An all-electric propulsion elliptical orbit transfer method based on radial and lateral thrust ratio

Abstract

The application discloses a full-electric propulsion elliptical orbit transfer method based on a radial and transverse thrust ratio, and is based on the practical engineering problems that electric propulsion applies continuous thrust near the perigee of an elliptical orbit to adjust the apogee height and applies continuous thrust near the apogee of the elliptical orbit to adjust the perigee height; according to the relationship between the satellite orbit height and the thrust direction when the satellite is near the perigee or the apogee, the perigee or apogee height is time-derivative, and the derivative result is equal to 0, so that the perigee or apogee height is ensured not to change with time, and finally the change relationship of the thrust direction of the satellite with time is obtained, unnecessary secondary orbit height change is avoided, fuel waste is reduced, and orbit control efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of aerospace orbit design, specifically a orbit-changing method based on the radial and lateral thrust ratio. It also includes an optimization method for adjusting apogee altitude at perigee and adjusting perigee altitude at apogee. Background Technology

[0002] Sending a satellite into its designated orbit is a prerequisite for its normal functioning. However, due to limitations in the rocket's capabilities, satellites often cannot be directly placed into their intended orbits. Therefore, satellites need to rely on their onboard fuel for orbital maneuvers. Currently, the commonly used orbital maneuvering methods are mainly divided into chemical propulsion and electric propulsion. Chemical propulsion allows satellites to achieve significant orbital changes in a very short time. However, because chemical propulsion often has a low specific impulse, large-scale orbital transfers require a large amount of fuel, posing a significant challenge to the tank volume and the satellite's total mass. Electric propulsion has a relatively higher specific impulse, and orbital maneuvers using electric propulsion consume less fuel to reach the same orbit. However, the thrust is also lower, and the orbital transfer process takes a very long time. The thrust arc is not insignificant relative to the orbital period, which is completely different from pulse propulsion. Due to the continuous low thrust, there is no closed-loop analytical solution in the dynamics, and numerical integration must be used to solve for the orbit. Therefore, when a satellite uses electric propulsion to apply thrust along the velocity direction to adjust its altitude near perigee, it also causes a change in perigee altitude. Similarly, when it applies thrust near apogee to adjust perigee altitude, it also causes a change in apogee altitude, thus lengthening the total orbit change time and reducing propulsion efficiency. Summary of the Invention

[0003] To address the problems of existing technologies, this invention designs an elliptical orbit transfer method based on the radial and lateral thrust ratio. The algorithm involves continuous all-electric propulsion near perigee to adjust apogee altitude while maintaining a constant perigee altitude, and applying continuous thrust near apogee to adjust perigee altitude while maintaining a constant apogee altitude.

[0004] The technical solution of this invention is: a method for elliptical orbit maneuvering based on the radial and lateral thrust ratio using all-electric propulsion. This method addresses the practical engineering problem of applying continuous thrust near the perigee of an elliptical orbit to adjust the apogee altitude and applying continuous thrust near the apogee to adjust the perigee altitude. Based on the relationship between the satellite's orbital altitude and the thrust direction during orbit maneuvering near perigee or apogee, the perigee or apogee altitude is differentiated over time, and the result is set to 0. This ensures that the perigee or apogee altitude does not change over time, avoiding the need for subsequent secondary orbit maneuvers to compensate for unnecessary changes in orbital altitude. Finally, the relationship between the satellite's thrust direction and time is obtained.

[0005] Furthermore, the method of applying continuous thrust near perigee to adjust apogee altitude involves the following steps:

[0006] Step 1: Give the orbital perturbation equation of the satellite, as shown in equation (1):

[0007]

[0008] in, μ is the Earth's gravitational constant, with a value of 3.986 × 10⁻⁶. 14 m 3 / s 2 S is the radial acceleration applied by the satellite thrust; T is the lateral acceleration applied by the satellite thrust; a is the semi-major axis of the satellite orbit; e is the eccentricity of the satellite orbit; E is the anomalous angle of the satellite in the orbit.

