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Master in Space and Satellite Technology
Space Environment:
Chapter 8: Radiation Environment
Space Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Radiation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Energetic Particle Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
RTG in Pioneer 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Radiation Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Biological Radiation Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Radiation Dose in Humans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Radiation Dose in Astronauts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Effects of Radiation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Solar Sail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Radiation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Radiation Pressure Cause . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Impact Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Theoretical Computation of RP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Simple Model of RP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Detailed Model of RP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Shadow Function: Cylindrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Shadow Function: Umbra/Penumbra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
ECSS Required Solar Flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Solar Flux Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Radiation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Earth Albedo Pressure: Knocke et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Earth Albedo Pressure: Knocke et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Earth IR Pressure: Knocke et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Effects of Radiation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Visualization of SRP Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1
Space Environment
Table of Contents
Introduction
The Sun and the Solar System
Planetary Environment
The Earth’s Magnetic Field
Earth’s Neutral Atmosphere
Terrestrial Ionosphere and Magnetosphere
Micrometeoroids and Space Debris
Vacuum and Microgravity
Radiation Environment
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Radiation Environment
In the context of Spacecraft-Space Environment Interactions, the term Radiation includes:
High energy particles (∼MeV): Penetrate bodies
Energetic particles: electrons, protons, neutrons, heavy ions.
Photons: Gamma rays, X-Rays
Natural electromagnetic radiation: Surface interaction
Solar spectrum
Earth Albedo
Earth IR emission
Solar wind particles
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2
Energetic Particle Sources
There are three natural sources of energetic particle radiation:
Galactic Cosmic Rays (GCR): Energetic nuclei from outside the Solar System, due to
Nova/Supernova explosions, or accelerated by interstellar fields ( 102-1013 MeV )
Trapped Radiation Particles: The trapped radiation or van Allen belts contain mostly
protons and electrons, gyrating around geomagnetic field lines. Protons may reach
30 MeV , electrons 3 Mev
Solar Proton Events (SPE): Energetic particles, mainly protons, emitted during solar flares.
( keV↔GeV )
And one artificial:
Radiosiotope Thermoelectric Generator or Radioisotope Heating Unit: Used for energy
when solar panels not available. Gamma rays and neutrons from Pu decay ( ∼10 Mev )
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RTG in Pioneer 11
Adapted from an image courtesy NASA
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Radiation Measurement
Energetic particles traverse matter, ionizing and interacting in different ways until eventually
absorbed (if object thick enough)
Radiation is measured by the amount of energy “deposited” on the object traversed
SI unit: gray (Gy): the amount of radiation that deposits 1 J per kg of material
Other fields of interest use different units. In Aerospace:
Rad: (radiation absorbed dose) the amount of any kind of energy that deposits 10−2 J per
kg of material (=0.01 Gy)
Roentgen: the amount of Gamma radiation or X-Rays that produces one electrostatic unit
of charge in one cm3 of standard temperature and pressure air (≃0.0097 Gy)
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Biological Radiation Measurement
Relative Biological Effectiveness (RBE): number of rad of X-ray or Gamma radiation that
produces the same biological damage as 1 rad of the radiation being used.
Roentgen Equivalent in Man (REM): product of the dose in ram and the RBE factor (SI: sievert;
1 Sv=100 rem)
Radiation RBE
X rays, gamma rays 1
Electrons ∼1
¡10 Mev protons 10
Alpha particles 10
Thermal neutrons 2.5
Fast neutrons 10
Source: Tribble
Cosmic ray in photographic emulsion.
Image courtesy Dr. David P. Stern, NASA
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4
Radiation Dose in Humans
Recommendations from National Council on Radiation Protection and Measurement (NCRP), and
International Commission on Radiological Protection (ICRP):
Exposure ICRP-60 (1991) NCRP-116 (1993)
Radiation workers
Stochastic 50 mSv annual, 100 mSv in 5 years 50 mSv annual, 10 mSv × age cu-
mulative
Deterministic 150 mSv to eye, 500 mSv annual to
skin
150 mSv annual to eye lens, 500
mSv annual to skin
General public
Stochastic 1 mSv annual, higher if 5 year avg.
