specs: submillimeter probe of the evolution of the cosmic ...cdhall/courses/aoe4065/oldreports/specs...

SPECS: Submillimeter Probe of the Evolution

of the Cosmic Structure

AOE 4065 - Space Design

Karen Amores Frances Durham Arash Ghaderi

Amanda Hibbert Michael Shoemaker Brian Verna

April 6, 2004

Contents

1 System Analysis 1

1.1 Mission Geometry Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 SPECS Configuration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Mission Geometry Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.1 Initial Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.2 Thermal Analysis Summary . . . . . . . . . . . . . . . . . . . . . . . 14

1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

ii

List of Figures

1.1 Solar radiation disturbance force at L2 as a function of spacecraft surface

area, and for different sun incidence angles, i, in degrees, given an assumed

reflectance factor of 0.6. Values of solar constant were selected for perihelion

( Fs = 1389 W/m2) and aphelion (Fs = 1296 W/m2). . . . . . . . . . . . . 3

1.2 Atmospheric drag force at perigee for different highly elliptic transfer orbits

as a function of spacecraft surface area. Drag coefficient chosen as 2.3 for all

cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Simple thermal model of MSC . . . . . . . . . . . . . . . . . . . . . . . . . . 9

iii

List of Tables

1.1 Radiation properties and equilibrium temperatures . . . . . . . . . . . . . . 10

1.2 Thermal conductivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Cryogenic fluid parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

iv

List of Acronyms

ADCS Attitude Determination and Control System

AHP Analytical Hierarchy Process

C&DH Command and Data Handling System

CMB Cosmic Microwave Background

COSMIC Constellation Observing System for Meteorology

CTA Cryogenic Telescope Assembly

DSN Deep Space Network

FIR Far Infrared

FIRST Far Infra-Red Submillimeter Telescope

GaAr Gallium-Arsenide

GALEX Galaxy Evolution Explorer

GN&C Guidance, Navigation, and Control

GSFC Goddard Space Flight Center

HST Hubble Space Telescope

InP2 Indium-Phosphide

IR Infrared

IRAS Infrared Astronomical Satellite

ISEE International Sun-Earth Explorer

L1,L2 Lagrange Point 1,2

LEO Low Earth Orbit

MEO Medium-Orbit

MLI Multi-Layer Insulation

v

vi LIST OF TABLES

MOE Measures of Effectiveness

NAC Needs Alterables and Constraints

NASA National Aeronautics and Space Administration

NiCd Nickel-Cadmium

NiH2 Nickel-Hydrogen

OSG outer shell group

OSR Optical Solar Reflectors

R3BP Restricted Three Body Problem

SE-L1 Sun-Earth L1 (Lagrange Point)

SfHe Superfluid Helium

Si Silicon

SIRTF Space Infrared Telescope Facility

SMM Submillimeter

SOHO Solar Heliospheric Observatory

SOME NASA’s Space Operations Management Office

SPECS The Submillimeter Probe of Evolution of Cosmic Structure

SUSI Sydney University Stellar Interferometer

TDRS Tracking and Data Relay Satellites

TPF Terrestrial Plane Finder

TSS Tethered Satellite System

TT&C Telemetry, Tracking, and Command System

USN Universal Space Network

VLTI Very Large Telescope Interferometer

VSD Value System Design

WMAP Wilkinson Microwave Anisotropic Probe

Nomenclature

γ Material strain

∆V Change in velocity

ηP Power efficiency

ηProp Propulsive efficiency

ηth Thermal efficiency

G Modulus of rigidity

σ Material stress

vii

Chapter 1

System Analysis

v′

s/m = v′

s/e = −v′

m/e = vm/e = rs = rm = rs/m (1.1)

Moon orbit

Moon SOI

Earth

The intent of this chapter is to qualitatively compare system synthesis options that deal

with overall aspects of the SPECS mission. This approach, as opposed to a quantitative

analysis, is done for several reasons. First, some aspects of the mission are too complex to

allow for a comprehensive numerical analysis at the present time (i.e. the dynamics of the

different tether formations, or the numerical methods needed to analyze the RTBP). Also,

since many different options exist in these areas, it is impractical to attempt to perform a

quantitative analysis for each option, especially under the current design schedule.

