Method for constructing propagation time difference model of pulsar reaching spacecraft and solar system centroid

Abstract

The invention relates to the technical field of astronomy and computer communication, in particular to a method for constructing a propagation time difference model for a pulsar to reach a spacecraft and a solar system centroid, which comprises the following steps of: establishing a rotation matrix through a Kepler law and an angular momentum conservation law on the basis of orbit parameters corresponding to the spacecraft when a photon reaches a detector; obtaining a three-dimensional position coordinate and a velocity vector of the spacecraft relative to the earth; simulating different photons through a Monte Carlo algorithm to examine a geometric propagation time delay model; the right ascension and declination and the time difference between the MJD and epochs are updated by considering the influence of pulse self-motion and are substituted into a geometric propagation time delay model and a gravitational red shift time delay model. And then, respectively establishing a Shapio time delay and a narrow relativistic dynamic clock slowdown effect. Geometric propagation time delay and gravitational red shift time delay which consider the influence of pulse self are added into a total time delay module; according to the method, the propagation time difference of the photons of the pulsar reaching the spacecraft and the solar system mass center can be accurately calculated.

Description

Technical Field

[0001] The present invention relates to the field of astronomy and computer communication technology, and in particular to a method for constructing a propagation time difference model between a pulsar reaching a spacecraft and the solar system mass center. Background Art

[0002] The principle of pulsar navigation (XPNAV) is similar to the principle of differential positioning of GPS (DGPS), both of which are based on arrival time ranging. DGPS determines the position and speed of the receiver by comparing the propagation time of the signal received by the ground monitoring station and the receiver from the same satellite. XPNAV realizes the positioning and navigation of the spacecraft by comparing the arrival time of the pulse at the center of mass of the solar system and the arrival time of the photon received by the spacecraft (satellite, etc.) from the same pulsar. Therefore, it is necessary to calculate the propagation time difference between the pulsar and the spacecraft and the center of mass of the solar system, and then solve the position of the spacecraft relative to the center of mass of the solar system. The formula for calculating this time difference is also called the time conversion equation. However, the existing time conversion model is not satisfactory. Summary of the invention

[0003] The purpose of the present invention is to solve the shortcomings existing in the prior art, and proposes a method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system, which can accurately calculate the propagation time difference between the pulsar photons and the spacecraft and the center of mass of the solar system.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system comprises the following steps:

[0006] Step S1: According to the orbital parameters of the spacecraft, a rotation matrix is ​​established through Kepler's law and the law of conservation of angular momentum to derive the three-dimensional position coordinates and velocity vector of the spacecraft relative to the earth;

[0007] Step S2: different geometric propagation delay mathematical models are established by different methods, and different photon test geometric propagation delay models are simulated by Monte Carlo algorithm;

[0008] Step S3: Considering the influence of pulse proper motion, update the right ascension and declination, and the time difference between MJD and epoch;

[0009] Step S4: Establish mathematical models of Shapiro delay, gravitational redshift delay, and moving clock slowing effect of special relativity respectively;

[0010] Step S5: Substitute the updated right ascension and declination due to the influence of the pulse proper motion into the unit direction vector formula pointing from the spacecraft to the pulsar to establish a new unit direction vector;

[0011] Step S6: Substitute the time difference between the MJD and the epoch established due to the influence of the pulse proper motion into the gravitational redshift delay model;

[0012] Step S7: Integrate the Shapiro time delay model, the mathematical model of the moving clock slowing effect of the special theory of relativity, the geometric propagation time delay model and the gravitational redshift time delay model that are established respectively.