¡ 1 mSv
1 mSv annual continuous; 5 mSv an-
nual infrequent
Deterministic 15 mSv annual to eye lens; 50 mSv
annual to skin
50 mSv annual to skin and extremi-
ties
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Radiation Dose in Astronauts
Radiation dose limits for deterministic effects in LEO:
NCRP 2000 (mSv)
Body organ 30-day limit 1-year limit career
Eyes 1000 2000 4000
Skin 1500 3000 6000
Bone marrow 250 500
Source: National Council on Radiation Protection and Measurement Report NCRP-132 (2000); NASA
Technical Memorandum 104782 (1993).
Shielding astronauts to even radiation worker level is prohibitive.
Principle: ALARA, As Low As Reasonably Achievable.
Exposure is limited to 3% risk of excess cancer fatality. This limits the mission length from 54
days (30-year female) to 268 days (55-year male).
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5
Effects of Radiation Environment
Mechanical: radiation pressure
Total dose effects:
Solar panel degradation
Sensor degradation
Electronics degradation
Dose rate effects
Ionization: currents in electronics, swamping signal
Single event effects (solar storms):
Latchup CMOS does not respond
Upset CMOS anomalous response
Total dose and rate: Effects on humans
ECSS-E-ST-10-04C specifies models/procedures for each type of EPR (Ann. B).
Further specifications: ECSS-E-ST-10-11C (Human factors), ECSS-E-ST-10-12C (radiation)
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Solar Sail
C
o
u
rt
es
y
N
A
S
A
-M
S
F
C
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6
Radiation Pressure
Electromagnetic radiation produces a force over the satellite
Sun
• Solar radiation: electromagnetic radiation from X-ray to ra-
diofrequency
(Rs)
• Solar wind: charged particles (mainly protons) and electrons (∼ 1−0.1%Rs)
• Earth Orbits: small winter/summer change
Earth
• Albedo: reflection and scattering of incident solar radiation (∼ 10− 35%Rs)
• Earth’s IR re-emission (∼ 17%Rs)
• Decreases with height
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Radiation Pressure Cause
Electromagnetic radiation carries:
Energy
Linear Momentum
Each photon has:
Speed v = cur
Energy e = hν = mc2
Linear momentum p =
hν
c
u
Solar flux Φ:
Energy flux per unit normal area at 1 AU from the
Sun: Solar Constant
Φ =
∆E
A∆t
Light speed: c = 2, 9979250 · 108 m/s Φ ≃ 1367 W/m2
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7
Impact Types
θ θ
p1 p2
n
Specular reflection: p2 = p1 + 2p1 cos θn
Reflectivity: ǫ = 1
Rad. Pressure Coefficient: CR = 1 + ǫ = 2
p1
p2
n
Diffuse reflection: p2 = p1/2n
Reflectivity: ǫ = 0− 1
Rad. Pressure Coefficient: CR = 1− 2
p1
Absorption: p2 = 0
Reflectivity: ǫ = 0
Rad. Pressure Coefficient CR = 1
p1
Transparency: p2 = p1
Reflectivity: ǫ = −1
Rad. Pressure Coefficient: CR = 0
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Theoretical Computation of RP
Force over an element of surface:
dFinc = (p1 − p2)N · ds =
(p1 − p2)
p1
max (−Φ · ds, 0)
c
N Number or particles per unit time and unit normal area
Φ Solar energy flux
Φ/c Linear momentum flux: Φ
c
≃ 4.56 · 10−6 N/m2
Integrate over all the surface exposed to radiation
Include radiation reflected/emitted by other parts of the satellite:
Thermal emision: dFemi = −aσT
4ds/c (a ∼ 1, σ = 5.661 · 10−8 WK4/m2, Boltzman
const.)
