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GeoSphereGeosynchronous Spherical Scattering Target for Century-long Monitoring of Solar Irradiance
Judge & Egeland 2015, MNRAS Letters
Ricky Egeland Montana State University / HAO Newkirk Fellow
SORCE 2015 Meeting – Savannah November 13, 2015
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How does the irradiance of the Sun vary on
century-long timescales?
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GeoSphere: The Sun as Star
ro ~ 42,164 km
Torbit ~ 24 h
d ~ 4 m, 20 mas albedo ~ 0.9 mV ~ 10 (example)
orbital inclination ~ 7.3º
Geosynchronous Spherical Scattering Target
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Size Constraints
mV
(↵) ⇡ mV,� � 2.5 log10
✓r2s
(ro
� r�)2a
q�(↵)
◆
�(↵) = [sin↵ + (⇡ � ↵) cos↵)] /⇡
Assuming Strömgren by bands:
(dsD)2 & 36m4
↵
Assuming 0.05% rms photon noise, integration time < 100 s:
(dsD)2 & 5800/��m4
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“What a stupid idea. Anyway, we’re already making these
measurements!”
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(Yeo et al. 2014, Space Sci. Rev.)
0.13 W m-2=0.01%0.26 W m-2=0.02%
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0.057%?
0.031%?
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(Haigh et al. 2010)
TSI
SORCE/SIM Spectral Difference 2004-2007
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“There’s no such thing as a stable orbit.”
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Stable Orbits
• See Freisen et al. 1992
• Two stable longitudes: 105ºW and 75ºE
• “stable plane” exists at 7.3º inclination which has a reduced amplitude of orbital plane excursions
• Proposed as a better alternative for “graveyard orbits” (Rosengren et al. 2013)
e, a
(Freisen et al. 1992)
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Boulder, CO; Apache Point, NM 105ºW Fairborn Obs., AZ; OAGH, Mexico 110ºW Lowell Observatory AZ; Kitt Peak, AZ 112ºW OAN, Mexico 115ºW CTIO, Chile 70ºW
105W 75E
Indian Astronomical Observatory 78ºE Xinjiang Astronomical Observatory, China 87ºE
Yunnan Astronomical Observatory, China 102ºE
Stable Longitude Observatories
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Observing View
Rigel
Orion Nebula2.8º
by Bill Livingston, NOAO. Kitt Peak, AZ, Jan 3, 2001
GeoSphere analemma (night)
7.3º
GeoSphere analemma (day)
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“That kind of precision is impossible from the ground”
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Automated Photometric Telescopes (APTs)
Today
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a
b
c
d: HD 30495Δd-b
Δc-a
Δb-a Δd-cΔd-a Δc-b
APT Group Observations
Observations a, b, c, d, a, skya, b, skyb, c, skyc, d, skyd,
a, b, c, d
20-30 s integrations per (b, y) band ~13 min per group
300 400 500 600 700 800Wavelength nm
0.0
0.5
1.0
1.5
2.0
2.5
Flux
, filt
er p
rofil
eb y
SORCE SIMPlanck function 5770K
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Yes!, e.g. “solar twin” 18 Sco with comparison star scatter ~0.02%
(Hall et al. 2007)
Could the APT program detect solar cycle variation?
~0.12%~0.03%
~0.07% TSI → ~0.0010 mag b, y → ~0.1% b, y (Lockwood 2007)
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Achieving Precisionx = t� c
Single difference:�2x
= �2t
+ �2c
Repeated measurements:Group of N comparisons: hciN =
1
N
NX
i=1
ci �2hciN =
1
N2
NX
i=1
�2i ⇡ 1
N�2c
x
N
= t� hciN
, �
2x
= �
2t
+1
N
�
2c
Group difference:
Repeat M group meas.:hxiNM =
1
M
X
j=1,M
(tM � hci) ,
�2hxiNM
=1
M
✓�2t
+1
N�2c
◆
Example N = 10, M = 5; 100 s integrations → 1.4 h
Every night:
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Achieving PrecisionWith one good group and n good nights in a year:
with: N ~ 10 (atmosphere, slew time)
M ~ 5 (integration time) n ~ 50 (yearly revolution, weather)
σc ~ 0.001 mag (comparison variability)
�hciNMn⇡
r1
nMN�c
� ⇡ 2⇥ 10�5 mag ⇡ 0.002%
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“GeoSphere will reflect light from the Earth and Moon, too.”
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FG
= F�G
(roG
, r�G
,↵,F�, aG)
+F�,refl(roG, r�G
,↵, a�,F�, aG)
+F�,refr(roG, r�G
,↵, T�,F�, aG)
F�,90�/F� ⇡ 4⇥ 10�3
F�,20�/F� ⇡ 5⇥ 10�5
FMoon
/F� ⇡ 3⇥ 10�6
GeoSphere Flux Ratios
{FG
, roG
, r�G
,↵, aG
} ! {F�, a�, T�}
Forward Model
Inverse Problem
↵
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“GeoSphere would move with respect to the background sky
throughout the year… comparison stars won’t stay
close by.”