[0013] Preferably, in step S1, the following steps are specifically included:

[0014] Step S1.1: Use Kepler's law to calculate the two-dimensional orbital plane r, and use the law of conservation of angle quantity to calculate the two-dimensional orbital plane velocity. The calculation formula is as follows:

[0015]

[0016] Where h = 5.23308462 × 10 4 (km 2 / s) orbital angular momentum constant, μ = 398600.4418 km 3 / s 2 is the magnitude of the Earth's gravitational constant, e is the eccentricity, and θ is the true anomaly angle, which is the angle from the perigee along the orbital path to the current position of the celestial body;

[0017] Step S1.2: Convert the radius r from the polar coordinate system to the Cartesian coordinate system and decompose the velocity v into radial velocity and tangential velocity:

[0018]

[0019] In the formula, r vec The position vector of the satellite in the two-dimensional plane, v vec The velocity vector of the satellite in a two-dimensional plane;

[0020] Step S1.3: Establish a rotation matrix to transform the two-dimensional orbital plane into the Earth Reference System (GCRS), which is divided into the rotation matrix of the ascending node right ascension Ω, the rotation matrix of the orbital inclination i, and the rotation matrix of the perigee argument ω; the formula is as follows:

[0021]

[0022] Where Ω is the right ascension of the ascending node, R Ω is the rotation matrix of the ascending node right ascension Ω, i is the orbital inclination, R i is the rotation matrix of the orbital inclination, ω is the perigee argument, R ω is the rotation matrix of the perigee argument;

[0023] Step S1.4: Use the rotation matrix R Ω Ri R ω , the position and velocity vectors in the two-dimensional orbital plane are converted into three-dimensional GCRS, and the formula is:

[0024]

[0025] In the formula, r GCRS is the position vector in the three-dimensional GCRS, v GCRS is the velocity vector in the three-dimensional GCRS;

[0026] Step S1.5: Convert the spacecraft's Earth Reference System (GCRS) to the Solar System Barycenter Coordinate System (BCRS) coordinates, and determine the unit direction vector pointing from the spacecraft to the pulsar based on the observed right ascension and declination values.

[0027] Preferably, in step S2, two geometric propagation delay mathematical models are established by two methods, and the formulas are as follows:

[0028]

[0029] In the formula, Δt Romer1 is the mathematical model of method 1, Δt Romer2 is the mathematical model of method 2, d sunpath and d satellitepath are the distances from the pulsar to the mass center of the solar system and from the pulsar to the satellite, is the satellite position vector relative to the Geocentric Celestial Reference System (GCRS), n is the direction unit vector of the pulsar position, c is the speed of light, (x crab ,y crab ,z crab ) is the coordinate of the pulsar equivalent to the mass center of the solar system, (x satellite ,y satellite ,z satellite ) are the coordinates of the satellite equivalent to the center of mass of the solar system, ra is the right ascension, and dec is the declination;

[0030] The Monte Carlo algorithm was used to test the mathematical model of method 1, which was superior.

[0031] Preferably, in steps S3 to S6, the influence of the pulse proper motion is considered, the right ascension and the declination are updated, and a new unit direction vector of the spacecraft pointing to the pulsar is established; and the time difference between the reduced Julian day and the reference epoch at the current corresponding moment is solved, and the formula is obtained as follows:

[0032]

[0033] Where Δα and Δδ are the changes in right ascension α and declination δ, MJD and pch_pm are the reduced Julian day and reference epoch, Δt is the time difference between the reduced Julian day and reference epoch at the current corresponding moment, and α is new and δ new is the updated right ascension and declination;

[0034] A new unit direction vector pointing from the spacecraft to the pulsar is established based on the updated right ascension and declination, using the following formula:

[0035] n new =(cos(α new )cos(δ new ),sin(α new )cos(δ new ),sin(δ new ))

[0036] The unit direction vector of the spacecraft pointing to the pulsar established by the updated right ascension and declination is updated to the geometric propagation model;

[0037] Determine the position coordinates of the pulsar based on the solar system barycenter coordinate system (BCRS), and then determine the distances of the pulsar from the solar system barycenter and the satellite, and you will get the new direction unit vector n new available:

[0038] n satellite,crab,new =d1·n new

[0039] Where n satellite,crab,new is the direction vector of the satellite pointing to the pulsar Crab, and d1 is the distance from the Crab Nebula to the Earth;

[0040] Then add it together, and the obtained position coordinates of the earth equivalent to the solar system's barycenter coordinate system can be obtained to obtain the position coordinates of the pulsar equivalent to the solar system coordinate system (BCRS):

[0041]

[0042] In the formula, n satellite,crab,new They are the position coordinates of the pulsar in the solar system coordinate system, the position coordinates of the satellite in the solar coordinate system, and the direction vector of the satellite pointing to the pulsar Crab.

