Method and System for Determining Lunar Orbit Expansion Rate Using Earth-Moon Clocks

Abstract

This invention discloses a method for determining the lunar orbit expansion rate using a lunar optical clock, comprising: acquiring the relative frequency deviation between a ground optical clock and a lunar optical clock obtained through continuous measurement via a two-way Earth-Moon time-frequency transfer link; the two-way Earth-Moon time-frequency transfer link is established between a lunar surface station and a ground station for realizing optical clock time-frequency signal comparison and laser ranging, wherein both the lunar surface station and the ground station are equipped with a frequency deviation better than 10. ‑20 This invention utilizes an optical clock of magnitude [missing information]; based on the gravitational redshift theory of general relativity, a physical relationship model is established between the rate of change of relative frequency deviation and the lunar orbit expansion rate; based on this physical relationship model, the lunar orbit expansion rate is calculated from the measured rate of change of relative frequency deviation. This invention achieves direct, continuous, and high-precision measurement of lunar orbit expansion, overcoming the limitations of traditional lunar laser ranging technology, and providing a new generation of measurement methods for the study of Earth-Moon system dynamics and fundamental physics verification.

Description

Technical Field

[0001] This invention relates to the fields of space measurement, fundamental geophysics, planetary science, and precision time and frequency technology, and in particular to a method for directly determining the lunar orbital expansion rate by precisely measuring the gravitational redshift between the Earth and the Moon using high-precision optical atomic clocks (optical clocks) deployed on the Earth and the Moon. Background Technology

[0002] The Moon is moving away from Earth at a rate of approximately 3.8 centimeters per year, a phenomenon known as lunar orbital expansion. The primary cause is the transfer of angular momentum from Earth's rotation to the Moon through tidal friction, leading to the slow expansion of the Moon's orbit. Accurately measuring this rate is crucial for understanding the evolutionary history of the Earth-Moon system, verifying general relativity and gravitational theories, understanding tidal interaction mechanisms, the early state of Earth's rotation, and deep space navigation and space mission planning. Currently, the most important technology for measuring changes in the Earth-Moon distance is Lunar Laser Ranging (LLR). This technology calculates the instantaneous Earth-Moon distance by emitting laser pulses from a ground-based observatory to a reflector on the lunar surface and measuring the round-trip time. Through decades of data accumulation, the long-term orbital evolution of the Moon is fitted, indirectly estimating the rate of lunar orbital expansion.

[0003] However, LLR technology has inherent limitations: (1) Time synchronization error: Traditional LLR relies on atomic clocks on Earth for time measurement, but due to the different gravitational potential fields of Earth and the Moon, relativistic time delay effects (such as gravitational redshift) will cause clock desynchronization, affecting ranging accuracy. Existing technologies usually use post-data correction, but cannot eliminate time drift in real time. Long-term accumulated errors can reach the picosecond (ps) level, corresponding to ranging errors of about millimeters. (2) Atmospheric interference: When the laser passes through the Earth's atmosphere, it is affected by turbulence, refractive index changes, etc., which causes the ranging signal to jitter, reducing short-term measurement accuracy (currently the best LLR ranging accuracy is about 1-2 cm, which is difficult to meet the needs of long-term trend analysis). (3) Low data sampling rate: Traditional LLR relies on optical observatories (such as APOLLO and MLRS sites), which are limited by weather and lunar phases, resulting in a low effective data acquisition frequency (usually only a few days a month), leading to greater uncertainty in long-term orbit fitting. (4) Accumulation of systematic errors: Existing methods rely on observations from a single earth station and cannot eliminate the effects of lunar libration and local topography of the corner reflector array, resulting in systematic bias. (5) Accuracy bottleneck: The current ranging accuracy of LLR has reached the centimeter level, but to detect weaker physical effects (such as the influence of gravitational wave background on orbit) or to more accurately constrain theoretical models, sub-millimeter or even higher precision measurement techniques are required.