[0009] Step 2: The relationship between the geocentric distance and orbital elements when the satellite is at its apogee and perigee is given, as shown in Equation (2):

[0010]

[0011] Where, r p r is the geocentric distance from the perigee. a The geocentric distance from the apogee;

[0012] Step 3: Since the purpose of this method is to keep the perigee orbital altitude constant during continuous thrust orbit changes, that is, to keep the perigee geocentric distance constant, it is necessary to keep the rate of change of the perigee geocentric distance with time at 0 during continuous thrust orbit changes, as shown in equation (3):

[0013]

[0014] Substituting equation (1) into equation (3) yields:

[0015]

[0016] This leads to equation (5):

[0017] 2e(Ssinf+Tcosf)+2T=(1+e)(Ssinf+Tcosf+TcosE) (5)

[0018] After rearranging equation (5), we can obtain equation (6):

[0019] (1-e)Ssinf=(2+ecosf-cosf-cosE-ecosE)T (6)

[0020] Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (7):

[0021]

[0022] Equation (7) is the expression for the thrust direction of a satellite with respect to its true perigee angle f when the satellite is continuously thrusting. By continuously changing the thrust direction according to this equation, a propulsion scheme in which the perigee height does not change with time when performing apogee lifting can be obtained.

[0023] Furthermore, the method of applying continuous thrust near the apogee to adjust the perigee altitude involves the following steps:

[0024] Step 1: Give the orbital perturbation equation of the satellite, as shown in equation (1):

[0025]

[0026] in, μ is the Earth's gravitational constant, with a value of 3.986 × 10⁻⁶. 14 m 3 / s 2 S is the radial acceleration applied by the satellite thrust; T is the lateral acceleration applied by the satellite thrust; a is the semi-major axis of the satellite orbit; e is the eccentricity of the satellite orbit; E is the anomalous angle of the satellite in the orbit.

[0027] Step 2: The relationship between the geocentric distance and orbital elements when the satellite is at its apogee and perigee is given, as shown in Equation (2):

[0028]

[0029] Where, r p r is the geocentric distance from the perigee. a The geocentric distance from the apogee;

[0030] Step 3: Since the purpose of this method is to keep the apogee orbital altitude constant during continuous thrust orbit changes, that is, to keep the apogee geocentric distance constant, it is necessary to keep the rate of change of the apogee geocentric distance with time at 0 during continuous thrust orbit changes, as shown in equation (8):

[0031]

[0032] Substituting equation (1) into equation (8) yields:

[0033]

[0034] This leads to equation (10):

[0035] e(Ssinf+Tcosf)+2T=Ssinf+Tcosf+(1+e)TcosE (10)

[0036] After rearranging equation (10), we can obtain equation (11):

[0037] (1+e)Ssinf=(-2-ecosf-cosf-cosE+ecosE)T (11)

[0038] Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (12):

[0039]

[0040] Equation (12) is the expression for the thrust direction of a satellite with respect to its true perigee angle f when the satellite is continuously thrusting. By continuously changing the thrust direction according to this equation, a propulsion scheme in which the perigee height does not change with time when performing apogee lifting can be obtained.

[0041] The beneficial effects of this invention are: the all-electric propulsion elliptical orbit apogee / perigee height adjustment optimization method of this invention achieves constant apogee / perigee height, avoids the need for secondary orbit change operations to compensate for unnecessary orbit height changes, reduces fuel waste, and improves orbit control efficiency. Attached Figure Description

[0042] Figure 1 To illustrate the change in perigee altitude with the number of orbital maneuvers when adjusting apogee altitude during continuous all-electric propulsion near perigee;

[0043] Figure 2 To illustrate the change in apogee altitude with the number of orbital rotations when adjusting apogee altitude during continuous all-electric propulsion near perigee;

[0044] Figure 3 To illustrate how the perigee altitude changes with the number of orbital maneuvers when applying continuous thrust near the apogee to adjust the perigee altitude;

[0045] Figure 4 The change of apogee altitude with the number of orbital maneuvers when applying continuous thrust near the apogee to adjust the perigee altitude. Detailed Implementation

[0046] The present invention will now be further described with reference to the accompanying drawings.

[0047] This embodiment presents an elliptical orbit transfer method based on the radial and lateral thrust ratio. The algorithm employs two approaches: continuous all-electric propulsion near perigee to adjust apogee altitude while maintaining a constant perigee altitude, and continuous thrust near apogee to adjust perigee altitude while maintaining a constant apogee altitude.

[0048] 1. Method of adjusting apogee altitude by applying continuous thrust (electric propulsion) near perigee.

[0049] First, the orbital perturbation equation of the satellite is given, as shown in equation (1):

[0050]

[0051] in, μ is the Earth's gravitational constant, with a value of 3.986 × 10⁻⁶. 14 m 3 / s 2 S is the radial acceleration applied by the satellite thrust, and T is the lateral acceleration applied by the satellite thrust. a is the semi-major axis of the satellite orbit, e is the eccentricity of the satellite orbit, and E is the anomalous angle of the satellite in the orbit.

