Century-Long Monitoring of Solar Irradiance and Earth's Albedo Using a Stable Scattering Target in Space

0.15 MB·English

by  Philip G. Judge

Mon.Not.R.Astron.Soc.000,1–5(2014) Printed7January2015 (MNLATEXstylefilev2.2)
Century-Long Monitoring of Solar Irradiance and Earth’s
Albedo Using a Stable Scattering Target in Space
⋆
Philip G. Judge and Ricky Egeland†
High Altitude Observatory, National Centerfor Atmospheric Research‡
P.O. Box 3000, Boulder CO 80307-3000, USA
5
Draftv6.13Nov2014
1
0
2
ABSTRACT

n An inert sphere of a few meters diameter, placed in a special stable geosynchronous
a orbit in perpetuo, can be used for a variety of scientific experiments. Ground-based
J observations of such a sphere, “GeoSphere”, can resolve very difficult problems in

6 measuring the long-term solar irradiance. GeoSphere measurements will also help us
understandtheevolutionofEarth’salbedoandclimate overatleastthenextcentury.

]
R Key words: Albedo, Planetary Radiation, Solar Activity, Solar Radiation, Spec-
S trophotometry, Variability
.
h
p
-
o
1 MOTIVATION theabsenceofharddata(e.g.Judge et al.2012).Irradiances
r
t have been measured from 1978 using radiometers in space
s The Sun is a very stable object. The Sun’s “irradiance”
a (e.g.Willson2014).Pre-flightcalibrationprecisionsof≈500
(bolometricfluxmeasuredsince1978fromabovetheearth’s
[ partspermillion(ppm),0.05%,havebeenachieved.Butin-
atmosphere) varies by 0.06-0.1% peak-to-peak, on time
dependentdata from different space missions havefailed to
1 scales of a 11 years (see, for example, recent reviews by
providetheneededlong-termstability.First,thehighlypre-
v Fro¨hlich 2013; Willson 2014). This variation follows the
cise irradiances measured bydifferent experimentsdifferby
3 wellknown“sunspotcycle”(Schwabe1844).Onshortertime
5 0.5-1% (see figure 1 of Willson 2014), i.e. disagreements of
scales,theevolutionanddiskpassageofsunspotgroupspro-
2 10to20σ,ontimescaleslongerthan11years.Thesesystem-
duce variations that are often 0.2%. Given that sunspots
1 atic thwart attemptsto measure variations longer than one
are magnetic (Hale 1908), these variations arise because of
0 satellite lifetime. Second, instrumental sensitivities change
a variable solar magnetic field. While of small amplitude,
. overmission lifetimes whichare, unfortunately,ratherclose
1 these changes are far more rapid than expected from first
0 to11years. Third,expensivenew radiometers mustbereg-
principles.Theyarebelievedtobegeneratedbyamagneto-
5 ularly launched.
hydrodynamicdynamo,drawingenergyfromdifferentialro-
1 We propose an alternative solution that can provide
tation and turbulence in the Sun’s interior. The dynamo
: society with solar brightness measurements that are stable
v engine changes the Sun from a benign object, stable over
over centuries at a time when climate change is of first im-
i time scales of 100,000 years and radiating essentially as a
X portance. Our long-term precision photometric goal is set
blackbodynear6000K,toarapidlyvaryingobject.Thedy-
r to 0.01% averaged over a week. This may not be achiev-
a namo also causes far more variable high energy UV and X- able, thusour less stringent requirement is a 0.1% precision
rayphotons(White1977),windvariations,andintermittent
over a century, which will uniquely constrain long-term so-
energetic particles and magnetized plasma clouds.
lar variations at a level still of great interest Shapiro et al.
The earth’s climate is sensitive to several factors, the
(2011); Lubin et al. (2012). We adopt high precision differ-
Sunis by far thelargest externalfactor. Herein lies a prob-
ential photometry of a target in space against stable en-
lem. We have no physical explanation of the solar dynamo,
sembles of stars. Nightly precisions of stellar observations
thus our understanding of irradiance changes remains em-
of “only” 0.1% are achieved with existing small telescopes
pirical.Nordowehaveaccuratemeasurementsofsolarvari-
(Younget al.1991;Henry1999),withseasonalaveragespre-
ability on time scales longer than decades. Long-term vari-
cise to 0.01%.
abilityisacontentiousandactiveresearcharea,plaguedby
⋆ Email:[email protected] 2 A SIMPLE SOLUTION
† AlsoaffiliatedwithMontanaState University
‡ TheNationalCenterforAtmosphericResearchissponsoredby Photometry of planets, asteroids and themoon present dif-
theNational ScienceFoundation ficultieswhen tryingtoextract solar variations near0.01%.
