for
System
An0rbitallmaging
Moonsat:
Mapping
the Moon
Donald L. tlght
Abstract
On 20 luly 1989, two decades afier the first Apollo landing
on the Moon, President GeorgeBush proposed a long-range,
continuing commitment that called for rcvisiting the Moon to
establish way-points for the long-range plan to land on Mars.
Accepting this challenge, NAs/ then established the Space
Exploration Initiative which plans to include a polar orbiting
lunar imager to map the Moon. Moonsat is proposed as such
a lunar imaging system. Spatial and spectral resolution requirements as proposed enable Moonsat to support mapping
of the lunar topography and to determine the composition of
soi]s and rocksfor mineraloglt and natural resource ossessment. Moonsat's design calls for sensinghigh resolution pixels in the panchrcmatic band from in-orbit stereo. The
position and uttitude of Moonsat will be taken from Earthbased tracking and, if feasible, the Global Positioning System
when Moonsat is on the visible side, and attitude wiII be
taken from star sensorstime-synchronized with the groundIooking linear array sensors.Moonsat's orbital altitude (too
km), period (118 min), spatial rcsolution (4 m), and swath
width (ss km) will provide full contiguous coveruge of the
Moon's surface. These data can be used for a variety of applications to support the Nation's Space Explorution Initiative.
lntroduction
The lunar exploration satellites Ranger, Surveyor, and Lunar
Orbiter all paved the way for Apollo's mission to the Moon
(Light, 1970).But, it was the highly successfulApollo Program that captured the eyes and ears of the world on 20 fuly
1969, when Apollo 11 Astronaut Neil Armstrong made his
"giant step" for mankind onto the surfaceof the Moon. Soon
'1,2,'1,3,
and 14 for
to follow were the remaining Apollo's
continued exploration, although Apollo rs had to turn back
before completing its mission. Then the final three Apollo's
15, 16, and't7 orbited a mapping system designedfor mapping the Moon. This system contained a frame camera(3inch focal length) integrated with a sta-rcamera for attitude
sensing,and a panoramic camera(24-inch focal length) for
high resolution photography of the landing sites (Light, 1972;
Light, 1gso; Doyle, 7970).
Thesetwo Apollo camerascollected miles of valuable
film from the Lunar landscape, but unfortunately the Apollo
missions were in near-equatorial orbits designed to land man
at the chosenlanding sites (NASA, 1973).The six landing
sites are between 10" south latitude to 27onorth latitude.
But, the 12 men who trod the lunar surfacein the course of
six Apollo missions could not venture more than five miles
U.S. Geological Survey, 511 National Center, Reston, VA
22092.
from their landed spacecraft. As a result of the restri-ctedgeographic scope of these missions, the astronautscould do litile more than scratch the surface in exploring the Moon' So,
the total surface of the Moon outside the Apollo sites has not
yet been sufficiently photographed.
Exploration
Goals
NewSpace
It has been 20 years since Apollo 17 (11 Decembet1'972)
landed on the Moon, and soon thereafteractive lunar exploration came to a close. After years without exploration activity, the Report of The National Commission on Space (Ncos)'
Ploneeringthe SpaceFrontier (Paine,1986),formulated an
aggressivecivilian space agenda to carry America into the
ziit Century. NCos iecommended that the first lunar outpost
be establishedwithin the next 20 years,and permanently occupied lunar bases,within the following decade.The report
noted that, as revisits to the Moon become more frequent,
the need will grow for larger base camps to serve as sgPply
centers,outpoits, etc. In July 1989 PresidentBush challenged
America: "... back to the Moon, back to the future. And this
time, back to stay. And ... a journey into tomorrow ... a
manned mission to Mars" (stafford, 199t; Asker, 1992).The
Iong-range goal is to land asbonauts on the planet Mars by
using the Moon as a way-point or outpost to support the development of the spacefrontier. Outpostswill permit the extension of lunar exploration for the purpose of both scientific
and resourcedevelopment.NAsA'sSpaceExploration Initiative should concentrate on a step-by-step program for establishing a lunar outpost. Adequate maps shorlld be made
before establishing such an outpost. To handle the program,
NAsA'sSpaceExploration OfEce is developing a 1O-yearplan
for planeiary cartography that addressesthe total program.
Although the plan is not yet final, it is known to support Lunar Scout Missions that would be polar orbiting resource
mappers collecting image data to support lunar exploration.
Plans may call fora scout launch in 1996, and a second
launch in 1998. A leading sensorcandidate is the High Resolution Stereo Camera being built for the Mars 94 mission under the auspicesof the FederalRepublic of Germany'sDLR
(Neukum, t-990;Neukum, 1992).To date, Congresshas not
funded the program, so plans are not specific at this time. In
any case, a near-polar orbiting satellite to photograph the
way for future explorations should be part of the plan. In
recognition of the need for a polar orbiting imager, the remainder of this paper developsthe concept called "Moonsat:
An Orbital Imaging System for Mapping The Moon." The
Photogrammetric Engineering & Remote Sensing,
Vol. 60, No. 12, December1s94, pp. 7427-742s.