[0043] The distances of the pulsar to the barycenter of the solar system and the satellite are determined by the Euclidean distance formula. The position coordinates of the pulsar equivalent to the barycenter coordinate system of the solar system, the position coordinates of the satellite equivalent to the barycenter coordinate system of the solar system, and the barycenter of the solar system are as follows. (The barycenter of the sun is the origin of the coordinate system);

[0044] set up for:

[0045]

[0046] set up for:

[0047]

[0048] In the formula, and The position coordinates of the pulsar are equivalent to the coordinate system of the solar system's center of mass, and the position coordinates of the satellite are equivalent to the coordinate system of the solar system's center of mass.

[0049] Substituting into the Euclidean distance formula, we get:

[0050]

[0051] Where d crabpath and d satellitepath are the distances from the pulsar to the mass center of the solar system and from the pulsar to the satellite, respectively.

[0052] The mathematical model can be obtained as follows:

[0053]

[0054] In the formula, Δt Romer is the geometric propagation delay.

[0055] Preferably, in step S7, the time difference Δt obtained by considering the pulse proper motion is substituted into the special relativity slow clock effect model to obtain the special relativity slow clock effect model with the pulse proper motion effect added, and the model is as follows:

[0056]

[0057] In the formula, v satellite represents the speed of the satellite relative to the center of mass of the solar system, and t represents the reference time in seconds. Substituting all the values ​​into the formula, we can get the specific value of time dilation Δt relativity .

[0058] Then establish the gravitational redshift delay model. First, according to the relationship between gravitational potential energy Φ and the mass M and distance r of the celestial body, The gravitational redshift delay Δt can be deduced RS Model:

[0059]

[0060] In the formula, G represents the gravitational constant, which is taken as 6.67430×10 -20 km 3 kg -1 ·s-2 , M represents the mass of the sun, which is taken as 1.989×10 30 kg, d ss represents the distance from the sun to the solar center of mass. satsun is the distance from the satellite to the mass center of the solar system;

[0061] Establish the Shapiro delay model:

[0062]

[0063] Where, d crabsun is the distance from the pulsar to the Sun’s mass center;

[0064] The obtained geometric propagation delay, Shapiro delay, gravitational red delay, and the slow clock effect of special relativity are integrated, and the influence of pulsar proper motion is considered to obtain the following mathematical model:

[0065]

[0066] Δt total It is the total delay of geometric propagation delay, Shapiro delay, gravitational red delay, and moving clock slow effect of special relativity.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] 1. The present invention takes into account multiple time delays, and incorporates geometric propagation delay, gravitational redshift delay, Shapiro delay and special relativity delay into the total time delay model of pulsar photons reaching the spacecraft and the center of mass of the solar system, which can make the total delay model more comprehensive.

[0069] 2. The present invention not only covers a variety of time delays, but also introduces the influence of pulse self-propulsion, so that the calculation of the total time delay is more accurate.

[0070] 3. The present invention establishes a variety of geometric propagation delay models, and uses the Monte Carlo algorithm to simulate different photon inspections and verifies the geometric propagation delay model with the highest accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A verification result diagram of the optimal model for geometric propagation delay established and verified for the present invention;

[0072] Figure 2 The flowchart of the present invention is to consider the pulse self and calculate the total delay. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the protection scope of the present invention. The embodiments described in the present invention are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present invention.

[0074] Example:

[0075] like Figure 1 As shown, a method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system is provided. In this embodiment, the method for determining the optimal model of geometric delay using Monte Carlo includes the following steps:

[0076] S1. The relative coordinates of the spacecraft in the earth coordinate system are obtained through the spacecraft orbit parameters.