[0004] Currently, the frequency stability and uncertainty of optical atomic clocks (optical clocks) have entered the 10-1 range.-19 This magnitude presents an opportunity for precise measurements. According to general relativity, clocks run at different rates at different locations in a gravitational field (gravitational redshift). Changes in the Earth-Moon distance directly lead to changes in the gravitational potential difference between the two locations, causing a relative frequency drift of optical clocks at both locations. Utilizing this physical effect, the rate of change of distance can be measured directly and with high precision. Therefore, there is an urgent need in this field for a new method that can overcome the limitations of LLR technology and directly and with high precision determine the rate of lunar orbital expansion using cutting-edge optical frequency technology. Summary of the Invention

[0005] To address the problem of low long-term ranging accuracy in existing laser lunar ranging technologies due to time asynchrony, atmospheric interference, and insufficient data sampling, this invention provides a millimeter-level accurate and long-term stable method for measuring the lunar orbit expansion rate by directly monitoring the rate of change of gravitational redshift between the Earth and the Moon. This enables continuous, high-precision, and direct measurement of the lunar orbit expansion rate.

[0006] According to one aspect of the present invention, a method for determining the rate of lunar orbit expansion using a lunar clock is provided, comprising:

[0007] The relative frequency deviation between a ground optical clock and a lunar optical clock is obtained through continuous measurements via a two-way Earth-Moon time-frequency transfer link. This link, established between a lunar station and a ground station, is used for optical clock time-frequency signal comparison and laser ranging. Both the lunar station and the ground station are equipped with sensors with a frequency greater than 10... -20 Light clocks of this magnitude;

[0008] Based on the gravitational redshift theory of general relativity, a physical relationship model is established between the rate of change of relative frequency deviation and the lunar orbit expansion rate.

[0009] Based on the physical relationship model, the lunar orbit expansion rate is calculated from the measured relative frequency deviation change rate.

[0010] As a further technical solution, the relative frequency deviation between the ground-based optical clock and the lunar optical clock is measured. After that, it also includes:

[0011] The periodic frequency variations caused by the first and second order Doppler effects resulting from the solid tides of the Earth and Moon, rotational deformation, solar gravitational potential, and relative motion are subtracted from the acquired relative frequency deviation data.

[0012] By using an environmental noise correction model, the frequency shifts caused by different environmental noises are corrected to obtain a frequency shift sequence reflecting the Earth-Moon gravitational potential difference. .

[0013] As a further technical solution, this involves obtaining a frequency shift sequence that reflects the gravitational potential difference between the Earth and the Moon. After that, it also includes:

[0014] Frequency shift sequence within a preset period By performing linear least squares fitting, the rate of change of relative frequency deviation caused by long-term changes in the Earth-Moon distance is obtained. ;

[0015] The lunar orbit expansion rate was calculated based on the physical relationship model between the rate of change of relative frequency deviation and the rate of lunar orbit expansion.

[0016] As a further technical solution, the relative frequency deviation between the ground-based optical clock and the lunar optical clock... Represented as:

[0017] ,

[0018] in, It is the frequency difference between the ground-based optical clock and the lunar optical clock. It is the nominal frequency of the clock at zero gravitational potential, and c is the speed of light. It is the transmission frequency of the Earth's surface after optical frequency conversion. It is the frequency received on the lunar surface. Here, is the nominal frequency of the time-frequency signal, and k is the conversion coefficient between the transmitted signal frequency and the optical clock signal frequency. The gravitational potential difference between the positions of optical clocks on the Earth and Moon surfaces. This is the gravitational potential correction caused by the higher-order gravitational redshift.

[0019] As a further technical solution, after obtaining the rate of change of relative frequency deviation caused by the long-term change in the Earth-Moon distance... After that, it also includes:

[0020] A correlation model combining the lunar orbital expansion rate α and the Earth-Moon distance: The physical relationship model between the rate of change of relative frequency deviation and the rate of lunar orbit expansion is expressed as follows:

[0021] ,

[0022] in, G represents the gravitational constant, and M represents the mass of the central celestial body. Represents the radius of the Earth. The initial distance between Earth and lunar surface stations is represented by α, which represents the rate of lunar orbital expansion. Indicates the time difference between Earth and lunar surface stations. The distance.