The alternative approach conducted in this chapter is to gather as much information as

possible from the literature dealing with tether formations, mission geometry, and thermal

control. Using this knowledge, along with engineering common-sense and intuition, we make

decisions on the overall direction in which the SPECS design should proceed. This reduced

set of options will then be optimized in following chapters, using similar analytic tools as

was done in the literature, where applicable.

1

2 CHAPTER 1. SYSTEM ANALYSIS

1.1 Mission Geometry Analysis

The disturbance forces and torques acting on the spacecraft must be quantified to determine

the size of the ADCS hardware. Following the argument used to exclude certain ADCS

sensors and actuators based on the space environment at L2 (see Tables ?? and ??), the

primary environmental disturbance acting on SPECS in its Halo orbit is the solar radiation

pressure.

The solar radiation pressure is related to certain parameters involving the geometry

of the space mission and the materials used on the spacecraft. The force caused by the

bombardment of the spacecraft by solar particles is18

Fsp =Fs

cAs(1 + q) cos i (1.2)

where Fs is the “solar constant”, or measure of solar radiation at a certain distance from the

sun, in units of W/m2, c = 3× 108m/s is the speed of light, As is the surface area, q is the

reflectance factor of the spacecraft material, and i is the sun incidence angle.

Figure 1.1 shows Fsp as a function of A for different mission geometry locations. The val-

ues of Fs are taken at the extreme locations of L2 as the Earth travels in its orbit around the

Sun. Thus, Fs = 1389 W/m2) at perihelion, and (Fs = 1296 W/m2) at aphelion(reference

something). The values of i represent the extreme cases, the minimum being 0 degrees, and

the maximum being the maximum angle between the Sun and the anti-boresight direction,

specified earlier as 20 degrees. An arbitrary value of q = 0.6 was selected, and values of As

ranging from 0 to 3 square meters are used.

If the spacecraft were to use the highly elliptic orbits (HEO) near the Earth prior to a

lunar swingby, it would experience different disturbance forces as compared with the oper-

ational orbit at L2. Namely, we must consider the aerodynamic, gravity gradient, magnetic

field, and solar radiation forces.

The worst case aerodynamic drag force would be experienced at the perigee of the elliptic

orbit, because both the velocity of the spacecraft and the density of the atmosphere are

largest here. The drag force, Fdrag, is written as18

Fdrag =1

2

[ρCdAV 2

](1.3)

1.1. MISSION GEOMETRY ANALYSIS 3

Figure 1.1: Solar radiation disturbance force at L2 as a function of spacecraft surface area,

and for different sun incidence angles, i, in degrees, given an assumed reflectance factor of

0.6. Values of solar constant were selected for perihelion ( Fs = 1389 W/m2) and aphelion

(Fs = 1296 W/m2).

where ρ is the atmospheric density, Cd is the drag coefficient, A is the surface area, and V

is the magnitude of the velocity.

The exact parameters of the HEO are not yet known, but the orbit would generally

have a radius of perigee, rp, in LEO and a radius or apogee, ra, extending to roughly the

location of the Moon’s orbit about the Earth. For these preliminary calculations, we use

rp =[

6578 6678 6778

]km, and rp = 384400 km. These three HEO orbit options yield

velocities at perigee of

Vp =[

10916 10832 10751

]m/s (1.4)

Using an arbitrary value of Cd = 2.3 (typical values are between 2 and 2.5), and mean

atmospheric density values at the altitudes corresponding to the distances of rp, we generate

the worst case drag forces shown in Figure 1.2 for varying surface areas.


Figure 1.2: Atmospheric drag force at perigee for different highly elliptic transfer orbits as

a function of spacecraft surface area. Drag coefficient chosen as 2.3 for all cases.

1.2 SPECS Configuration Analysis

This section lists the advantages and disadvantages of the tether formations described in

detail in Section ??. The four options are TetraStar, Triangle, Hex, and Triangle+Radial.

Results from previous simulations are combined with concepts from the operation of the

SPECS formation to reduce the number of ideas into a more manageable set for future

detailed analysis.

The control of the TetraStar and Triangle formations were modelled previously using

feedback control with asymptotic tracking.21 The simulations considered two mission sce-

narios for SPECS: the stabilization of a particular relative equilibrium motion of the for-

mation, which would be used between observations, and the motion of the bodies as the

tethers are deployed or retracted, as would be done during an actual observation. Both were

shown to be controllable, with TetraStar requiring less control effort due to the presence of

the countermasses. The control effort in the radial direction for TetraStar was negligible

when compared with Triangle. One advantage of the simplicity of Triangle compared with

1.2. SPECS CONFIGURATION ANALYSIS 5

TetraStar is that parameter estimation is easier for the former.