(cid:13)c 2014RAS
2 Philip Judge and Ricky Egeland
Planetshaveatmosphere-relatedalbedovariations(forNep- Table 1.Conditionsfora4mGeostationarysphere
tune,mV ≈8,theyare≈4%,Lockwood et al.1991).Aster-
oidshavevariablebrightnessesdependentontheirrotational
Parameter value
aspect and highly variable geocentric distances. The moon
is so bright and extended, with diverse phase-dependent
brightnessesof its features, that accuraterelative photome- Environmentalconditions atGeoSphere
try with standard stars is not possible. Geocentricdistancero km 42,164
We suggest that a diffuse object, “GeoSphere”, be SolarmV −26.74
placed in a stable geosynchronous orbit (GSO). The need EarthmV (β=90◦,quadrature) −20.6
EarthmV (β=20◦) −16.0
faonruanhemighculmevbeelreodf gspeohmereet.ricAssypmhmereetroyf aarfgeuwesmsettreornsgdlyiafmor- MoonmV ∼>−12.74
eter hasmV ≈10 at opposition independentof orientation, PhysicalandobservableGeoSphere properties
and the optical appearance of a star (Table 1. Placed at Adoptedspherediameterds m 4
L2,mV ≈18).PhotometricobservationsofGeoSpherewith Angulardiameter arcsec 0.0196
ground-based telescopes can in principle provide century- Adoptedalbedoa 0.9
long monitoring of GeoSphere’s brightness at 0.01% preci- q (phaselawparameter) 1.5
sion (Younget al. 1991; Henry 1999) using statistical aver- mV (opposition) 10.08
agesofmany(≈20+),nightlyobservations.Ifthescattering mV (quadrature) 11.32
propertiesofthesphereinorbitcanbemeasured,calibrated
and/or modeled at thesame level of precision, solar bright- Notes:“Lambert’slaw”forscatteredradiationisassumed,corre-
sponding to a perfectly diffusing sphere. Magnitudes were com-
ness variations will follow. GeoSphere should spin with a
period ofafewseconds,less thanatypicalintegration time putedassumingthedistancetothesphereisro−r⊕.βistheangle
betweenthegeocenter-GeoSphereline andgeocenter-Sun line.
of precision photometry (a minute).
Table 1 lists conditions for a 4m sphere as seen from
Earth. We adopt a 4m diameter only because fairings of
large launch vehicles extend to 5m. Smaller vehicles might mV = 8 have a daily rms precision of 1 milli-magnitude in
be used with on-orbit expansion of a pre-compacted sphere b and y. Scaling to the brightness of GeoSphere, telescopes
(e.g.,a“Hobermansphere”).UsingdatafromAllen(1973), of1.5mdiameterareneededtomeasurethebrightnessofa
the Johnson mV-magnitude when the sphere is at angle α 4mdiameterGeoSphereatthesamedailylevelofprecision.
from the anti-Sunpoint, is, with radius rs =ds/2: With telescope time devoted exclusively to GeoSphere, the
mV(α)≈−26.74−2.5log10(cid:18)(ro−rs2r⊕)2aqφ(α)(cid:19). (1) pinretchiHseiooswnteelwvlaeilrrl,AimqPupTarloipvtareotoigvvreealrmytshd.eiff0e.r1e%ntnoigbhstelryvamteioannssrmepusotrtbede
Here we use a perfectly diffusing sphere whose phase func- made to permit differential photometry of GeoSphere
tion φ(α) obeys Lambert’s law: against stars. Objects in GSO are observed most simply
by switching off a telescope’s astronomical drive. In time
φ(α)=[sinα+(π−α)cosα)]/π (2) t the Earth’s rotation sweeps out 15′′cosδ t of sky, where
δ is the object’s declination. As a result, background stars
for which q=1.5. ObservingGeoSphereclose toopposition
gives φ(α≪1)≈1, and mV =10.08. passing neartoGeoSpherewill contributetotheintegrated
flux. Consider a photometer fed from an aperture in the
Younget al. (1991, their table 1) calculate exposure
telescope’s focal plane of 5′′ diameter, δ = 0◦, and t = 100
times needed to achieve 0.05% RMS photon noise in the
Str¨omgren b and y filters at 4670 and 5470 ˚A, with widths seconds. The area covered is 6 × 10−4 square degrees. If
of160and240˚Arespectively.AssumingmV(GeoSphere)= the average number of stars with visual magnitude > m is
10.08, an integration time of <100s, we findthat telescope N(m,b)persquaredegreeat Galactic longitude b,thenthe
∼
numberof stars crossing the field per 100s observation is
aperture D and GeoSphere diameter ds must satisfy:
(dsD)2 ∼> 36 m4 (Stromgren by at opposition). (3) n=6×10−4N(mV,b).