[0023] As a further technical solution, when establishing a physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate, the following are included:

[0024] Acquire at least 10 years of Earth-Moon distance data and time-frequency comparison data, and record the time series of relative frequency deviation and Earth-Moon distance;

[0025] By using a real-time correction model based on various environmental influences during bidirectional time-frequency transmission and dual-frequency link comparison technology, combined with the recorded time series, the relative frequency deviation change rate is separated.

[0026] A physical relationship model is established between the relative frequency deviation change rate and the lunar orbit expansion rate.

[0027] As a further technical solution, the method also includes:

[0028] Multiple ground stations are set up on Earth and connected to each other via fiber optic links to measure the gravitational potential difference between different ground stations in real time.

[0029] The gravitational potential difference between the Earth and the Moon is corrected in real time based on the gravitational potential difference between the different ground stations.

[0030] According to one aspect of the present invention, a system for determining the lunar orbit expansion rate using a lunar optical clock is provided, comprising a two-way time-frequency transfer subsystem between the Earth and the Moon and a data processing subsystem, wherein...

[0031] The Earth-Moon two-way time and frequency transfer subsystem is used to establish a two-way time and frequency transfer link between the ground station and the lunar station, realize optical clock time and frequency signal comparison and laser ranging, and continuously measure the relative frequency deviation between the ground optical clock and the lunar optical clock. Both the lunar station and the ground station are equipped with a frequency deviation better than 10... -20 Light clocks of this magnitude;

[0032] The data processing subsystem is used to establish a physical relationship model between the rate of change of relative frequency deviation and the lunar orbit expansion rate based on the theory of gravitational redshift in general relativity; and to calculate the lunar orbit expansion rate from the measured rate of change of relative frequency deviation based on the physical relationship model.

[0033] As a further technical solution, the Earth-Moon bidirectional time and frequency transfer subsystem includes at least an optical clock, a femtosecond optical comb, a time and frequency comparison unit, a frequency signal transmission and reception unit, a GNSS receiver, a laser reflection prism, an environmental monitoring unit, and a data acquisition and storage unit.

[0034] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the method for determining the lunar orbit expansion rate using a lunar clock.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] (1) Direct measurement: Directly observe the rate of change of gravitational redshift (gravitational potential of Earth-Moon station) caused by orbital expansion, rather than through secondary derivation of distance data, the physical concept is clear;

[0037] (2) Ultra-high precision potential: utilizing 10 -20 The optical clock, with its magnitude of 10,000, can theoretically achieve a sensitivity of millimeters or even sub-millimeters to measuring the rate of change of distance, far exceeding the long-term trend fitting accuracy of the current LLR. At the same time, multiple stations are established on the ground and connected by optical fibers to monitor the gravitational potential difference caused by changes in the position of the ground stations in real time, and to use this gravitational potential difference to make real-time corrections when measuring the gravitational redshift of the Earth and the Moon.

[0038] (3) Continuous monitoring: It can realize real-time, continuous long-term monitoring of lunar orbit expansion, detect possible small fluctuations or periodic modulations in the rate, and achieve higher resolution lunar orbit expansion rate by monitoring the rate of change of gravitational redshift (rate of change of gravitational potential difference).

[0039] (4) Technological progress: It has broken free from the dependence on old corner reflectors on the lunar surface and applied the most advanced high-precision atomic clock technology and time-frequency comparison technology to the measurement of lunar orbital expansion rate, representing the development direction of the next generation of deep space ranging and gravity measurement;

[0040] (5) Multiple scientific objectives: While measuring the lunar orbit expansion rate, the high-precision Earth-Moon frequency comparison data obtained can also be used to test general relativity, limit dark matter parameters, detect gravitational waves and other cutting-edge basic physics research. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic flowchart of a method for determining the lunar orbit expansion rate using a lunar clock, provided in an embodiment of the present invention.