The countermasses used in TetraStar allow for less control effort, however, they present

problems of their own. First, this simulation assumed that the countermasses were un-

controlled, which would present a major problem for plane changes (i.e. repointing the

formation’s boresight). Also, adding extra dead weight simply to allow for more controlla-

bility seems like an unwise decision. Options for placing subsystems on the countermasses

(such as distributing the communications, computing, or power systems) were considered.

But since each countermass, along with the CSC and MSC, are isolated from one another,

they would all need dedicated systems. In other words, a communications system could not

simply be placed on a countermass, because it would also need its own dedicated subsystems

to operate (power, thermal, ADCS, etc.) Likewise, the uncontrolled countermasses could be-

come controlled by placing an ADCS and thruster system on them, but the same argument

about the necessary subsystems still applies.

Neither Triangle nor TetraStar as described in that study made mention of the control

method for the CSC. Only the dynamics of the MSC and possible countermasses were ana-

lyzed. Thus, we have added the Triangle+Radial configuration as a modification of Triangle.

Here, radial tethers extend from the CSC to each MSC. The alternative to using radial teth-

ers is identical to Triangle, where the position of the CSC in the center of the triangle is

assumed to be controlled with thrusters. The advantage of the Triangle+Radial system is

that there are no countermasses, and the overall tether system is simpler than TetraStar.

Also, radial tethers would presumably cut down on propellent cost to maintain the position

of the MCS, as in the case of Triangle. The disadvantage is that this particular system has

not been studied to the same extent as the others, to our knowledge. It is impossible to com-

ment conclusively on the controllability of this formation, but it is conceivable that methods

similar to those used by Triangle could be modified for Triangle+Radial. Additionally, this

idea will allow for some creativity in the design process, rather than repeating previous work.

Lastly, the Hex configuration was mentioned in a different report by a member of the

Goddard SPECS team.20 One advantage of this formation is that to some degree it is less

complicated than TetraStar. Since there are no tethers connecting masses along the angular

direction, initial deployment might be easier. Again, the main disadvantages is the use of


countermasses.

On the topic of countermasses, it is conceivable that mirrors could also be placed on the

countermasses and thus make them a more useful component of the formation. In essence,

as the “inner mirrors” are spiralling outward during the observation, the “outer mirrors”

(countermasses) would act to control the position of the inner mirrors, as well as take their

own measurements. This is an interesting idea that would add usefulness and redundancy

to the formation. However, it is likely infeasible in the sense that the motion of the inner

mirrors are strictly defined, and a complete observation only requires a Nyquist sampling

of the area covered by the variable baseline, as mentioned previously. In other words, it

is unclear whether observations made by these outer mirrors would be of any use to the

interferometry mission.

After making these qualitative comparisons, based in part on quantitative data from

previous studies, the Triangle and Triangle+Radial formations will be retained for further

analysis. The major trade to be investigated is whether radial tethers or central thrusters

are more effective at controlling the position of the MSC with respect to the CSC. The Hex

and TetraStar configurations will be excluded from further consideration, due to the added

complexity and mass. However, if after further analyzing the two triangle formations it is

found that they require a large mass of propellent for formation control, it might be worth

revisiting the countermasses in an overall mass comparison.

1.3 Mission Geometry Analysis

This section lists comparisons between different mission geometry options described in detail

in Chapter ??. Specifically, three transfer and parking orbit combinations are compared:

direct transfer to L2 from a LEO parking orbit, lunar swingby to L2 from a LEO parking

orbit, and lunar swingby to L2 from highly elliptic phasing orbits.

One advantage of the direct transfer to L2 from a LEO parking orbit is the shorter time of

flight. The ISEE-3 spacecraft, which travelled directly to L1, took about 2 months to reach its

destination.12 Since the direct method does not rely on any lunar gravity swingby maneuvers,

another advantage is a less restrictive launch window. However, the direct transfer technique

1.3. MISSION GEOMETRY ANALYSIS 7

requires more ∆V without the help of the lunar swingby.