In thegeneral case of a spectral sampling of w ˚A,
Using data from (Allen 1973, §117), for mV = 10,
(dsD)2 ∼>5800/w m4. (4) log10N(mV,b) varies between 1.25 (Galactic latitude b =
0◦)and0.55(b=90◦);formV =20wefindlog10N(mV,b=
Forobservationswiththew=10˚AsamplingoftheSORCE- 0,90)=5.0 and 3.4 respectively. For b=0 (worst case), 60
SIMinstrument(Harderet al.2000)forexample,thends = starsofmagnitude20orbrighterwillcrosstheaperture;for
4m and D∼>6m. mV ∼< 10, on average 1 in 100 such integrations will have
one star of brightness similar to GeoSphere affecting the
integrations. One solution might be to feed three mutually
calibratedphotometersfromthefocalplaneofthetelescope,
3 SOLAR BRIGHTNESS OBSERVATIONS
offset along a line of constant declination. With GeoSphere
Narrow-band photometric measurements of solar-like stars measured from one part of the focal plane, the same stars
are routinely made using small (< 0.8) Automated Photo- can be measured within a second before and after the tar-
∼
electricTelescopes(APTs,Henry1999;Hall et al.2009).In get in the other photometers, allowing subtraction of their
practice, combiningall sources oferror, those brighterthan contribution.
(cid:13)c 2014RAS,MNRAS000,1–5
GeoSphere 3
4 EARTH ALBEDO VARIATIONS satellites in GSO around earth, and < 300 other small de-
∼
tectedobjectslargeenoughforconcern(Kessler et al.2011,
Changes in Earth’s albedo might be monitored observing
Figure2.2).ThelargestthreattoGeoSphereisfromsmaller
GeoSphere close to quadrature, where it is illuminated by
natural micrometeoroids.
the Earth’s sunlit hemisphere. Then α0 ∼< π/2, φ(α0) ∼< Conversely,anon-powered GeoSphererepresentsacol-
1/π andthebrightnessofGeoSpherefrom directsunlightis
lision hazardtootherspacecraft in GSO.TheInternational
mV ∼> 10.96. Using mean earth albedo data (Allen 1973), Telecommunication Union (ITU) has mandated an end-of-
scattered light from the Earth adds ≈ 0.4% of the direct
life strategy for GSO objects, with ability to move out of
solar flux to the GeoSphere at quadrature. By measuring
the GSO region a requirement for new satellites. The sci-
GeoSphere’sdifferentialbrightnessasitcrossesthesky,with
ence goals of GeoSphere are to remain in orbit for perpe-
statistical averaging, the goal of of 0.01% precision might
tuity,withnopre-plannedend-of-lifeanticipated.The“sta-
be achieved. Long-term relative changes in Earth’s albedo
bleplane”solutionsfoundbyFriesen et al.(1992)minimize
greater than 2.5% should be measurable by GeoSphere.
relative speeds between objects in these orbits, and reduce
space debris by reducing both impact rate and debris scat-
ter. If these orbits are adopted as “graveyard orbits”, there
5 TECHNICAL CHALLENGES will beno ITU problem.
5.1 Orbital stability
5.3 Secular changes in scattering properties
TheorbitsofGSOsatellites areperturbedbynon-spherical
componentsoftheEarth’sgravitationalfield,bylunarinflu- The GSO space environment is not “clean”. Surfaces ex-
encesandbymomentumtransferfromsolarradiation.Even posed to propellant, silicone, and/or exposed to the solar
so,certainorbitsarestableenoughoverdecades,forthepur- UVfluxandionizingradiation,changetheirreflectiveprop-
poses discussed here. Orbital drift through the Poynting- erties(Deveret al.2012).Oxidationisaseriousissueinlow
Robertson effect is unimportant for conceivable area-to- earthorbit(LEO)whereoxygendensitiesare105−6 cm−3in
mass ratios for a sphere. Quoting from the conclusions of typicalmodels,butoxygenconcentrationsinGSOaresome
Friesen et al. (1992): 105 times smaller. Instead, in GSO, high energy particles
and photons are the larger concern. For example, the ab-
“Orbitsoflargesatellitesareradiallystablethroughout there-
sorptance (1 minus albedo) of white paints commonly used
gionwithin2000kmaboveandbelowthegeosynchronousradius.