[0043] Figure 2 This is a schematic diagram illustrating the principle of using a lunar clock to determine the rate of lunar orbit expansion, as provided in an embodiment of the present invention. Detailed Implementation

[0044] The purpose of this invention is to provide a method for determining the lunar orbit expansion rate using a lunar optical clock, which solves the problem of low long-term ranging accuracy caused by time asynchrony, atmospheric interference and insufficient data sampling in existing laser lunar ranging technology. This method aims to provide a millimeter-level accurate and long-term stable lunar orbit expansion rate determination scheme by directly monitoring the rate of change of gravitational redshift between the Earth and the Moon, so as to achieve continuous, high-precision and direct measurement of the lunar orbit expansion rate.

[0045] In this invention, firstly, a ground station needs to be established on Earth. As mentioned in the background, the lunar orbital radius expands by approximately 3.8 cm per year. Both the ground station and the lunar station need to be equipped with optical clocks capable of sensing millimeter-level changes, and the long-term stability of these optical clocks needs to reach 10. -20 The magnitude is significant. To accurately determine the lunar orbit, multiple ground stations need to be constructed, connected by a fiber optic network. This network allows for real-time monitoring of changes in gravitational potential at each station caused by variations in the Earth's surface. This data is used to correct for the Earth-Moon gravitational potential difference during orbital measurements, ensuring accuracy. This is because Earth stations are affected by tidal forces, causing variations in gravitational potential and vertical position, necessitating real-time corrections between relevant ground stations.

[0046] Secondly, an optical frequency link is used to connect the optical clocks between the Earth and lunar stations. Preliminary measurements of the Earth-Moon orbit are performed using LLR technology. By comparing the two-way Earth-Moon optical frequencies, the effects of Doppler, atmospheric, and tidal effects during link propagation are eliminated, allowing for precise extraction of gravitational redshift to obtain changes in the gravitational potential difference between the Earth and the Moon. Furthermore, based on long-term stable monitoring, the change in the Earth-Moon distance is deduced from the changes in the gravitational potential difference, thus obtaining the expansion rate of the lunar orbit.

[0047] The core of this invention is to establish a two-way optical frequency comparison link between Earth and the Moon, combined with multi-station collaborative Earth-Moon gravitational redshift measurement and a dynamic error correction model, to achieve precise measurement of the Earth-Moon gravitational potential difference, thereby enabling high-precision measurement of the lunar orbital expansion rate. The implementation process may include:

[0048] (1) Establish a time-frequency comparison system between the Earth and the Moon. Establish and operate systems with an accuracy better than 10 on both the Earth and the Moon. -20 A high-power optical clock, with multiple observation stations set up on Earth and connected by fiber optic links, to measure the gravitational potential difference between different stations in real time.

[0049] Specifically, deploying a high-precision optical clock time-frequency comparison system on the moon includes: achieving a long-term stability of 10... -20The system includes a high-precision optical clock, a high-precision femtosecond optical comb, a time-frequency comparison unit, a frequency signal transmission and reception unit, a high-precision GNSS receiver, a laser reflecting prism, an environmental monitoring system, and a data acquisition and storage system. Ground stations are evenly distributed across the Earth, each equipped with a high-precision optical clock time-frequency comparison system (with the same structure as the lunar deployment). Different ground stations are connected by fiber optic links, enabling real-time Earth-Moon optical clock time-frequency comparison and ground station optical clock fiber optic time-frequency comparison. The gravitational potential difference between different stations obtained from the ground station optical clock fiber optic time-frequency comparison can be used to correct the gravitational potential difference between the Earth and the Moon in real time.

[0050] Meanwhile, a data processing center needs to be set up on the ground to receive data sent back from the lunar station and transmit environmental noise frequency shift correction data to the moon, as well as to process the comparison data between the Earth and the lunar clock in real time.