[0077] S2. Two methods are used to establish two models for calculation, and then the Monte Carlo algorithm is used to simulate and evaluate the two models. First, the model of method 1 is used, the MJD value is substituted into the formula, and then the position coordinates of the geocentric celestial sphere in the solar system barycenter coordinate system (BCRS) are obtained by looking up the DE series ephemeris table. The satellite's geocentric celestial reference system (GCRS) is converted to the solar system barycenter reference system (BCRS) coordinates by adding the position coordinates of the earth relative to the solar system barycenter and the position coordinates of the satellite relative to the geocentric celestial reference system (GCRS).

[0078] S3. The values ​​of right ascension (α) and declination (δ) obtained by spacecraft observations are used to determine the direction unit vector from the satellite to the pulsar. By consulting the literature, we know the distance from the Crab Nebula where the Crab pulsar is located to the center of mass of the solar system. By combining this distance with the previously obtained direction unit vector from the satellite to the pulsar plus the position coordinates of the earth relative to the center of mass of the solar system, we can deduce the coordinates of the pulsar relative to the solar system center of mass coordinate system (BCRS).

[0079] S3. The distances from the pulsar to the satellite and the center of mass of the solar system are derived from the coordinates of the pulsar and satellite positions. Finally, the difference between the two obtained distances and the speed of light are combined with the vacuum geometry propagation formula to obtain the vacuum geometry propagation delay model of method one.

[0080] S4. The dot product of the converted satellite direction vector and the direction unit vector obtained above is taken to obtain the projection of the satellite's vector based on the solar coordinate system (BCRS) on the direction unit vector of the vector pointed by the satellite to the pulsar, which is approximately the distance difference between the pulsar photon reaching the center of mass of the solar system and the photon reaching the satellite.

[0081] S5. Finally, the distance difference and the speed of light are combined with the vacuum geometry propagation formula to obtain the vacuum geometry propagation delay model of method 2.

[0082] S6. Finally, the Monte Carlo algorithm is used to establish the standard deviation of right ascension α and declination δ in a small range. The stability and accuracy of the two models are compared under the conditions of simulating 10,000 random generation of right ascension α and declination δ within the standard deviation range.

[0083] like Figure 2 As shown, in this embodiment, considering the pulse self-propulsion, calculating the total delay includes the following steps:

[0084] S1. First, solve the time difference Δt=MJD-pch_pm between the reduced Julian day and the epoch corresponding to the current time.

[0085] S2. Use proper motion parameters to calculate the changes in right ascension α and declination δ. For the convenience of calculation, radians are used as units.

[0086]

[0087] S3. According to the changes in right ascension and declination within Δt, the updated right ascension and declination of the pulsar can be obtained by combining the initial positions of the right ascension and declination of the pulsar. The new position is converted into a unit direction vector.

[0088] S4. Taking the updated right ascension and declination into consideration, the updated unit direction vector replaces the direction unit vector of the original geometric propagation delay.

[0089] S5. Determine the position coordinates of the pulsar based on the solar system barycenter coordinate system (BCRS) and then determine the distances of the pulsar from the solar system barycenter and the satellite, respectively. A mathematical model of geometric propagation delay can be obtained.

[0090] S6, substituting the time difference obtained in step S1 into the time delay of the slowing effect of the moving clock in special relativity A time delay model of the special relativistic clock slowing effect taking into account the proper motion of the pulsar can be obtained.

[0091] S7. Establish the Shapiro time-delay model. G(represents the gravitational constant, which is 6.67430×10 - 20 km 3 kg -1 ·s -2 ), M(represents the mass of the sun, which is taken as 1.989×10 30 kg), d ss (represents the distance from the sun to the sun's mass center). satsun (is the distance from the satellite to the center of mass of the solar system).crabsun (is the distance from the pulsar to the sun's mass center). Since the distance from the sun to the sun's mass center is negligible, the formula can be simplified to

[0092] S8. Establish the gravitational redshift delay, based on the relationship between gravitational potential energy Φ and the mass M and distance r of the celestial body: The gravitational redshift delay model is derived:

[0093] S9. According to the delay model established above, the total delay model is obtained by summing:

[0094]

[0095] The description and practice disclosed in the present invention are easy to think and understand for ordinary technicians in the technical field, and several improvements and modifications can be made without departing from the principles of the present invention. Therefore, modifications or improvements made without departing from the spirit of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system, characterized in that: The steps include: Step S1: According to the orbital parameters of the spacecraft, a rotation matrix is ​​established through Kepler's law and the law of conservation of angular momentum to derive the three-dimensional position coordinates and velocity vector of the spacecraft relative to the earth; Step S2: different geometric propagation delay mathematical models are established by different methods, and different photon test geometric propagation delay models are simulated by Monte Carlo algorithm; Step S3: Considering the influence of pulse proper motion, update the right ascension and declination, and the time difference between MJD and epoch; Step S4: Establish mathematical models of Shapiro delay, gravitational redshift delay and moving clock slowing effect of special relativity respectively; Step S5: Substitute the updated right ascension and declination due to the influence of the pulse proper motion into the unit direction vector formula pointing from the spacecraft to the pulsar to establish a new unit direction vector; Step S6: Substitute the time difference between the MJD and the epoch established due to the influence of the pulse proper motion into the gravitational redshift delay model; Step S7: Integrate the Shapiro time delay model, the mathematical model of the moving clock slowing effect of the special theory of relativity, the geometric propagation time delay model and the gravitational redshift time delay model that are established respectively.

2. The method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system according to claim 1, characterized in that: In step S1, the following steps are specifically included: Step S1.1: Use Kepler's law to calculate the radius r of the two-dimensional orbital plane, and use the law of conservation of angular quantity to calculate the velocity v of the two-dimensional orbital plane. The calculation formula is as follows: Where h = 5.23308462 × 10 4 (km 2 / s) is the orbital angular momentum constant, μ = 398600.4418 km 3 / s 2 is the magnitude of the Earth's gravitational constant, e is the eccentricity, and θ is the true anomaly angle, which is the angle from the perigee along the orbital path to the current position of the celestial body; Step S1.2: Convert the radius r from the polar coordinate system to the Cartesian coordinate system and decompose the velocity v into radial velocity and tangential velocity: In the formula, r vec is the position vector of the satellite in the two-dimensional plane, v vec is the velocity vector of the satellite in the two-dimensional plane; Step S1.3: Establish a rotation matrix to transform the two-dimensional orbital plane to the Earth Reference System GCRS, which is divided into the rotation matrix of the ascending node right ascension Ω, the rotation matrix of the orbital inclination i, and the rotation matrix of the perigee argument ω; the formula is as follows: Where Ω is the right ascension of the ascending node, R Ω is the rotation matrix of the ascending node right ascension Ω, i is the orbital inclination, R i is the rotation matrix of the orbital inclination, ω is the perigee argument, R ω is the rotation matrix of the perigee argument; Step S1.4: Use the rotation matrix R Ω R i R ω , the position and velocity vectors in the two-dimensional orbital plane are converted into three-dimensional GCRS, and the formula is: In the formula, r GCRS is the position vector in the three-dimensional GCRS, v GCRS is the velocity vector in the three-dimensional GCRS; Step S1.5: Convert the spacecraft's Earth reference system GCRS to the coordinates of the solar system barycenter coordinate system BCRS, and determine the unit direction vector from the spacecraft to the pulsar based on the observed right ascension and declination values.

3. The method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system according to claim 1, characterized in that: In step S2, two geometric propagation delay mathematical models are established by two methods, and the formulas are as follows: In the formula, Δt Romer1 is the mathematical model of method 1, Δt Romer2 is the mathematical model of method 2, d sunpath and d satellitepath are the distances from the pulsar to the mass center of the solar system and from the pulsar to the satellite, is the satellite's position vector relative to the geocentric celestial reference system GCRS, n is the direction unit vector of the pulsar's position, c is the speed of light, (x crab ,y crab ,z crab ) is the coordinate of the pulsar equivalent to the mass center of the solar system, (x satellite ,y satellite ,z satellite ) are the coordinates of the satellite equivalent to the center of mass of the solar system, ra is the right ascension, and dec is the declination; The Monte Carlo algorithm was used to test the mathematical model of method 1, which was superior.