The second option is an extension of the first, which retains the LEO parking orbit but

instead replaces a direct transfer with a lunar swingby. As mentioned previously, this method

cuts down on the required ∆V . The disadvantage, however, is the more restrictive launch

window.12

Lastly, the lunar swingby to L2 from elliptic phasing orbits is advantageous because of

the ability to correct for launch errors compared to the other two methods, as well as a

less restrictive launch window compared to the second option. Also, the time spent in these

elliptic orbits about the Earth allows for increased time to perform in-orbit checkout tasks,

such as calibrate sensors and thrusters. One disadvantage of these highly elliptic phasing

loops is that the spacecraft must pass in and out of the LEO environment numerous times,

potentially causing problems. Such lessons can be learned from the WMAP spacecraft,

which performed such a maneuver. Because of the varying thermal environments in these

highly elliptic orbits, it is believed that moisture formed into ice on the shaded side of the

solar panels of WMAP near apogee. As the spacecraft reentered the thermally active LEO

environment at perigee, this ice caused outgassing and created an unexpected force on the

spacecraft.25 Additionally, the spacecraft’s radiation hardening was increased to account for

the passes in and out of the Van Allen belts.17

It is clear that each mission geometry option has associated pros and cons that require

further modelling in order to make educated design decisions. For example, the highly elliptic

phasing loops could drive down mass by reducing the required ∆V , and thus the onboard

propellent. However, if such an orbit also requires added mass from radiation and thermal

hardening, more information must be modelled before deign trades can be made. At this

point in the design process, it is useful to characterize the direct transfer as one extreme, the

elliptic phasing orbits with lunar swingby as the opposite extreme, and the lunar swingby

from LEO as lying somewhere in the middle of the spectrum.


1.4 Thermal Analysis

The SPECS mission has strict thermal constraints due to its mission and payload. The

thermal control of SPECS may be analyzed in two parts: warm instruments and cold in-

struments. The first thermal system encompasses thermal control of the power and commu-

nications subsystems. The onboard computer and power storage devices operate at about

room temperature, with a minimum requirement of 265 K. The second thermal system in-

cludes the scientific instruments and optics, specifically the cooled mirrors on the MSC and

the detectors on the CSC. The temperature requirement of the mirrors is 4 K, which is the

ambient temperature at L2. The detectors require an operating temperature of 4 K, as well,

because images within the submillimeter and infrared wavelengths will be contaminated if

any components of the spacecraft radiate heat towards the photon detectors.

1.4.1 Initial Thermal Model

The principles of heat transfer provide the fundamental relationships underlying calculations

for thermal modeling. Heat transfer is divided into three major areas: convection, conduction

and radiation. Convection is the situation in which a material in contact with a circulating

fluid transfers heat to or from the fluid. However, since the space environment is a vacuum,

convection is mainly considered in determining the affects of atmospheric heating during

launch, and is not a factor in the external thermal analysis of other mission segments.

Conduction is heat transfer within a solid or between solids. Radiation is heat transfer

through electromagnetic waves.

The preliminary model of SPECS consists of simple geometric figures. The mirrors are

approximately flat disks, each with a diameter of 4 meters, while the central body can be

approximated as a spherical spacecraft. Assuming an isolated system, first-order estimates

are used to determine the thermal performance.

The external thermal protection of the MSC is roughly modeled in Figure 1.3, which

shows a heat shield that faces the Sun and intercepts radiation from the mirrors. These heat

shields are assumed to be perpendicular to the Sun’s rays and the backs of the shields are

insulated such that the plate neither absorbs nor emits energy toward the mirrors. Also, the

1.4. THERMAL ANALYSIS 9

energy dissipated inside the plate is taken as zero.

Figure 1.3: Simple thermal model of MSC

The law of conservation of energy states that

qabsorbed + qdissipated − qemitted = 0 (1.5)

where qabsorbed is the absorbed energy, qdissipated is the dissipated energy, and qemitted

is the emitted energy.18 Using the preliminary model, the terms in Eq. (1.5) are defined as

qdissipated = 0 (1.6)

qabsorbed = GSAα (1.7)

qemitted = εσT 4 (1.8)

where GS = 1, 418 W/m2 is the solar flux, A is the projected area of the flat plate, and σ =

5.67051× 10−8 W/(m2K4) is the Stefan-Boltsmann constant. The equilibrium temperature,


Teq, can be found by rewriting Eq. (1.5) using Eqs. (1.6) through (1.8)

GSAα = εσT 4eqA (1.9)

which yields

Teq =(

GSAα

εσ

) 14

(1.10)

Chapter 3 discusses materials with desirable thermal properties. The heat shield of SPECS

requires materials that result in low temperatures when radiated by light. Such materials

include white enamel, white epoxy, silver-coated Teflon, Aluminum-coated Teflon, and OSRs.