Radioelectric emision: Femi ≃ Ẇ/c
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8
Simple Model of RP
For simple numerical simulation: global coefficient CR:
Frad = νPradCRA⊙
Assume force along flux vector −r⊙ (panels normal to Sun line)
RP Coeff CR ≃ 1− 2 (Differential determination)
Radiation pressure: Prad =
Φ
c
=
Φ
c
−r⊙
r⊙
( Prad = 4.56 · 10
−6 N/m2)
Area exposed to sun A⊙ (6= ram area for drag)
Area exposed changes with attitude/Solar panels do not
Shadow function ν : Earth shadow cone blocks the Sun
Radiation pressure torque → rotation/attitude control
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Detailed Model of RP
Account for the reflection/absorption and surface orientation of each section of the satellite
Fi = −ν Prad
1AU2
r⊙2
cos θiAi [(1− ǫi) e⊙ + 2ǫi cos θi ni]
Shadow function ν with light/umbra/penumbra
Must know satellite attitude, shape ni, cos θi and surfaces ǫi
Reflections from other parts of the satellite
Requires a detailed model of the satellite (FEA)
Material ǫ 1− ǫ CR ≃ 1 + ǫ
Solar panel 0.21 0.79 1.21
H-G antenna 0.30 0.70 1.30
Al-Mylar solar sail 0.88 0.12 1.88
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9
Shadow Function: Cylindrical
r⊙
Watch integration step close to boundary!
b
b
Simplified shadow function: cylindrical shadow cone:
ν =
{
1 Lighted
0 Inside shadow cylinder
Cf. Vallado
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Shadow Function: Umbra/Penumbra
Umbra
Penumbra
Penumbra
Cf. Montenbruck
Regions of the shadow cone: lighted, umbra, penumbra
ν =



1 Lighted
∈ [0, 1] Penumbra
0 Umbra
Penumbra: compute visible fraction of Sun surface Watch step size!
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10
ECSS Required Solar Flux
Constant model: Solar radiation constant
Mean solar flux at 1 AU (ESA): Φ = 1366.1 W/m2
Max flux (Perihelium, winter solstice): Φ = 1412.9 W/m2
Min flux (Aphelium, summer solstice): Φ = 1321.6 W/m2
cf. ECSS-E-ST-10-04C, Table 6-2
Annual variation model:
Φ =
1358
1.004 + 0.0334 cosDaph
W/m2
Daph: annual phase. Angle from Aphelium (approx. 4th July).
From Smith and Gottlieb, 1974, cited by Vallado and Wertz. Easily adapted to ECSS-E-ST-10-04C-stated values:
Φ =
1366.1
1.0003+0.03343 cosDaph
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Solar Flux Changes
Time changes of Flux:
Summer-Winter: 3.4%
11-year Sun cycle: 0.1%
UV+ part very variable (F10.7, atmospheric models), but holds little energy
High-energy solar electromagnetic flux
Type
Wavelength Average Φ Worst-case Φ
(nm) (W/m2) (W/m2)
Near UV 180-400 118 177
UV ¡ 180 2.3 · 10−2 4.6 · 10−2
UV 100-150 7.5 · 10−3 1.5 · 10−2
EUV 10-100 2 · 10−3 4 · 10−3
X-rays 1-10 5 · 10−5 1 · 10−4
Flare X-rays 0.1-1 1 · 10−4 1 · 10−3
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11
Radiation Pressure
Solar radiation pressure: (pure absorption: CR = 1)
Prad =
Φ
c
= 4.56 · 10−6
W s
m3
(
N
m2
)
Earth Radiation Pressure
Earth albedo (only day side): < 475 W/m2, average: 0.3Φ
IR emision (10-20% day/night): < 260 W/m2, average: 230
Changes with Earth surface: Sea, ice, land. . .
