PDF《Support for the thermal origin of》

10 and

11 spacecraft was con- structed at the Jet Propulsion Laboratory (JPL) in col- laboration with the Applied Sciences Laboratory (ASL). The geometric and thermal models of the spacecraft were constructed using the SINDA/3D thermal modeling soft- ware [15]. While the software provides the capability to build a numerical model directly from CAD drawing ?les, no such ?les exist for a spacecraft designed

40 years ago. For this reason, the model was built in a more te- dious manner by specifying the coordinates of the ver- tices of each modeled spacecraft surface, using available blueprints and recovered project documentation. The spacecraft geometric model was built with a Monte Carlo based radiation analyzer (TSS) to calculate the radia- tive exchange factors using infrared emittance values for modeled surfaces speci?ed within it. The model incorpo- rated approximately 3,300 surface elements, 3,700 nodes, and 8,700 linear conductors. The spacecraft thermal- mechanical con?guration is simulated by a network of

2 Earth FIG. 1: Illustrative representation of the thermal model of the Pioneer

10 spacecraft evaluated at

40 AU. Top left: spacecraft body interior (temperature range: blue ?16? C, red +10? C);

Bottom left: spacecraft exterior (blue ?155? C, red ?108? C);

Right: entire spacecraft (blue ?213? C, red +136? C). Un- modeled struts that connect the RTGs to the spacecraft body are indicated with yellow-black dashed lines. TABLE I: Pioneer

10 telemetered power at select heliocentric distances. Externally vs. internally located components are indicated where applicable (only

5 out of

11 distances shown). Power (W) Description

3 AU

10 AU

25 AU

40 AU

70 AU Science, internal 12.6 12.6 11.9 8.8 0.8 Science, external 6.4 8.4 6.4 6.4 0.0 Subsystems 20.2 20.2 20.4 20.2 19.5 Electrical, internal 63.2 46.3 35.5 28.4 17.5 Electrical, external 8.1 4.7 2.7 2.3 0.1 TWTa thermal 18.6 18.6 19.8 19.5 21.2 Transmitter 9.2 9.2 8.0 8.3 6.6 Total consumed 138.3 120.0 104.7 93.9 65.8 RTG generated 148.5 127.1 107.1 94.0 67.2 Cable loss 6.9 5.3 4.0 3.2 1.7 Total available 141.6 121.8 103.1 90.8 65.5 Di?erence +3.4 +1.8 ?1.6 ?3.1 ?0.4 aTraveling wave tube ampli?er. thermal capacitance, conductive couplings, and radiative exchange factors between all surfaces and to deep space. The software numerically solves the energy equation using equipment power dissipation from the spacecraft ?ght telemetry records (see Table I). RTG power was esti- mated using the well-known half-life, τ = 87.74 yr, of the

238 Pu radioisotope fuel: Qrtg(t) = 2?(t?t0)/τ Qrtg(t0), where t0 = July 1,

1972 and Qrtg(t0) = 2578.179 W. The objective was to calculate the temperature distribution of all spacecraft surfaces. To accommodate the limitations imposed on us by thermal modeling software, the angular distribution of the radiative emission from the spacecraft to space was calculated by solving the thermal radiation equations with the spacecraft positioned at the center of ?400 ?300 ?200 ?100

0 100

1975 1980

1985 1990

1995 2000

10 20

30 40

50 60

70 80 Thermal power (W) Heliocentric distance (AU) FIG. 2: Pioneer

10 thermal power contributing to sunward acceleration, including solar heating and re?ected solar ra- diation (hollow circles), solar heating only (hollow squares) with re?ected solar radiation removed, and all solar e?ects removed (?lled circles). Positive values indicate radiation di- rected away from the Sun, resulting in a sunward acceleration of the spacecraft. a large (i.e., with radius of

40 high-gain antenna, or HGA, diameters), black spherical control surface. The amount of spacecraft radiative emission absorbed by each element of this control surface corresponds to the amount of mo- mentum carried in this direction. The model incorporated some parameters the values of which were less well known: e.g., the e?ective emissivities of multilayer insulation blankets or conductive couplings of certain structural elements. Redundancies in the ?ight telemetry were used to re?ne the estimates of these pa- rameters and validate the model. The primary objective was to reproduce the known thermal power of the RTGs by choosing suitable temperature boundary conditions that, in turn, had to agree with telemetered temperature readings. In the ?nal results, the modeled RTG thermal power was within 1% of the known value, while modeled RTG ?n root temperatures were always within ±2 K of the ?ight telemetry. Both spacecraft utilized a louver system for thermal management [6]. Louvers mounted on bimetallic springs opened in response to high interior temperatures, al- lowing excess thermal radiation to escape the spacecraft more freely. Louver geometry for twelve two-blade and two three-blade louver assemblies was integrated into the model. Movements of the modeled blade positions (and the resulting calculated louver e?ective emittance) were based on the average temperature of the two nodes on the edge of the element that corresponded to the physical lo- cation of the actuator housings for each louver assembly. In addition to the internally generated heat, the Sun was also a signi?cant source of heating, particularly at the smaller heliocentric distances. Since the spacecraft was facing the Sun, the solar energy was absorbed pri- marily by the HGA which largely shadowed the rest of the spacecraft from direct solar irradiation except for the RTGs. The solar e?ect became evident as the ab-