Table 1.1 displays the equilibrium temperature by which each of these materials may be

compared.

Table 1.1: Radiation properties and equilibrium temper-

atures.18

Material Measurement

temperature (K)

α ε Equilibrium

Temperature, T

(K)

White enamel 294 0.252 0.853 293

White epoxy 294 0.248 0.924 286

Silvered teflon 295 0.08 0.68 239

Aluminized teflon 295 0.163 0.08 267

OSR (quartz over silver) 295 0.077 0.79 222

For these five material options, the equilibrium temperature shows a lower value than

the ambient (measurement) temperature, especially the quartz-over-silver-material. Their

performance in deep space may provide a way to thermally control components that require

a low operational temperature.

One alternative of the power subsystem is solar panels. Each solar panel can be modelled

as a flat plate, with its surface normal to the Sun direction. At the L2 location, the top

surface of the array is assumed to receive direct solar energy, while the bottom half receives

albedo and Earth infrared radiation. The following equations use Eq. (1.5) once more to


determine the equilibrium temperature of the solar arrays. The absorbed energy includes

the direct energy, infrared, and albedo. The variables are described below the equations as

they are first introduced.

qabsorbed − qemitted − qpower generated = 0 (1.11)

qabsorbed = GSAα + qIAε sin2 ρ + GSaAαKa sin2 ρ (1.12)

where

qI = Earth infrared emission = 237± 21 W/m2

ρ = Earth angular radius = arcsin(

RE

H+RE

)RE = Earth radius = 6, 378.14 km

H = Spacecraft altitude

a = albedo = 30%± 5%direct solar energy

Ka = 0.644 + 0.521ρ− 0.203ρ2

and

qemitted = 2σεAT 4 (1.13)

qpower generated = ηGSA (1.14)

where η is the solar array efficiency.

Rewriting Eq. (1.11) using Eqs. (1.12) through (1.14) yields

GSAα + qIAε sin2 ρ + GSaAαKa sin2 ρ− 2σεAT 4 − ηGSA = 0 (1.15)

Solving for the worst-case scenarios determines the range of temperatures in which the solar

panels will operate. The worst-case hot scenario occurs when the satellite is in full view of

the sun’s solar rays and the Earth’s infrared emissions. The worst-case cold scenario occurs

when the arrays are in the Earth’s shadow and cannot see any sunlit parts of the Earth.

That case yields no direct solar, albedo, or electric power generation.

Tmax =

[GSα + qIε sin2 ρ + GSaαKa sin2 ρ− ηGS

2σε

] 14

(1.16)

Tmin =

[qIε sin2 ρ

2σε

] 14

(1.17)


Further thermal modeling will require knowledge of the type and sizing of the solar panels.

Finally the central body cannot be assumed a flat plate, but rather a sphere with the

surface area equivalent to that of the predicted central body. The same analysis is done

using Eq. (1.5).18

Tmax =[ACGSα + AFqIε + AFGSaαKa + QW

Aσε

] 14

(1.18)

Tmin =[AFqIε + QW

Aσε

] 14

(1.19)

where AC is the cross-section area of the spherical satellite, A is the surface are of the

spherical satellite, F = (1 − cos ρ)/2 is the view factor of an infinitesimal sphere viewing a

finite sphere, and QW is the electrical power dissipation in Watts.

Numerical values for the temperatures depend upon the chosen materials and the size of

the central body. The equations presented above provide reasonable first-order estimates as

a part of the preliminary design process.

When the operating temperature range of different components does not overlap, the

thermal subsystem design must thermally isolate those components from one another. Al-

though the spacecraft will be placed in a near vacuum environment, the conductive heat

transfer from a warm component to a cool component is also an issue for SPECS. Some

instruments on SPECS strictly require a temperature no greater than 4 K. The thermal

subsystem must restrict the heat transfer from the other spacecraft components to the cold

instruments, and maintain the temperature of the cool components by transferring waste

heat to a heat sink. The following are some examples of materials used for space applica-

tions and their thermal conductive property. Materials with high conductivity are typically

used for passively controlling the temperature of components and transferring heat to a heat

sink, and materials with very low conductivity are often used for insulation.