Must divide visible Earth in surface elements . . .
Spherical Harmonics model for emissivity
Only for very high precision: diminishes with height
Knocke, P.C. et al, “Earth Radiation Pressure Effects on Satellites.” Proceedings of the AIAA/AAS Astrodynamics
Specialist Conference, Washington DC, 1988, pp. 577-586.
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Earth Albedo Pressure: Knocke et al.
Divide Earth in N surface elements i (about 20)
r̈
ERP
=
N
∑
i=1
CR
(
νiai cos θ
⊕
i +
1
4
ǫi
)
Prad
AS
m
cos θSi
dA⊕i
πr2i
ei
νi: shadow function of surface i:
{
Albedo: See Sun and Sat
IR: See Satellite
ai: albedo factor: sea 0.05, cloud/snow 0.6, average 0.34
ǫi: emissivity of surface element, average 0.68·disk/sphere
cos θ⊕i : angle of Earth surface element i with Sun
cos θSi : angle of satellite surface with Earth element i
ei: unit vector from element dA
⊕
i to satellite at a distance r
2
i
Compute separately for Albedo and IR
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12
Earth Albedo Pressure: Knocke et al.
Albedo variability with latitude and season:
a = a0 + a1 P1 (sinφ) + a2 P2 (sinφ)
a1 = c0 + c1 cos [ω (JD − to)] + c2 sin [ω (JD − to)]
where
t0 Epoch
ω Earth orbit pulsation, 2π/365.25
φ Equatorial geocentric latitude
JD Julian Date
Pn Legendre polynomial of degree n
a0 = 0.34 , a2 = 0.29
a1 : c0 = 0 , c1 = 0.1 , c2 = 0
Longitude considered through Sun angle and shadow function.
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Earth IR Pressure: Knocke et al.
Earth IR radiation variability with latitude and season:
e = a0 + e1 P1 (sinφ) + e2 P2 (sinφ)
e1 = k0 + k1 cos [ω (JD − to)] + k2 sin [ω (JD − to)]
where
t0 Epoch
ω Earth orbit pulsation, 2π/365.25
φ Equatorial geocentric latitude
JD Julian Date
Pn Legendre polynomial of degree n
e0 = 0.68 , e2 = −0.18
e1 : k0 = 0 , k1 = −0.07 , k2 = 0
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13
Effectsof Radiation Pressure
Small, except for light satellites; important in GEO
Periodic changes in all elements (yearly: e, orbital: a)
Secular changes in Ω, ω
Small change with solar activity
Comparison with atmospheric drag:
aaerod
apr
=
1
2
ρ CDA/m v
2
rel
Prad CR A⊙/m
≃
ρv2rel
Prad
⇒ equal at ∼ 800km
A and A⊙ assumed to be similar.
Application:
Propulsion: solar sails
Maneuver: flaps in solar panels
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Visualization of SRP Effects
−∆v
∆v
e
Periodic variation of vector e
normal to the sun vector.
After one year, it returns to
original value
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14
	Space Environment
	Radiation Environment
	Energetic Particle Sources
	RTG in Pioneer 11
	Radiation Measurement
	Biological Radiation Measurement
	Radiation Dose in Humans
	Radiation Dose in Astronauts
	Effects of Radiation Environment
	Solar Sail
	Radiation Pressure
	Radiation Pressure Cause
	Impact Types
	Theoretical Computation of RP
	Simple Model of RP
	Detailed Model of RP
	Shadow Function: Cylindrical
	Shadow Function: Umbra/Penumbra
	ECSS Required Solar Flux
	Solar Flux Changes
	Radiation Pressure
	Earth Albedo Pressure: Knocke et al.
	Earth Albedo Pressure: Knocke et al.
	Earth IR Pressure: Knocke et al.
	Effects of Radiation Pressure
	Visualization of SRP Effects