Satellites placed in such orbits can be expected to go no more on spacecraft increases by factors of 1.3 to 2.8 after ≈ 100
than 50 km above their original apogees or more than 50 km days exposure to solar-like UV and energetic electrons in
below their perigees for at least several centuries, barring colli- LEO(Deveret al.2012,Table4).Toachieveanalbedosta-
sions.... ‘A stable plane’ exists at the GSO distance.. for which bility over a century, GeoSphere’s surface should be a sim-
orbitplanemotionisquitelimited...iftheinitialangularmomen- ple metal, alloy, or crystalline material not susceptible to
tum vector of a circular GSO is aligned with the 7.3◦ displaced suchchanges,liketelescopeopticsinspace.Suchsubstances
axis about which precession takes place for the initially equato-
would need testing before launch, and perhaps “pre-aged”
rialcase, orbitplanemotionwillbelimitedto 1.2◦ of theinitial
bydeep exposureto energetic ions, electrons and photons.
plane.”
All objects in GSO develop craters, punctures and
A50kmchangeinorbitalradiusgivesa1mmagchange chemicalcontaminationfrommicrometeoroid(MM)impact.
inbrightness.Thesetheoreticalconsiderationsareborneout Man-madeorbitaldebrisislessimportantinGSOorbitsand
in part by measurements of the orbits of abandoned satel- isneglectedhere(Kessler et al.2011).Weconsiderparticles
lites.INTELSAT1,abandonedonDecember21969,hasre- mostlyinexcessof1micronsize, thosethataresmaller be-
mained in an orbit with semi-diameter between 42,130 and ingexpectedtoexhibitunboundorbitsbecauseofthestrong
42,200 km with eccentricity between 0 and 1.6×10−3 (e.g. solar radiation pressure.
Ulivieri et al. 2013) for over 41 years. There are two lon- As damage accumulates the phase function of Geo-
gitudes of orbital stability arising from higher order terms Sphere will evolve from, for example, Lambertian to
in the dynamic equations (Friesen et al. 1992), 105W and cratered, or lunar-like. Diverse datasets collected from ex-
75E, runningthrough western North Americaand themid- tended space missions indicate the effects of MM impacts
dle of Asia respectively. These would be the desired orbits on surfaces. The large solar cells on space station MIR in-
for GeoSphere. dicated an accumulated surface coverage of MM damage
of 0.045% in 10 years of exposure in LEO (Smirnov et al.
2000). Measurements in GSO are rarer. But the gravita-
5.2 Collision hazard tional focusing for typical MMs is modest (v ∼20 km s−1)
Friesen et al. (1992) compute the “collision hazard” for or- compared with Earth escape speed (vesc = 11−4 km s−1
inLEOandGSOrespectively)andsofluxeswillbesimilar.
bitsofsmallinclination(closingspeedoftwoobjectsinGSO
being vcsini with vc theorbital speed of 3 km s−1): Gereso≈Sp0h.e4r5e%wiplleraccceunmtuurlya,tea MfraMctisounraflacreatdeakma=ge4.t5h×at1c0o−v5-
CH = vcσ s−1, (5) y−1. Like the moon, cratering enhances 180◦ scattering at
2π2R2∆R
the expense of scattering at smaller angles. Changes to the
where σ ≈ π(ds/2)2 is the geometric cross section of the geometric albedo may besmaller, dependingon thesurface
collidingobjects,RistheGSOradiusand∆Rthermsalti- material used and the surface optical contamination. Spill-
tuderangeoftheobject,∼50km.Perimpactingobjectthis over of impact debris beyond the craters’ areas should be
becomes 1 impact in 109 years. There are only of order 400 negligible if electrical potentials of attraction (polarization
(cid:13)c 2014RAS,MNRAS000,1–5
4 Philip Judge and Ricky Egeland
ornetcharge)arelessthanthekineticenergyofanycharged tobeimportantatthelevelof0.001%onlyforafewminutes
exploding debris ejected outwards from the sphere. as GeoSphere entersand exits theEarth’s shadow.