00/0
0099-1l.12/94 | 6072-1427$3.
@ 1994 American Society for Photogrammetry
and Remote Sensing
Tlele 1.
Map Scale
1:5,000,000
1: 250,000
(Rc)
Recor,rueruoeo
Mnp Sclle nto Gnouto REsoLUTtoN
Rg m/pixel
1,000
50
4-10
7
Use
GIobal
Regional
Science
Landing sites
Earth sensing systems previously proposed by Colvocoresses
(1e82)and Light (1ee0).
ScaleandResolution:
Spatial
andSpectral
In a recent book about geographic information systems, Star
and Estes(19s0), emphasizedthe four Ms, (measure,map,
monitor, and model) as essentials for improving our understanding of the world around us. The folowing Moonsat
concept is designed to permit the four Ms. Even though all
Moonsat Concept is suggestedas a candidate for NASA's
data are not scale related, most are, and therefore it is useful
SpaceExploration Initiative this decade.
to establish a scale relationship among the data. Establishing
a product scale, even for lunar maps, sets up a basis for
Requirements
quantifying the accuracy requirements for sensor measurefurMoonsat
During the pre-Apollo years, NASAconvened two conferences ments that would be taken by Moonsat. Becausethe image
for lunar scientists interested in lunar exploration. The first
map, contours, and digital elevation model (onu) comprise a
was convenedin Falmouth, Massachusetts,19-31 fuly 1965.
complete description of the Moon's surface, specificatibns for
The second such conference was convened at Santa Cruz.
image maps, contour intervals, and DEMscan be used to esCalifornia, 31 |uly to 13 August 1967, to update, as necestablish Moonsat'ssystem design characteristics.
sary, the findings of the Falmouth conference. Both conferTo support scientific study, the Planetary Cartography
ences contained Geodesyand Cartography Working Groups
Working Group suggested1:s0,000-scaletopographic prodwhose reports document a set of scientific obiectivesin this
ucts. Smaller scale products can be made from the 1:50,000area.
scqle imagesacquired by Moonsat. The 1:5,000-scaleproduct
At these conferencesthe Geology and Geophysics Workfalls outside of Moonsat's design characteristics. Be if
ing Groups proposed requirements for cartographic support
graphic or on digital media, the topographic product carrbe
of their own programs.Generally,this cartographicsupport
thought of as providing three basic kindi of information: (1)
was implied rather than stated explicitly, but the essential
content, (2) location, and (3) elevation. Then the U.S. Nasteps in the developmentof geodetic/cartographicknowledge tional Map Accuracy Standards (nN4As)can serve as a basis
of the Moon were developed.
for sensor system requirements for content (ground spatial
resolution), location (spatial position), and elevation (stereo
o Establisha selenodeticcoordinatesystemrelatedunambigumeasurement for elevations, contours, or digital elevation
ously to the right ascension-declinaiion system.
model data).Basedon the NMaS,the standard error of locao Describe, in sufEcient detail, the gravitational field of the
tion coordinatesmay not exceed
Moon.
a Derive a reference figure with respect to a point which is representative of the Moon's center of mass.
a Establish a three-dirrensional geodetic control network over
the lunar surface in terms of latitude, longitude, and height
above the chosen reference figure,
The GeologyWorking Groups at both conferencesagreed
upon the need for maps at scalesas small as 1:5,000,000for
covering the whole Moon and large-scalemaps at 1:
1,000,000,1:250,000,1:50,000,and as largeas 1:5,000for
specific sites. NASA'scurrent Planetary Cartography Working
Group (Doyle, 7992)has suggestedonly four map scales,as
shown in Table 1. The typical ground resolution (Rg)per
pixel that is sufficient for each scale is also given. The manager of the Lunar Scout Program at NASA's|ohnson Space
Center has suggesteda 4-metre pixel size (M.G. Conley, personal communication, 1992).
Given these geodeticand cartographicobjectives,it is essential that a Lunar orbital imaging system be designed to
produce a remote sensingdatabasethat meets the essential
needs of the SpaceExploration Initiative (M.D. Griffin, personal communication, 1991).The majority of these needs can
be satisfiedwith a system such as Moonsat that can collect
data to produce the following products:
o High-spatial-resolution
panchromaticimageryin stereofor
compiling
-image maps,
-digital elevationmodels(onus),
-topographic maps,and
----controlpoint network:
o Multispeciralimageryfor
-mineralogy, soil composition, and rock types; and
-searching
for traces of water ice near the poles.
