vega will become the north star.

Because of the precession of the earth's axis, the celestial pole and vernal equinox move on the celestial sphere, and the celestial coordinate system based on it will inevitably change accordingly. For the equatorial coordinate system, the right ascension and declination of the star will change, and for the ecliptic coordinate system, the yellow longitude of the star will change. But the precession of the earth axis does not change the declination angle, that is, when the earth axis precesses, the included angle between the earth axis and the earth orbit plane is always 66 34'.

It should also be noted that the moving angles of the celestial pole and vernal equinox caused by the precession of the earth's axis are relatively small, and there will be no big movement for a long time. Therefore, we can still say that the positions of the celestial pole and vernal equinox are unchanged, and the right ascension, declination and yellow longitude of stars can also be roughly considered as unchanged. Catalogs and maps based on this can still be used for a long time.

The rotation speed of the earth

The revolution of the earth is a periodic circular motion, so the revolution speed of the earth includes angular velocity and linear velocity. If the sidereal year is used as the period of the earth's revolution, then the average angular velocity of the earth's revolution is 360 degrees per year, that is, after 365.2564 days, the earth will revolve 360 degrees, that is, about 0.986 degrees per day, that is, about 59' 8 "per day. The total length of the earth's orbit is 940 million kilometers, so the average linear speed of the earth's revolution is 940 million kilometers per year, that is, after 365.2564 days, the earth revolves 940 million kilometers, that is, 29.7 kilometers per second, about 30 kilometers per second.

According to Kepler's second law of planetary motion, the revolution speed of the earth is related to the distance between the sun and the earth. The angular velocity and linear velocity of the earth's revolution are not fixed values, but change with the distance between the sun and the earth. When the earth passes the perihelion, the revolution speed is fast, and the angular velocity and linear velocity both exceed their average values. The angular velocity is11'1"/day, and the linear velocity is 30.3km/s; When the earth is at perihelion, the revolution speed is slow, and the angular velocity and linear velocity are lower than their average. The angular velocity is 57 ′11″/day, and the linear velocity is 29.3km/s. Every year, the earth passes through perihelion at the beginning of 65438+ 10 and apohelion at the beginning of July. Therefore, from the beginning of 65438+ 10 to the beginning of July of that year, the distance between the earth and the sun gradually increased, and the revolution speed of the earth gradually slowed down. From the beginning of July to the beginning of 65438+ 10 of the following year, the distance between the earth and the sun gradually narrowed and the revolution speed of the earth gradually accelerated.

We know that the vernal equinox and the autumnal equinox are equally divided on the ecliptic. If the revolution speed of the earth is uniform, then the time required for the sun to run from the vernal equinox to the autumnal equinox should be the same as the time required for the sun to run from the autumnal equinox to the vernal equinox, which is half of the whole year. However, the revolution speed of the earth is uneven, so the time to travel the same distance must be unequal. Depending on the sun from the vernal equinox to the summer solstice to the autumnal equinox, the earth's revolution speed is slow, which takes more than 186 days, which is longer than half of the whole year. This is the summer half year in the northern hemisphere and the winter half year in the southern hemisphere. Relying on the sun from the autumnal equinox to the vernal equinox through the winter solstice, the revolution speed of the earth is relatively fast, which takes 179 days, less than half of the whole year. This is the winter half year in the northern hemisphere and the summer half year in the southern hemisphere. It can be seen that the change of the revolution speed of the earth is the fundamental reason for the unequal length of the four seasons on the earth.

First of all, understand a few nouns:

1, one light year: refers to the distance traveled by light in one year. Note that light years are units of length.

2. The revolution of the earth: Our earth revolves around the sun along an ellipse with a small eccentricity at a speed of 29.79 kilometers per second. It takes 365 days and 6 hours to walk around 940 million kilometers, which is about a year. (The average distance between the sun and the earth is 65.438+0.5 billion kilometers)

Of course, the landlord's question can be understood as: how many times does light travel in a year? Answer; Because 1 light-year is the distance traveled by light in one year, one revolution of the earth is the arc length traveled by the earth in one year, and the time is one year. Therefore, the ratio of distance is the ratio of the speed of light of 300,000 km/s to the revolution speed of the earth of 29.79 km/s: n = 300,000 /29.79 = 10000 times.

On the supplementary question: What is the distance of the earth's revolution around the sun? The distance here is actually the circumference, the arc length of a week. We already know that the radius of the earth's orbit is 65.438+0.5 billion kilometers, so it is easy to calculate the circumference. According to the formula s = 2× 3.14×1.500 million, about 940 million kilometers.