Damage of 0.45% in area translates to smaller than GeoSphere will be measured only when out of eclipse
0.45% changes in scattered light. The albedo after time t (α > 10.9◦) not at opposition. A thin earth crescent is al-
in yearsis ways visible. Table 1 shows that when separations β of the
SunandEarthare20◦,theusingLambertianscattering,the
at =(1−kt)a0+(kt)b=a0−kt(a0−b) (6) Earth is 10.8 magnitudes dimmer than the Sun (a flux ra-
where a0 is the initial albedo and b the albedo of damaged tio of 2×104). While below our target precision, this extra
areas.Sinceb>0MM-induceddegradationinalbedooccurs light is something to be considered in analyzing GeoSphere
slowerthan(1−kt)a0.Nevertheless,itshouldbemitigated, data.Most likelyonewillsolvefortheSun’sbrightnessand
modeledand/ormeasured.Onesolutionmightbetoexpose suitableparameterizations ofalbedo andphasefunctionsof
GeoSphere to cosmic-like dust particles to mimic a suffi- GeoSphereand Earth in the analysis.
ciently long exposure (> k−1 y) in geosynchronous orbit, For a GSO, GeoSphere observations are best made
such that the phase function remains constant. A hyperve- within a few hours of midnight, daily. Irradiance variation
locity gun1 might be used. Another might be to calibrate data show significant power (excluding flares which can be
thescatteringpropertiesofGeoSphereusingfutureground- identified and removed) on time scales of hours and days,
based stable laser sources. that is related in both phase and amplitude to the decadal
variations. Using hourly irradiance data from the VIRGO
instrument(Fr¨ohlich et al. 1997),wefindthatsamplingev-
5.4 Comparison Stars ery3 dayssuffices toreducehigh frequencyaliasing to10%
of thetotal variance.
To achieve long term precisions of fractions of milli-
Lastly, care should betaken to determinethepolariza-
magnitudes,aGeoSphereobservingprogram wouldhaveto
tion properties of a GeoSphere which is always irradiated
devote effort to identifying suitably non-varying compari-
anisotropically. This can be determined prior to flight and
son stars. This is not a trivial task (Henry 1999; Hall et al.
usinglaboratorymodels,aswellasmeasureddirectlyduring
2009).Geosynchronous objects circumnavigate thecelestial
from telescopes on theground.
equatoronceperday,therightascensionatoppositiondrift-
ing about 1 degree/day. GeoSphere would therefore require
asignificant numberof cross-calibrated comparison starsin
order to place its differential magnitude on a uniform scale
throughout the year. Typical separations within photomet-
ric standard groups of three stars are near 3◦ and always 6 CONCLUSIONS
less than 13◦ (Hall et al. 2007; Lockwood et al. 2007). Asa
Wehavesuggestedthataninertscatteringspherebeplaced
roughestimate,foramaximumintra-groupseparationof4◦,
inaverystablegeosynchronousorbitinordertomakemea-
wefindthat345highlystablestarsdistributedalongthece-
surements of the solar flux variations, and measurements
lestialequatorwouldneedtobeidentified,withmagnitudes
of the Earth’s changing albedo. There are technical chal-
near that of GeoSphere.
lenges but no fundamental show-stoppers in making these
Henry (1999) found that stars of spectral class F0-F3
measurements.Toachieveaprecisionbetterthan0.1%over
and A8-A9 have rms probabilities of long-term (seasonal)
centuries,micrometeoroid-inducedsurfacedegradationmust
stability better than 0.0005 mag of 63.3% and 87.5% re-
bemitigated,modeledand/ormeasured.Suchprecisionsare
spectively, and that short-term photometric stability tends
ofgreatinteresttobothsolarandterrestrialclimatechange
to correlate with long-term stability. These findings should
physics.
be used in any comparison star search. The observing pro-
There is perhaps a direct conflict with ITU’s require-
gram of the current Kepler K2 Mission schedules two ≈75
ment for exit strategies on GSO spacecraft. But if the
day pointings falling within ±10 degrees of the celestial
community adopts the “stable plane” orbits identified by
equator,and will obtain precise photometriclightcurves for
Friesen et al. (1992) as “graveyard orbits”, the ITU man-
thousands of stars covering about 10% of the region of in-
datewillnotbeapplicablewithaGeoSphereplacedinsuch
terest. The planned Transiting Exoplanet Survey Satellite
an orbit.