[0052] Then, the relationship between the geocentric distance and orbital features at the satellite's apogee and perigee is given:

[0053]

[0054] Where, r p r is the geocentric distance from the perigee. a is the geocentric distance from the apogee.

[0055] Since the purpose of this method is to keep the perigee orbital altitude constant during continuous thrust orbit changes (that is, the perigee distance remains constant), it is necessary to keep the perigee distance changing with time at a rate of 0 during continuous thrust orbit changes, as shown in equation (3):

[0056]

[0057] Substituting equation (1) into equation (3) yields:

[0058]

[0059] This leads to equation (5):

[0060] 2e(Ssinf+Tcosf)+2T=(1+e)(Ssinf+Tcosf+TcosE) (5)

[0061] After rearranging equation (5), we can obtain equation (6):

[0062] (1-e)Ssinf=(2+ecosf-cosf-cosE-ecosE)T (6)

[0063] Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (7):

[0064]

[0065] This formula is the expression for the thrust direction of a satellite during continuous thrust (electric propulsion) as a function of the satellite's true perigee angle f. By continuously changing the thrust direction according to this formula, a propulsion scheme in which the perigee altitude does not change with time during apogee lifting can be obtained.

[0066] 2. Method of adjusting perigee altitude by applying continuous thrust (electric propulsion) near apogee.

[0067] First, the orbital perturbation equation of the satellite is given, as shown in equation (1).

[0068] Then, the relationship between the geocentric distance and orbital elements when the satellite is at its apogee and perigee is given as shown in Equation (2).

[0069] Since the purpose of this method is to keep the apogee orbital altitude constant (i.e., the apogee geocentric distance constant) during continuous thrust orbit changes, it is necessary to keep the rate of change of the apogee geocentric distance with time at 0 during continuous thrust orbit changes, as shown in equation (8):

[0070]

[0071] Substituting equation (1) into equation (8) yields:

[0072]

[0073] This leads to equation (10):

[0074] e(Ssinf+Tcosf)+2T=Ssinf+Tcosf+(1+e)TcosE (10)

[0075] After rearranging equation (10), we can obtain equation (11):

[0076] (1+e)Ssinf=(-2-ecosf-cosf-cosE+ecosE)T (11)

[0077] Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (12):

[0078]

[0079] This formula is the expression for the thrust direction of a satellite during continuous thrust (electric propulsion) as a function of the satellite's true perigee angle f. By continuously changing the thrust direction according to this formula, a propulsion scheme in which the perigee altitude does not change with time during apogee lifting can be obtained.

[0080] Example

[0081] The initial orbit had a perigee altitude of 700 km and an apogee altitude of 1400 km, while the target orbit had a perigee altitude of 700 km and an apogee altitude of 7444 km. The satellite weighed 1827 kg and was equipped with four 80 mN electric propulsion engines with a thruster specific impulse of 1600 s. The satellite used this method to perform continuous thrust maneuvers near perigee. The total fuel consumption and maneuver duration are shown in Table 1.

[0082] Table 1

[0083] satellite quality 1827 kg Satellite initial perigee altitude 700 km Satellite initial apogee altitude 1400 km Thrust magnitude during orbit change 0.08 N Number of thrusters during orbit change 4 tower Thrust specific impulse during trajectory change 1600 s Peri-geometry jet laps 2540 laps Perimeter jet phase 159 deg Time required for apogee elevation 239.5201 day The corresponding apogee altitude after the orbital change 7444 km The corresponding perigee altitude after the orbital change 700 km

[0084] The curves showing the changes in perigee and apogee altitudes over time during satellite orbit changes are as follows: Figure 1 and Figure 3 As shown.

[0085] The initial orbit had a perigee altitude of 700 km and an apogee altitude of 1400 km, while the target orbit had a perigee altitude of 1122 km and an apogee altitude of 1400 km. The satellite weighed 1827 kg and was equipped with four 80 mN electric propulsion engines with a thruster specific impulse of 1600 s. The satellite used this method to perform continuous thrust maneuvers near the apogee. The total fuel consumption and maneuver duration are shown in Table 2.

[0086] Table 2

[0087]

[0088]

[0089] The curves showing the changes in perigee and apogee altitudes over time during satellite orbit changes are as follows: Figure 3 and Figure 4 As shown.