[0051] (2) Establish a two-way time-frequency transmission link between Earth and the Moon. In order to achieve time-frequency comparison between Earth and Moon optical clocks, the gravitational redshift term in general relativity needs to be extracted. The lunar optical clock and the ground optical clock need to be connected and calibrated over a long period of time. Laser pulses are synchronously emitted from at least three laser stations around the world to a corner reflector array on the lunar surface. The laser emission and reception timestamps are recorded (based on the Earth-Moon optical clock) and the instantaneous Earth-Moon distance is calculated. To address the various environmental impacts during the two-way time-frequency transfer process, it is necessary to monitor and correct atmospheric delay (using real-time meteorological data and turbulence models), lunar libration, and tidal effects in real time to ensure accurate extraction of the gravitational redshift signal. It should be noted that this embodiment of the invention only uses a corner reflector for initial distance measurement; the actual lunar orbital expansion rate is obtained through gravitational potential difference inversion. This method has lower requirements for distance accuracy compared to LLR and does not rely on a corner reflector to ensure measurement accuracy.

[0052] By continuously comparing frequencies between the Earth and the Moon, the relative frequency deviation between the Earth's optical clock and the lunar optical clock was measured. :

[0053] (1),

[0054] in, It is the frequency difference between the ground and the moon's light clocks. It is the nominal frequency of the clock at zero gravitational potential, and c is the speed of light. It is the transmission frequency of the Earth's surface after optical frequency conversion. It is the frequency received on the lunar surface. Here, is the nominal frequency of the time-frequency signal, and k is the conversion coefficient between the transmitted signal frequency and the optical clock signal frequency. E and M represent the gravitational potentials of the positions of light clocks on the Earth and Moon surfaces, respectively. The gravitational potential difference representing the position of an optical clock on the surface of the Earth and the Moon. This represents the gravitational potential correction caused by higher-order gravitational redshifts. For ease of representation, higher-order quantities will be ignored in subsequent calculations, and corrections will only be made in the final results.

[0055] The gravitational potential at any point on the Earth's surface can be expressed as:

[0056] (2),

[0057] Where G represents the gravitational constant, and M represents the mass of the central celestial body (Earth, Moon). This represents the radius of the Earth. In the experiment, we established an inertial reference frame with the Earth as the reference point, and the gravitational effects of celestial bodies such as the Moon and the Sun on the Earth's surface were corrected according to the Earth's tidal model. The position of the atomic clocks at the lunar surface stations remains unchanged; therefore, the gravitational effect of the Moon on the surface atomic clocks is considered constant. ,in, This represents the product of the gravitational constant of the Moon's surface and the Moon's mass. This represents the distance from the lunar surface atomic clock to the lunar center of mass. Therefore, the gravitational potential of a lunar surface station can be expressed as... (3),

[0058] Where L represents the distance between stations on the Earth and the Moon. It can be represented as:

[0059] (4),

[0060] in, This indicates the frequency shift caused by the moon's gravity. This indicates the frequency shift caused by the Earth's atmosphere. This indicates the frequency shift caused by the deep space environment. , and Both are frequency shifts caused by the environment.

[0061] (3) Frequency ratio Convert to distance measurement. Assume the initial distance between the Earth and the Moon is... any time The distance is Here we assume the Earth's radius Unchanged, therefore If the term is a constant, then the rate of change of the relative frequency deviation can be expressed as:

[0062] (5),

[0063] Therefore, by measuring the change in the frequency ratio, the change in the rate of change of the relative frequency deviation can be obtained, and thus, the following can be derived: The changes, thus obtaining The changes.

[0064] The correlation model between the lunar orbit expansion rate α (unit: meters / year) and the Earth-Moon distance can be expressed as:

[0065] (6),

[0066] in Substitute the above formula (6) into... It can be obtained from Since the value of α is very small, expanding the formula yields:

[0067] (7),

[0068] Substituting formula (7) into formulas (5) and (1) yields the change in the relative frequency deviation rate:

[0069] (8),

[0070] Therefore, by monitoring the frequency ratio over a long period of time The rate of change of the lunar orbit can be used to obtain the lunar orbit expansion rate α.