Table 1.2: Thermal conductivities.18

Material Conductivity, W/(m K)

Copper 398

Aluminum alloy 2017 164


Aluminum alloy 3003 156

Aluminum alloy 2219-0 172.9

Aluminum alloy 6061-T6 167.7

Glass fiber block 0.0317

Urea formaldehyde 0.0317

Polystyrene 0.0288

Air 0.026

Polyurethane 0.0231

The main thermal control system under consideration for SPECS is a cryogenic system.

A cryogenic system is typical for infrared detectors, and enables the operation of the payload

of SPECS within the temperature range of −271◦ C to − 150◦ C. The cryogenic system

is divided into two types: an active refrigeration system and an expendable cooling system.

Active refrigeration is suitable for long duration missions such as SPECS, which has an

expected lifetime of at least five years. This system requires electric power and a thermal

radiator that expels its waste heat into space. Large satellites use radiators with flexible

pipes, rotating fluid joints, and high performance pumped fluid loops. The downfalls with

active refrigeration are the additional weight, vibrations, and the decrease of reliability over

time. An expendable cooling system is much simpler, more reliable, and less expensive.

Unfortunately, these systems are mainly used for short mission life; otherwise the stored

cryogen tanks can become very large and heavy.

The type of cryogen is also another component of the thermal subsystem that must

be chosen after optimizing its options. Stored cryogen can vary in fluid or solid helium,

ammonia, methane, or other solutions or compositions. The cryogen is absorbed by the

components in the satellite and expels heat in the form of vented gas. Small satellites make

use of isothermal or conductive materials and small-scale pumped fluid loops. Due to the

size and lifetime of SPECS, the team will have to explore refrigeration options to meet

constraints. Table 1.3 lists a few examples of liquid cryogen and their fluid parameters.

Table 1.3: Cryogenic fluid parameters.26


Fluid parameter Cryogenic fluid

He H2 Ne N2

Triple point temperature (K) 2.17 13.8 24.6 63.1

Triple point pressure (atm) 0.051 0.070 0.423 0.128

Boiling temperature at 1 atm Tb (K) 4.22 20.4 27.2 77.3

Liquid density at Tb (kg/m3) 125 70.8 1212 808

Critical temperature (K) 5.19 32.3 44.4 126.1

Critical pressure (atm) 2.21 12.92 27.1 33.8

Heat of vaporization (kJ/kg) 20.9 442 860 199.7

Cp saturated liquid (J/kg K) ∼ 2500 ∼ 9800 ∼ 440 ∼ 2040

Cp saturated gas (J/kg K) 5200 14200 1030 1040

Enthalpy triple point to 300 K (kJ/kg) ∼ 1578 ∼ 4400 ∼ 367 ∼ 432

Thermal cond. liquid at Tb (W/m K) 0.027 0.119 0.04 0.14

Thermal cond. gas at Tb (W/m L) 0.011 0.021 0.014 0.0075

Viscosity liquid at Tb (kg/m s) 3.53× 10−6 1.34× 10−5 ∼ 7× 10−5 1.58× 10−4

Viscosity gas at Tb (kg/m s) 0.91× 10−6 1.05× 10−6 4.32× 10−6 ∼ 5.3× 10−6

Not only must the type of cryogen be explored, but also its process of refrigeration. The

type of cryocooler is chosen based on vibration tendency, efficiency, and reliability. Also, the

construction of the connections of a cryocooler to the cooled instrument must be considered.

SPECS may use heat pipes or flexible copper straps to carry the heat load.

1.4.2 Thermal Analysis Summary

The thermal subsystem must consider the operating temperature ranges of the internal

components. The power design will affect the thermal subsystem because the components

of the power subsystem, such as the batteries, must operate near room temperature. The

optics and observation instruments require thermal isolation from other internal components,

in addition to thermal protection from the external environment. The simplified model of

the spacecraft enables the estimation of heat transfer values to guide the preliminary design

of the thermal control system of the spacecraft.

1.5. SUMMARY 15

1.5 Summary

This chapter summarizes the thermal subsystem, mission geometry, and tether configuration

comparisons, which were detailed in Chapter 3. Qualitative analysis allows the educated

disposal of undesirable system alternatives. This preliminary analysis results in the outline

of a concept, which will guide further study. Many design options remain to be quantitatively

optimized and analyzed in subsequent chapters.

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BIBLIOGRAPHY 17

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