4. The method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system according to claim 1, characterized in that: In step S3 to step S6, the right ascension and declination are updated considering the influence of the pulse proper motion, and a new unit direction vector of the spacecraft pointing to the pulsar is established; and the time difference between the reduced Julian day and the reference epoch at the current corresponding moment is solved, and the formula is obtained as follows: Where Δα and Δδ are the changes in right ascension α and declination δ, MJD and pch_pm are the reduced Julian day and reference epoch, Δt is the time difference between the reduced Julian day and reference epoch at the current corresponding moment, and α is new and δ new is the updated right ascension and declination; A new unit direction vector pointing from the spacecraft to the pulsar is established based on the updated right ascension and declination, using the following formula: n new =(cos(α) new )cos(δ new ),sin(a new )cos(δ new ),sin(δ new )) The unit direction vector of the spacecraft pointing to the pulsar established by the updated right ascension and declination is updated to the geometric propagation model; Determine the position coordinates of the pulsar based on the solar system barycenter coordinate system BCRS, and then determine the distances of the pulsar from the solar system barycenter and the satellite respectively, and you will get the new direction unit vector n new available: n satellite,crab,new =d1·n new Where n satellite,crab,new is the direction vector of the satellite pointing to the pulsar Crab, and d1 is the distance from the Crab Nebula to the Earth; Adding it together, the position coordinates of the Earth equivalent to the solar system's barycenter coordinate system can be obtained to obtain the position coordinates of the pulsar equivalent to the solar system's BCRS coordinate system: In the formula, They are the position coordinates of the pulsar in the solar system coordinate system, the position coordinates of the satellite in the solar coordinate system, and the direction vector of the satellite pointing to the pulsar Crab; The distances of the pulsar to the barycenter of the solar system and the satellite are determined by the Euclidean distance formula. The position coordinates of the pulsar equivalent to the barycenter coordinate system of the solar system, the position coordinates of the satellite equivalent to the barycenter coordinate system of the solar system, and the barycenter of the solar system are as follows; set up for: set up for: In the formula, and The position coordinates of the pulsar and the satellite in the coordinate system of the solar system's barycenter are equivalent to each other; Substituting into the Euclidean distance formula, we get: Where d crabpath and d satellitepath are the distances from the pulsar to the mass center of the solar system and from the pulsar to the satellite, respectively; The mathematical model can be obtained as follows: In the formula, Δt Romer is the geometric propagation delay.

5. The method for constructing a propagation time difference model between a pulsar and a spacecraft and the center of mass of the solar system according to claim 1, characterized in that: In step S7, the time difference Δt obtained by considering the pulse proper motion is substituted into the special relativity slow clock effect model to obtain the special relativity slow clock effect model with the pulse proper motion effect added, and the model is as follows: In the formula, v satellite represents the speed of the satellite relative to the center of mass of the solar system, and t represents the reference time in seconds. Substituting all the values ​​into the formula, we can get the specific value of time dilation Δt relativity ; Then establish the gravitational redshift delay model. First, according to the relationship between gravitational potential energy Φ and the mass M and distance r of the celestial body, The gravitational redshift delay model can be deduced: In the formula, G represents the gravitational constant, which is taken as 6.67430×10 -20 km 3 kg -1 ·s -2 , M represents the mass of the sun, which is taken as 1.989×10 30 kg, d ss represents the distance from the sun to the solar center of mass, d satsun is the distance from the satellite to the center of mass of the solar system; Establish the Shapiro delay model: Where, d crabsun is the distance from the pulsar to the Sun’s mass center; The obtained geometric propagation delay, Shapiro delay, gravitational red delay, and the slow clock effect of special relativity are integrated, and the influence of pulsar proper motion is considered to obtain the following mathematical model: Δt total It is the total delay of geometric propagation delay, Shapiro delay, gravitational red delay, and moving clock slow effect of special relativity.

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