Thermal Radiation Effects on Deep-Space Satellites Part 2

Transcription

1 Thermal Radiation Effects on Deep-Space Satellites Part 2 Jozef C. Van der Ha Fundamental Physics in Space, Bremen October 27, 2017

2 Table of Contents Mercury Properties & Parameters Messenger Satellite Model Overview of SRP & TRP Models SRP & TRP Analytical Results Mercury Temperature Model Geometry & Orbital Models Results for Infra-Red & Albedo Effects Conclusion JvdHa-2

3 Mercury Orbital & Thermal Characteristics Mercury s Orbit has High Eccentricity and Inclination: e M 0.2; i M 7 Mercury has High Daytime Surface Temperatures (2 nd after Venus!): up to 720 K = 450 C but only 100 K at Night Mercury s Rotation Rate is 1.5 Times its Mean Orbital Rate (i.e., 3 : 2 Resonance between Rotation and Orbit Motion) Mercury s Day (i.e., Time between two Sun Passages over the Same Meridian) is Extremely Long: 176 Earth Days As a Result, Variations in Local Solar Elevation and Surface Thermal Characteristics Occur only very Gradually Mercury s Rotation Axis is Close ( 0.01 ) to Orbit Plane Normal Subsolar Points are Practically on Equator At Perihelia (Aphelia) They are Called: Hot (Warm) Poles JvdHa-3

4 Variation of Solar Radiation Energy e 0.2 JvdHa-4

5 Mercury s Orbital & Thermal Input Parameters a : Mercury s orbital semi-major axis in [AU] e : Mercury s orbital eccentricity i : Mercury s orbital inclination 7.00 Ω : Mercury s longitude of ascending node ω : Mercury s longitude of perihelion M : Mercury s mean longitude µ M : Mercury s gravitational parameter (GM) in [km 3 s -2 ] R M : Mercury s equatorial (and polar) radius in [km] o M : Mercury s obliquity of rotation axis to orbit plane 0 P rot : Mercury s sidereal rotational period in [days] P orb : Mercury s sidereal orbital period in [days] P syn : Mercury s synodic orbital period in [days] d M : Mercurian day in [days] A b : Mercury s Bond albedo coefficient 0.12 α M : Mercury s surface thermal absorption coefficient 0.88 ε M : Mercury s surface thermal emissivity coefficient 0.82 JvdHa-5

6 Mercury s Unique Thermal Environment Mercury s Incident Solar Flux is much Higher than Earth s Non-Gravitational Effects on Satellite Solar Radiation (SR) Satellite s Thermal Radiation (TR) Mercury s Infra-Red Radiation (IR) Mercury s Albedo Reflection (AL) JvdHa-6

7 Messenger Unique Trajectory Design End of Life: April 2015 JvdHa-7

8 Messenger Orbiting Mercury JvdHa-8

9 Messenger In-Flight Spacecraft Configuration JvdHa-9

10 SRP Input Parameters for 10-Plates Configuration ID Component Area RA DE ρ s ρ d 1 X- Sunshield wing Center Sunshield X+ Sunshield wing X facing (2-way) Z facing (2-way) Y+ facing (backside) X+ Solar panel, front X- Solar panel, front X+ Solar panel, back X- Solar panel, back JvdHa-10

11 Accelerations due to Solar Radiation Pressure Total Acceleration Induced by SRP on Satellite with n Surfaces A j a = a + a + a SRP, j absorbed, j specular, j diffuse, j n {( ) ( ) }, a = c A cosϑ 1 ρ s+ 2 ρ / 3 + ρ cosϑ n SRP SRP j j s j d s j j j = 1 n { } 2 a = c A f s+ g n [m / s ] SRP SRP j j j j j = 1 JvdHa-11

12 Accelerations due to Thermal Heat Flux Recoil Acceleration due to Thermal Radiation Diffuse Emission I 0 n θ I = I 0 cosθ Emitted Heat Flux: 2 a = C Ther Ther n m s 3 with: qther = εσt 2 [ / ] 4 Flat Surface (Temperature T) a Ther C Ther Factor 2/3 is due to Lambert s Law 4 qther A εσt A = = c m c m 2 [ m/ s ] A: Area m: Satellite Mass c: Speed of Light JvdHa-12

