Lunar orbit

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The moon orbits the earth in 27.32 days. Earth and Moon The center of mass of is 4700km away from the earth center (0.73 times the radius of the earth's equator) centroid work. The average distance between the moon and the center of the earth is 385000 kilometers, about 60 times the radius of the earth. The average speed in orbit is 1.023 km/s fixed star The background of the moon moves about 0.5 ° per hour, which is equivalent to the apparent diameter of the moon. The orbit of the moon is different from that of natural satellites of most planets. It is close to Ecliptic Plane, not the equatorial plane of the earth. The inclination of the lunar orbital plane to the ecliptic plane is only 5.1 °, Autorotation shaft The dip angle is only 1.5 °.

Chinese name: Lunar orbit
Foreign name: lunar orbit
Inclination: 5.145°

Speed: 1.023 km/s
Distance: 385000 km
Nature: Apparent diameter of the moon
Location: About 1700km below the surface

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Comparison of the sizes of the near and far months.

The long-term average distance between the mass center of the moon and the mass center of the earth is about 385000 km, equivalent to 60 times the radius of the earth, or 30 times the diameter of the earth. The common centroid of the two is about 4670 kilometers away from the center of the earth, that is Surface It is about 1700 km down. The diameter ratio of earth and moon is 4:1, and the mass of earth and moon is 81:1.

Mean of lunar orbit Eccentricity It is 0.0549. The non-circular orbit causes obvious changes in the size of the diameter and angular velocity when observing the moon from the earth. For a fictitious observer at the center of mass, the average angular displacement of the moon every day is 13. 5% to the east 176358 °, the direction of the orbit is not fixed in space, but keeps moving with time, one of which is the precession of the arch point line: the elliptical lunar orbit slowly rotates counterclockwise, and the complete rotation is 8.850 years (3233 days). Another sport is Track plane Its axis is perpendicular to Ecliptic Clockwise precession of. The time precession of the intersection of the lunar orbit and the ecliptic is 18.6 years (6793 days).

The inclination of the lunar orbit to the ecliptic plane is 5.145 °. Lunar Autorotation shaft There is no orbital plane perpendicular to the revolution, so the inclination constant of the lunar equator relative to the orbital plane is 6.688 °. Perhaps someone tried to explain that the inclination between the lunar equator and ecliptic should always vary between the sum (11.833 °) and the difference (1.543 °) of these two values from the precession of the lunar orbital plane. However, in 1721, Jia Ke Cassini This problem has been solved because the rotation of the lunar precession axis has the same speed as the orbital plane, but the phase difference is 180 °. Therefore, although the rotation axis of the moon is not fixed relative to the star equator Plane and Ecliptic It is always kept at 1.543 °.

The period of the moon

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There are many different ways to define the moon to complete an orbital period. fixed star The moon is relative to a distant star, about 27.32 days. In contrast, the new moon is the time when the moon returns to its original phase, about 29.53 days. New Moon than Sidereal month Long, because the Earth Moon system revolves around the sun within a limited distance. After a star month, it will take more time to return to the original geometric corresponding position. Other definitions include perigee to perigee（ Perigee month ）, from the ascending node to the ascending node（ Node month ）And on Ecliptic coordinates Go up and back to the same yellow meridian（ Month to month ）。 Due to the influence of the slow precession, the length of the last three months is slightly different from that of the star month, and the month length over the years is about 30.4 days (1/12 year).

name	Value (days)	definition
Sidereal month	27.321 661	Relative to distant stars (13.369 star months per year)
New Moon	29.530 589	Relative to the sun (phase of the moon, 12.369 new moon every year)
Month to month	27.321 582	Relative to the spring equinox (advance to 26000 Julian years)
Perigee month	27.554 550	Relative to perigee (recesses in 3232.6 days=8.8504 Julian year)
Node month	27.212 221	Relative to the ascending node (precession period 6793.5 days=18.5996 Julian years

Tidal evolution

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Lunar Universal gravitation Is caused by the ocean tide The cause of. If the earth's ocean has a global consistent depth, the moon will transform the solid earth (with only a small amount of change) and ocean into an ellipsoid, and the highest point will appear directly at the point facing the moon and the point away from the moon. But because the earth has an irregular coastline And the changing ocean depth, we can only imagine this ideal state. Generally speaking, the fluctuation period of the tidal current is synchronous with the orbital period of the moon around the earth, but it will follow Lunar phase change 。 Although rare, in some parts of the earth the tides rise and fall only once a day.