[0071] (4) Long-term observation and orbital expansion rate. Ranging data for at least 10 years, time-frequency comparison data were collected and time series were recorded. Using the modified models and dual-frequency link comparison techniques implemented in (2) and (3), the Earth-Moon gravitational redshift is separated, and the frequency shift of the atomic clock caused by the gravitational redshift effect is extracted. Then, the accurate lunar orbit expansion rate α is obtained using the model of gravitational redshift and lunar orbit expansion rate α (Formula 8). By outputting the rate of change of the Earth-Moon gravitational potential difference, the above model can determine the annualized expansion rate of the lunar orbit and its uncertainty.

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0073] like Figure 1 and 2 As shown in the embodiment of the present invention, the method for determining the lunar orbit expansion rate using a lunar clock includes the following steps:

[0074] Step 1, System Establishment: (a) Select ground-based optical clock stations in areas with stable atmospheric conditions and slow crustal movement. Each station is equipped with a strontium lattice optical clock with a frequency stability better than 10. -20 (a) Optical antennas are used for Earth-Moon time-frequency signal comparison and laser ranging. (b) A geologically stable region (such as a lava plain on the near side of the Moon) is selected on the Earth-facing side of the Moon to deploy a lunar optical clock station. This station carries an optical clock optimized for the lunar environment and is equipped with an environmental monitoring and control system and a small optical antenna. (c) A two-way time-frequency transmission link is established between the Earth and the Moon. The ground station and the lunar station transmit dual-frequency signals to each other and compare them with the local optical clock, and send the comparison results back to the ground along with the local clock signal. The ground station achieves high-precision frequency comparison by measuring the frequency and time of the time-frequency signals.

[0075] Step 2, Two-way Frequency Comparison and Data Acquisition: During the 10-year mission period, based on the visible time between Earth ground stations and lunar stations, two-way frequency comparisons will be conducted between different Earth ground stations and lunar stations, 24 / 7. The frequency deviation between the Earth ground optical clocks and the lunar surface optical clocks will be accurately recorded. Simultaneously, using the laser time-of-flight method, the Earth-Moon distance was precisely measured at every moment. The accuracy reaches the millimeter level. All data... timestamp The auxiliary data (such as platform attitude and temperature) are packaged and transmitted back to the ground data processing center.

[0076] Step 3, Gravitational Redshift Separation and Modeling: (a) Data Processing Center Precise corrections were made. Using accurate models of Earth and Moon rotation, and solid-state tides (including Earth tides and lunar tides), these known periodic gravitational redshift effects were adjusted. Extracted, retaining only the gravitational potential difference between Earth and the atomic clocks on the surface of the Earth and the Moon. (b) Subtract the first and second order Doppler effects caused by the relative motion between the Earth and the Moon; (c) Accurately correct the frequency shifts caused by different environmental noises using an environmental noise correction model; (d) After the above processing, obtain the frequency shift sequence reflecting the gravitational potential difference between the Earth and the Moon. .

[0077] Step 4, Lunar orbit expansion rate extraction: (a) For up to 10 years The data is fitted using linear least squares to obtain its slope. Assuming the fitting accuracy can reach 1×10⁻⁶. -20 / day. (2) Calculate the lunar orbit expansion rate α based on the physical relationship model of the Earth-Moon system.

[0078] The method described in this invention is also applicable to measuring the orbital evolution of other planetary systems, such as Mars and its moons. All variations, modifications, and equivalent substitutions based on the concept of this invention are within the scope of protection of this invention.