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GeoSphere Group Observations
1h 2h 3h 4h 5h 6h
90ºmidnight midnight
15 days later15º
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“If your basis of comparison is always changing, observational
errors will constantly add”
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Achieving PrecisionContinuous Measurement Throughout Year
d4 = (z }| {c4 � c3 +
z }| {c3 � c2 +
z }| {c2 � c1), �2
d4 = (�24 + 2�2
3 + 2�22 + �2
1)
dj = (cj � . . .� c1), �2dj = (�2
j + ⌃+ �21)
�2dj = 2(j � 1)�2
c
For L longitude bands of N stars over n nights:
e.g.
Average over many years for a 1/√Y reduction
hdiL =1
L
LX
j=1
dj, �2(hdiL) =1
L
LX
j=1
�2dj = (L� 2)�2
c ! (L� 2)
nN�2c
L = 25, N = 10, n = 50, �2(hdiL) ⇡ 0.046�2c .
�c ⇡ 0.001 ! � ⇡ 2⇥ 10�4 mag ⇡ 0.02%
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“Space isn’t empty – the GeoSphere will degrade”
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GeoSphere Albedo Stability• Oxidation: Negligible ~1-10 O/cm3 at 42,000 km
• Micrometeorite cratering: Extrapolating from LEO measurements, ~0.45% area/century
•
• Pre-crater before launch? (b → a0)
• Photochemical changes?
• Use simple material: metal, alloy, or crystalline material?
• Characterize/pre-burn before launch?
• In-situ monitoring via ground-based lasers during eclipses?
a(t) = a0 � kt(a0 � b)
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“It is just too expensive to launch something that big into
such a high orbit.”
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Engineering Considerations• Materials?
• How to launch a d-meter inert object into a specific orbit?
• Expandable?
• Inflatable?
• Hokkaidō Hoberman Sphere, 1.4→5.9 m
• NRL PERCS design 1→10 m
• Piggyback mission as a 2nd faring?
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“It’s still too expensive. You will never get funding for a century-
long program.”
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Conclusions• The GeoSphere program could provide a
measurement of spectral irradiance variations in visible wavelengths with sufficient precision to monitor secular variations above ~0.002% (sparse series) or ~0.02% (continuous series)
• Stable orbit allows ground-based observation indefinitely.
• Needs work investigating suitable materials, degradation, and deployment strategy.
see Judge & Egeland 2015, MNRAS Letters
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“There aren’t enough stable comparison stars in the sky”
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Stable Comparison Abundance
(Henry 1999)
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“GeoSphere would move with respect to the stars! – your data
would be polluted by background stars”
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Stellar Noise• Background stars pass behind GeoSphere moving at 15ʺ ·
cosδ · t, creating photometric noise for observations
• e.g. 5ʺ aperture, mag 10 GeoSphere, 100 s integrations: 1 in 100 integrations contain object of comparable magnitude
• Therefore, one needs to measure flux of these passing stars to subtract from the signal
Focal Plane
GeoSphere photometer
Background Pre
Background Post
Sky motion
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(Kopp & Lean 2011) (Lean et al. 2005)
GeoSphere (yearly 1σ)
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Other Applications• Earth albedo variations
• Measure uy variations to check spectral cycle phase relationships
• Radar/Laser calibration sphere (c.f. PERCS, Bernhardt et al. 2008)
• (B-V)Sun ; Sun as a calibration “standard star”
• Large catalog of flat-activity stars
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Observation Program• In a 6h night, GeoSphere moves 6h in RA across the
celestial sphere
• Its position at local midnight moves ~1 deg/day, or ~1/15 h RA/day
• Therefore, GeoSphere can be observed in conjunction with an object for about 6·15=90 days
• APT stars have one group of comparison stars; GeoSphere must have many groups; a large ensemble
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(Fig. SPM.5, IPC
C 5th Assessm
ent Report, 2013)
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(Shapiro et al. 2011)
0.9%?
0.4%?
“… the observational data do not allow to select and favor one of the proposed reconstructions. Therefore, until new evidence becomes available, we are in a situation where different approaches and hypothesis yield different solar forcing values.”
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“Directly detecting [Maunder Minima-like] changes requires 1) instrument stabilities <0.001%/year and measurement continuity, and/or 2) measurements having absolute accuracy uncertainties <0.01%, as intended for the Glory/TIM and TSIS/ TIM instruments, so that measurements separated by several decades could detect secular changes.”
(Kopp & Lean 2011)
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0.001 mag change ≈ 0.1%
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HD 30495 variabilitytarget amplitude ~ 0.02 mag ~ 1.8% target uncertainty ~ 0.0006 mag ~ 0.059%
target amplitude ~ 0.003 mag ~ 0.28% target uncertainty ~ 0.0003 mag ~ 0.027%
comp. yr-yr scatter ~ 0.0008 mag ~ 0.073% comp. uncertainty ~ 0.0002 mag ~ 0.018%
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Stable Orbits
• Freisen et al. 1992 numerically simulated unpowered geosynchronous orbits on century time scales
• “worst case” radii excursions of up to 50 km for all near-geosynchronous orbits
• ~1 mmag variation ⇒ in situ tracking needed
• Observations: INTELSAT, abandoned 1969
• “Stable longitudes” exist at 75E and 105W about which orbits oscillate
e, a
(Freisen et al. 1992)