Due to the rotation of the earth, the tidal bulges will be slightly ahead of the axis of the Earth Moon system, which is the direct result of friction and energy dissipation caused by the movement of sea water at the bottom of the sea and the entrance and exit of the bay. Each bulge will exert a small amount of gravity on the moon, because the earth will drive this bulge forward, and the bulge closest to the moon will slightly pull the moon forward along the lunar orbit; The bulge on the side facing away from the moon has the opposite effect. However, the bulges closer to the moon also have a greater impact on the moon because of their close distance, so the result is that the rotational inertia of the earth gradually shifts to the rotational inertia of the lunar orbit. This makes the moon's orbit slowly and gradually away from the earth, and the amount of movement is about 3.8 cm every year. To maintain Conservation of angular momentum The rotation speed of the earth is gradually slowing down, making the Earth's day extend by about 17 microseconds every year (this number will increase the Earth's day by one second every 60000 years, one minute every 4 million years, and four hours every billion years. Back then, when dinosaurs came and went on the earth 65 million years ago, the length of a day was 23 hours.). See Tidal Acceleration for more detailed descriptions and references.

Therefore, the moon is gradually moving away from the earth and into a higher orbit NASA and Jet Propulsion Laboratory (JPL) believes that this process will continue for another 2 billion years. At that time, the orbits of the earth and the moon will become "rotation orbit resonance", and the moon will circle about every 47 days Earth revolution One circle (27.32 days), and the rotation of the earth and the moon is also the same cycle, that is, they always circle each other with the same side. In addition, it is hard to say what changes will happen to the Earth Moon system.

Libration

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The moon is Synchronous rotation , which means that it always rotates towards the earth on the same side, but because of the Eccentricity In fact, this is just an average phenomenon. This is the result that the angular velocity of the orbit around the earth will change, so it cannot be equal to the constant rotation speed. When the moon Perigee Its self rotation speed is the slowest relative to the orbital speed, which allows us to see the back area of longitude that is 8 degrees to the east (right). Conversely, when the moon Apogee Its rotation is the fastest relative to the orbital speed, so you can see the longitude 8 degrees west of the back. This is longitude Libration 。

Because the lunar orbit Ecliptic The inclination is 5.1 °, so the Autorotation shaft When it circles the earth again, it will face and stay away from the earth. This change is called latitude libration, which can cross the polar region in latitude Bipolar See the area of 7 ° on the back of each side. Finally, because the distance between the moon and the earth is only 60 times the radius of the earth, the libra on Sunday can see more than one degree in longitude. For the same reason, the degree of latitude can also be seen from the parallax between the two poles.

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The earth and the moon orbit around the sun together

Orbital motion of the moon

When explaining the solar system, the earth is always described as a point in orbit around the sun, while the moon is a point in orbit around the earth. This may give people the concept that the moon moves around the earth, but when viewed from the position of the sun, the moon sometimes lags behind or overtakes the earth, because it is not easy to detect the relative orbital speed of 1 km per second of the earth, and the speed of 30 km per second of the earth in orbit around the sun.

Unlike other satellites in the solar system, the complete orbit of the moon is very similar to that of the earth. Its concave surface is always facing the sun, and there is no bulge or ring. However, it cannot be said that the moon turns around the sun instead of around the earth, because even if the sun's gravity is "turned off", the moon will still circle the earth with the same star and moon as now. If the Earth Moon system is located farther from the sun, where the orbital speed is less than 1 km/s, the motion of the moon will indeed recede in the sun centered non rotating coordinate system.

Track parameters

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Semi major axis~384748km

Perigee distance~364 397 km

Apogee distance~406 731 km

Average eccentricity 0.0549006

(0.044 – 0.067)

Average orbital inclination (right Ecliptic ） 5.145°

Average axis inclination (to equator) 6.688 °

Average axis inclination (to the ecliptic) 1.543 °

Nodal retrogression cycle 18.5996 years

Retrogression period of arch point line: 8.8504 years

Weight field

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moonscape Gravitational acceleration It is about 1/6 of the earth's surface, and the distribution of the lunar gravity field is very uneven. There are gravity anomalies in some lunar sea basins, called mass nodules. The anomaly of the lunar gravity field affects the orbit of the spacecraft orbiting the moon for a long time.

The extremely complex gravity field of the moon makes the orbit of the lunar satellite have different characteristics compared with that of the earth satellite. There is no atmosphere above the moon, and the satellite orbit will not be attenuated due to atmospheric resistance, but the moon satellite running in a lower circular orbit may still fall to the moon after a period of time under the influence of gravity. The influence of the lunar gravity field will cause the eccentricity of its satellite orbit to become larger, which means that the satellite orbit becomes flat^[1] 。

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