[0090] As can be seen from the case studies, applying electric propulsion (continuous small thrust) near perigee to adjust apogee altitude and applying electric propulsion (continuous small thrust) near apogee to adjust perigee altitude can both keep the perigee or apogee altitude essentially constant, avoiding subsequent secondary orbit change operations. This has significant engineering implications for efficient satellite orbit change.

[0091] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for all-electric propulsion elliptical orbit change based on radial and lateral thrust ratio, characterized in that: This study addresses the practical engineering problem of applying continuous thrust near the perigee of an elliptical orbit to adjust the apogee altitude, and vice versa. Based on the relationship between satellite orbital altitude and the thrust direction during orbital maneuvers near perigee or apogee, the time derivative of the perigee or apogee altitude is calculated and set to zero to ensure that the perigee or apogee altitude does not change over time. This avoids the need for subsequent secondary orbital maneuvers to compensate for unnecessary changes in orbital altitude, ultimately yielding the relationship between the satellite's thrust direction and time.

2. The all-electric propulsion elliptical orbit change method based on radial and lateral thrust ratio according to claim 1, characterized in that, The specific steps for adjusting apogee altitude by applying continuous thrust near perigee are as follows: Step 1: Give the orbital perturbation equation of the satellite, as shown in equation (1): in, μ is the Earth's gravitational constant, with a value of 3.986 × 10⁻⁶. 14 m 3 / s 2 S is the radial acceleration applied by the satellite thrust; T is the lateral acceleration applied by the satellite thrust; a is the semi-major axis of the satellite orbit; e is the eccentricity of the satellite orbit; E is the anomalous angle of the satellite in the orbit. Step 2: The relationship between the geocentric distance and orbital elements when the satellite is at its apogee and perigee is given, as shown in Equation (2): Where, r p r is the geocentric distance from the perigee. a The geocentric distance from the apogee; Step 3: Since the purpose of this method is to keep the perigee orbital altitude constant during continuous thrust orbit changes, that is, to keep the perigee geocentric distance constant, it is necessary to keep the rate of change of the perigee geocentric distance with time at 0 during continuous thrust orbit changes, as shown in equation (3): Substituting equation (1) into equation (3) yields: This leads to equation (5): 2e(Ssinf+Tcosf)+2T=(1+e)(Ssinf+Tcosf+TcosE)(5) After rearranging equation (5), we can obtain equation (6): (1-e)Ssinf=(2+ecosf-cosf-cosE-ecosE)T(6) Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (7): Equation (7) is the expression for the thrust direction of a satellite with respect to its true perigee angle f when the satellite is continuously thrusting. By continuously changing the thrust direction according to this equation, a propulsion scheme in which the perigee height does not change with time when performing apogee lifting can be obtained.

3. The all-electric propulsion elliptical orbit change method based on radial and lateral thrust ratio according to claim 1, characterized in that, The specific steps for adjusting perigee altitude by applying continuous thrust near the apogee are as follows: Step 1: Give the orbital perturbation equation of the satellite, as shown in equation (1): in, μ is the Earth's gravitational constant, with a value of 3.986 × 10⁻⁶. 14 m 3 / s 2 S is the radial acceleration applied by the satellite thrust; T is the lateral acceleration applied by the satellite thrust; a is the semi-major axis of the satellite orbit; e is the eccentricity of the satellite orbit; E is the anomalous angle of the satellite in the orbit. Step 2: The relationship between the geocentric distance and orbital elements when the satellite is at its apogee and perigee is given, as shown in Equation (2): Where, r p r is the geocentric distance from the perigee. a The geocentric distance from the apogee; Step 3: Since the purpose of this method is to keep the apogee orbital altitude constant during continuous thrust orbit changes, that is, to keep the apogee geocentric distance constant, it is necessary to keep the rate of change of the apogee geocentric distance with time at 0 during continuous thrust orbit changes, as shown in equation (8): Substituting equation (1) into equation (8) yields: This leads to equation (10): e(Ssinf+Tcosf)+2T=Ssinf+Tcosf+(1+e)TcosE(10) After rearranging equation (10), we can obtain equation (11): (1+e)Ssinf=(-2-ecosf-cosf-cosE+ecosE)T(11) Finally, the ratio between the satellite's radial acceleration and tangential acceleration is obtained, as shown in equation (12): Equation (12) is the expression for the thrust direction of a satellite with respect to its true perigee angle f when the satellite is continuously thrusting. By continuously changing the thrust direction according to this equation, a propulsion scheme in which the perigee height does not change with time when performing apogee lifting can be obtained.

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