13 SRP Inputs & Acceleration Results (at Perihelion) For Ideal Attitude, Symmetry Assures that SRP Force is Along y-axis Parameters Arrays Sunshields # 1, 2, 3 area (m 2 ): projected area (m 2 ): C-SRP (m/s 2 ): E E E E-07 α : ρ : ρ s : ρ d : mass (kg): 700 Accelerations (m/s 2 ): E E E E-07 Total Acceleration (m/s 2 ): E-07 JvdHa-13

14 SRP Induced Acceleration Results over Orbit JvdHa-14

15 TRP Inputs & Acceleration Results (at Perihelion) Ideal Attitude Assures that also TRP-Induced Force is Along y-axis Parameters Arrays Sunshields # 1, 2, 3 area (m 2 ): C-TRP(m/s 2 ): 1.472E E E E-19 alpha: epsilon: mass (kg): 700 Accelerations (m/s 2 ): E E E E-08 Percentages (%): Total Acceleration (m/s 2 ): E-07 (= 15.2 % of SRP) JvdHa-15

16 TRP Induced Acceleration Results over Orbit JvdHa-16

17 Variation of Temperature over Orbit - 1 Too High! Operating Temperatures of Solar Cells Should be < 150 C JvdHa-17

18 Variation of Temperatures over Orbit - 2 Therefore, Solar Arrays Must be Off-Pointed by Angle of 25 Operating Temperature Limit for Solar Cells JvdHa-18

19 Mercury Sub-Solar Latitudinal Temperature Model Heat Balance Conditions for Infinitesimal Latitude Bands T S ( d ) = M αm S σεmd 2 M 0.25 (, ) = ( )( cos ) T d ϕ T d ϕ 0.25 P M S M TS o = 723 K ( Perihelium) JvdHa-19

20 Mercury Surface Temperature as Function of Phi Angle JvdHa-20

21 Mercury Hemispherical Temperature Model Heat Balance Condition over Entire Daylight Hemisphere α S ( πr ) ( )( 2 ) M = σεm TM dm πrm M dm αm S TM ( dm ) = 2 2 σεmdm 0.25 This Hemispherical Temperature is (0.5) 0.25 = 84.1 % of Subsolar T S When Using Baseline Values α M = 0.88 and ε M = 0.82, We Find Equilibrium Temperatures over Mercury s Daylight Hemisphere: 608 K at Mercury s perihelion 494 K at Mercury s aphelion JvdHa-21

22 Geometry of Mercury Albedo Reflection on Satellite JvdHa-22

23 Grid Configuration over Mercury s Surface AZ i = π + 2π az i 1 EL j = π 2 + π el ( ) ( for i =1,2,...,az) ( j 0.5) ( for j =1,2,...,el) Number of grids: Azimuth : az = 100 Elevation : el = 50 Grid point position vector: R ij = R M cos EL j cos AZ i cos EL j sin AZ i = R M n ij sin EL j n ij : unit surface normal at g ij JvdHa-23

24 Geometrical View-Factor Modeling for IR & AL View Factor: f cosδ cosδ 1, ij 2, ij, k ij, k = 2 π rij A k If δ 1,ij π/2 or δ 2,ij,k π/2: f ij,k = 0 JvdHa-24

25 Modular Simulink Model for Mercury Orbiter JvdHa-25

26 SIMULINK SPACECRAFT MODEL JvdHa-26

27 Messenger Orbit about Mercury Mercury-Sun Coordinate System P M, Q M, W M MESSENGER ORBIT: a = km Period = 12 h e = 0.74 i = ω = JvdHa-27

28 Visualization of Messenger Test Orbits Noon-Midnight Orbit Dawn-Dusk Orbit JvdHa-28

29 Analytical & Numerical Results JvdHa-29

30 Accelerations over Mercury Year (Simulink) Red: SR Green: TR Blue: IR Yellow: AL JvdHa-30

31 Conclusions Solar Radiation Intensity at Mercury is up to 10 x Larger than at Earth Location We Present Analyses & Results of SR, TR, IR, & AL Radiation Effects on the Mercury Orbiter MESSENGER by Means of Analytical & Numerical Approaches TR & IR Effects Introduce Appreciable Accelerations on Messenger Trajectory with Both up to 25 % of SRP AL Effect is Appreciable only over a Small Interval and is Significantly Smaller than TR & IR : 5 % of SRP High-Fidelity Thermal Models are Essential for Robust Satellite Thermal Subsystem Design Also they Improve Deep-Space Navigation by Enhancing Trajectory Prediction Models JvdHa-31

32 Our Publications on Thermal Radiation - 1 JvdHa-32

33 Our Publications on Thermal Radiation - 2 JvdHa-33