[0079] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a system for determining the lunar orbit expansion rate using a lunar optical clock, comprising a lunar two-way time-frequency transfer subsystem and a data processing subsystem. The lunar two-way time-frequency transfer subsystem is used to establish a lunar two-way time-frequency transfer link between a ground station and a lunar station, enabling optical clock time-frequency signal comparison and laser ranging, and continuously measuring the relative frequency deviation between the ground optical clock and the lunar optical clock. Both the lunar station and the ground station are equipped with optical clocks of better than 10⁻²⁰. The data processing subsystem is used to establish a physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate based on the general relativistic gravitational redshift theory; and to calculate the lunar orbit expansion rate from the measured relative frequency deviation change rate based on the physical relationship model.

[0080] Furthermore, the Earth-Moon bidirectional time and frequency transfer subsystem includes at least an optical clock, a femtosecond optical comb, a time and frequency comparison unit, a frequency signal transmission and reception unit, a GNSS receiver, a laser reflection prism, an environmental monitoring unit, and a data acquisition and storage unit.

[0081] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the method for determining the lunar orbit expansion rate using a lunar clock.

[0082] In summary, the method of this invention deploys high-precision optical atomic clocks on Earth and the Moon and establishes a two-way time-frequency transmission link between Earth and the Moon to accurately measure the relative frequency deviation between the two clocks. Furthermore, through data processing, it separates the long-term gravitational redshift drift rate caused by changes in the Earth-Moon distance, and then directly calculates the lunar orbital expansion rate based on a general relativity model. This invention achieves direct, continuous, and high-precision measurement of lunar orbital expansion, overcoming the limitations of traditional lunar laser ranging technology, and providing a new generation of measurement methods for the study of Earth-Moon system dynamics and fundamental physics verification.

[0083] This invention makes full use of high-precision optical clocks, femtosecond optical combs, time-frequency comparison and other related technologies to achieve ultra-long-distance, ultra-high-precision, long-term continuous monitoring of Earth-Moon orbital changes, providing a brand-new technical means and experimental platform for high-precision determination of Earth-Moon gravitational potential difference and lunar orbital expansion rate.

[0084] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the rate of lunar orbit expansion using a lunar geocentric clock, characterized in that, The method comprises: Obtaining the relative frequency deviation between the ground optical clock and the lunar surface optical clock measured continuously via a moon-earth bidirectional time-frequency transfer link; the moon-earth bidirectional time-frequency transfer link is established between a lunar surface station and a ground station, and is used for realizing optical clock time-frequency signal comparison and laser ranging, wherein the lunar surface station and the ground station are both configured with an optical clock with an order of magnitude better than 10 -20 ​ Based on the general theory of relativity gravitational redshift theory, the physical relationship model between the relative frequency deviation rate and the lunar orbit expansion rate is established, including: the relative frequency deviation between the ground optical clock and the lunar surface optical clock is expressed as: ， wherein, is the frequency difference between the ground optical clock and the lunar surface optical clock, is the nominal frequency of the clock at zero gravitational potential, c is the speed of light, is the transmission frequency of the earth surface after the light frequency conversion, is the frequency received by the lunar surface, is the nominal frequency of the time-frequency signal, is the conversion coefficient between the transmission signal frequency and the optical clock signal frequency, is the gravitational potential difference of the earth and the lunar surface optical clock position, is the gravitational potential correction caused by the high-order gravitational redshift. The physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate a is represented as: The physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate a is represented as:​ ， in, G represents the gravitational constant, and M represents the mass of the central celestial body. Represents the radius of the Earth. This indicates the initial distance between stations on the Earth and the Moon. Indicates the time difference between Earth and lunar surface stations. The distance; Based on the physical relationship model, from the measured relative frequency deviation change rate The monthly orbit expansion rate is calculated.

2. The method of claim 1, wherein the method further comprises: In measuring the relative frequency deviation between the ground optical clock and the lunar surface optical clock Further comprising: Subtracting periodic frequency variations caused by the first and second order Doppler effects of the Earth and the Moon solid tides, rotation deformation, solar gravitational potential, and relative motion from the obtained relative frequency deviation data; The frequency shift caused by different environmental noises is corrected by using an environmental noise correction model to obtain a frequency shift sequence reflecting the geolunar gravitational potential difference .