(TESS)willobtainprecisephotometrictimeseriesof27-day
Finally,oneyearofubphotometricobservationsofGeo-
duratation for bright FGK-type stars in the entire equato-
Sphere should reveal phase relationships in spectral irradi-
rial region. These surveys will allow refinement of a list of
ancechangesaboveandbelow400nm,resolvingadebateof
candidates for GeoSpherecomparison stars.
importance to climate science (Harder et al. 2009).
5.5 Other Problems
In GSO, thermally-induced geometric changes are domi-
natedbyeclipsesatequinoxes.Wefindsuchorbitalchanges ACKNOWLEDGMENTS
We are grateful for discussions with Giuliana de Toma,
1 For example, The White Sands Test Fa- Roberto Casini, and a conversation with Aaron Rosengren,
cility Remote Hypervelocity Test Laboratory, JamesGarryandDuncanSmithviaResearchGate.Theref-
http://www.nasa.gov/centers/wstf/laboratories/hypervelocity. eree is thankedfor very useful suggestions.
(cid:13)c 2014RAS,MNRAS000,1–5
GeoSphere 5
REFERENCES
Allen C. W., 1973, Astrophysical Quantities, Athlone
Press, Univ.London
Dever J., Banks B., de Groh K., Miller S., 2012, Hand-
book of Environmental Degradation of Materials, Chapt.
29. Degradation of Spacecraft Materials, Elsevier, Ams-
terdam, 2nd edition
Fro¨hlich C., 2013, Space Sci. Rev. 176, 237
FriesenL.J.,Jackson,IVA.A.,ZookH.A.,KesslerD.J.,
1992, J. Geophys.Res. 97, 3845
Fro¨hlich C., Crommelynck D. A., Wehrli C., Anklin M.,
DewitteS.,FichotA.,FinsterleW.,Jim´enezA.,Chevalier
A., Roth H.,1997, 175, 267
Hale G. E., 1908, ApJ 28, 315
Hall J. C., HenryG. W.,Lockwood G. W.,2007, AJ 133,
2206
Hall J. C., Henry G. W., Lockwood G. W., Skiff B. A.,
Saar S.H., 2009, AJ 138, 312
HarderJ.W.,FontenlaJ.M.,Pilewskie P.,RichardE.C.,
Woods T. N., 2009, Geophys.Res. Lett. 36, 7801
Harder J. W., Lawrence G. M., Rottman G. J., Woods
T.N.,2000, inW.L.Barnes(ed.),EarthObservingSys-
temsV,Vol.4135 ofSociety of Photo-Optical Instrumen-
tation Engineers (SPIE) Conference Series, p.204
Henry G. W., 1999, PASP 111, 845
JudgeP.G.,LockwoodG.W.,RadickR.R.,HenryG.W.,
Shapiro A. I., SchmutzW., Lindsey C., 2012, A&A 544,
A88
Kessler D. J. et al., 2011, Limiting Future Collision
Risk to Spacecraft. An assessment of NASA’s meteoroid
and orbital debris programs, Technical report, National
Academy of Sciences
Lockwood G. W., Skiff B. A., Henry G. W., Henry S.,
Radick R. R., Baliunas S. L., Donahue R. A., Soon W.,
2007, ApJS 171, 260
Lockwood G. W., Thompson D. T., Lutz B. L., Howell
E. S., 1991, ApJ 368, 287
Lubin D., Tytler D., Kirkman D., 2012, ApJ 747, L32
Schwabe H., 1844, Astron. Nachr. 21(495), 233
ShapiroA.I.,SchmutzW.,RozanovE.,SchoellM.,Haber-
reiter M., ShapiroA. V., NyekiS., 2011, A&A 529, A67
Smirnov V., Semenov A. S., Sokolov V., Konoshenko V.,
KovalyovI., 2000, Space Debris 2, 1
Ulivieri C., Circi C., Ortore E., Bunkheila F., Todino F.,
2013, Journal of Guidance Control Dynamics 36, 935
White O. R. (ed.), 1977, The Solar Outputand Its Varia-
tions, Colorado Assoc. Univ.Press, Boulder
Willson R. C., 2014, Ap&SS 352, 341
YoungA.T.,GenetR.M.,BoydL.J.,BoruckiW.J.,Lock-
wood G.W.,HenryG.W.,HallD.S.,SmithD.P.,Bali-
umas S.L., DonahueR., Epand D. H., 1991, PASP 103,
221
(cid:13)c 2014RAS,MNRAS000,1–5