3. The method of claim 2, wherein the method further comprises: In obtaining the frequency shift sequence reflecting the geolunar gravitational potential difference Further comprising: Frequency shift sequence for a predetermined period Linear least square fitting is performed to obtain the rate of change of the relative frequency deviation caused by the long-term variation of the earth-moon distance ; According to a physical relationship model between the relative frequency deviation rate and the lunar orbit expansion rate, the lunar orbit expansion rate is calculated.

4. The method of claim 1, wherein the method further comprises: In establishing the physical relationship model between the relative frequency deviation rate and the lunar orbit expansion rate, the method comprises: Obtaining the time series of the relative frequency deviation and the Earth-Moon distance by using at least 10 years of Earth-Moon ranging data and time-frequency comparison data; Using a real-time correction model based on various environmental influences in the two-way time-frequency transfer process and a dual-frequency link comparison technology, and combining the recorded time series, the relative frequency deviation rate is separated out; A physical relationship model between the relative frequency deviation rate and the lunar orbit expansion rate is established.

5. The method of claim 1, wherein the method further comprises: The method further comprises: A plurality of ground stations are set up on the Earth, and the ground stations are connected by optical fiber links to determine the gravitational potential difference between different ground stations in real time; According to the gravitational potential difference between the different ground stations, the gravitational potential difference between the Earth and the Moon is corrected in real time.

6. System for determining the rate of lunar orbit expansion using a lunar clock, characterized in that, The method comprises a two-way time-frequency transfer subsystem and a data processing subsystem, wherein The moon-earth bidirectional time-frequency transfer subsystem is configured to establish a moon-earth bidirectional time-frequency transfer link between the ground station and the moon surface station, realize light clock time-frequency signal comparison and laser ranging, and continuously measure the relative frequency deviation between the ground light clock and the moon surface light clock, wherein the moon surface station and the ground station are both configured with a light clock with an accuracy better than 10 -20 orders of magnitude. The data processing subsystem is configured to establish a physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate based on a general relativity gravitational redshift theory, and calculate the lunar orbit expansion rate based on the physical relationship model and the measured relative frequency deviation change rate. The establishment of the physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate comprises: calculating the relative frequency deviation between the ground optical clock and the lunar surface optical clock is represented as: ， wherein, is the frequency difference between the ground optical clock and the lunar surface optical clock, is the nominal frequency of the clock at zero gravitational potential, c is the speed of light, is the emission frequency of the earth surface after the light frequency conversion, is the frequency received by the lunar surface, is the nominal frequency of the time-frequency signal, is the conversion coefficient between the emission signal frequency and the optical clock signal frequency, is the gravitational potential difference of the earth and the lunar surface optical clock position, is the gravitational potential correction caused by the high-order gravitational redshift. The physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate a is represented as: The physical relationship model between the relative frequency deviation change rate and the lunar orbit expansion rate a is represented as:​ ， in, G represents the gravitational constant, and M represents the mass of the central celestial body. Represents the radius of the Earth. This indicates the initial distance between stations on the Earth and the Moon. Indicates the time difference between Earth and lunar surface stations. The distance; Based on the physical relationship model, from the measured relative frequency deviation change rate The monthly orbit inflation rate is calculated.

7. The system for determining the lunar orbit expansion rate using the lunar swingby clock according to claim 6, wherein, The two-way time-frequency transfer subsystem comprises at least an optical clock, a femtosecond optical comb, a time-frequency comparison unit, a frequency signal transmitting and receiving unit, a GNSS receiver, a laser reflection prism, an environment monitoring unit, and a data acquisition and storage unit.

8. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium stores computer instructions, and the computer instructions cause the computer to perform the method for measuring the lunar orbit expansion rate by using the Earth-Moon optical clock according to any one of claims 1 to 5.

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