Moonsat'sdesign characteristicsare somewhatsimilar to the
L422
o, (m) : 0.3 X 10-3 X (map scale number),
(1)
and the standard error of elevations should not exceed
or (m) : 0.3 X (contour interval)
(Z)
Table 2 shows the NMASand typical contour intervals for
four map scales.
Table 2 establishesthe 1:50,00o-scaleaccuracycriteria
for location and elevations.Becausespatial resolution requirements for ground pixel size can be related to elevation accuracy and contour intervals, the pixel size is set by the
required contour interval. Using this technique, the required
contour interval of the final product can be used to establish
the geometric characteristics of the Moonsat mission.
Detemlnlng
PlxelShetu SpatlalResolutlon
Two different methods, one using a printing criterion and
one using a photogrammetric criterion, have been developed
(Light, 1990) to determine the appropriate pixel size of the
sensor footprint on the ground. The printing criterion asTreLe2. NMASRrournerra.rililT:"*toN AND
TyprcAL
Coxroun
Map Scale
250,000
100,000
50,000
25,OOO
Contour Interval (CI) : 3.3 dA
Typical contour interval (m)
10
20
30 40
50
100
Location
o, (m)
IJ
30
IJ
/.J
J
*1:50,000 scale requires oh :
10
10
10
10
20
20
20
20
40
100
50
40
+3 m for the smallest CI of 10 m.
MooruslrSerusoR
Specrnrl CxlRlctentsttcswrrx AppucrloNsAND ucts, including DEMsand image maps for a wide variety of
Trale 3.
lunar GISapplications.
SPATTALRESoLUTToN
Spectral region
Bandwidth
0rm)
Application
or centets
1. Panchromatic
0.40-{.80
2. Blue
0.40
3. Green
0.56
4. Red
5. Near infrared
o.70
0.95
6. Near infrared
7.20
Spatial
resolution (m)
Crater density, morphoIogy, topo mapping,
and PEtvts
Ti and Fe content, soil
maturity
Distinguish highland
rocks versus basalts
Ferric iron detection
Ferrous iron absorption in olivine and
pyroxene
Ferrous iron absorption shoulder
10
10
10
10
sumes that the typical l5O-line/inch lithographic printing
screen (actually 300 lines/inch) can transfer all the information that can be used at normal viewing distance by the human eye when observing quality image printing. The
relationship between ground pixel size (m/pixel) and image
scale (Is) is given by the following:
--J-E
x Js
Pixel size Prl : Il9h3oo lines " 39.37inE
P s = 8 . 4 7 x 1 0 _ sx I s
(3)
Example: for Is : 50,000,
Ps : 4.2mlpixel.
The secondmethod (Light, 1990) uses the well-known paralIax equation from photogrammetry as the criterion to
determine the pixel size needed (seeTable 2) to compute elevationsaccurateto meet cn : 3 m, which supports a 10-m
contour interval (cr).
The equation using the photogrammetric criterion is
SpectnlSenslng
andResolutlon
Several insightful articles published by lunar scientists (Nash
and Conel,1974;Charetleet aL,1974; Soderblomand Boyce,
1976; Head et al., 7g7B)generally concernedthemselveswith
characterization of lunar surface units using remote observa'
tions from different wavelengths. These articles form the basis for the multispectral wavelengths suggestedfor Moonsat.
Electromagnetic and particle radiation are the only
sources of information available to the remote observer of the
lunar surface. Sunlight is either passively reflected or absorbed by the lunar surface. Absorbed radiation is converted
to heat and re-emitted as thermal radiation. Solar radiation
in the spectral region of 0.3 to 2.5 y'm reflected from rocks
and soils has two major components:(1) specular (first-surface) reflectance, and (2) diffuse scattering. Only a few portions of this part of the electromagnetic spectrum have been
measured and shown to be useful and/or practical for remote
observations of planetary surfaces.Becauseof this, the spectral bands suggestedfor Moonsat are selected within the 0.3to 2.5-pm region. Basically, multispectral sensingon the
Moon is to support mapping the topography (0.40 to 0'80
p,m) and scienlific investigations of the properties of surface
materials.As shown in Table 3, conclusionscan be drawn as
to the composition of the surface materials of the Moon, specifically, iron (Fe) and titanium (Ti) content'
Overall, the multispectral capability suggestedfor Moonsat should permit
o investigationof surfacefeaturesand determinationof their
morphologyand structuraland/ormagmaticcauses;
. determinationof the chemicaland mineralogicalcomposition
and physicalstateof solid surfaces;and
o geoscientific
interpretation
and thematic mapping.
Table 3 lists the suggestedspectralbands for Moonsat.
TheMoon's
06italGharacteristics
The Moon's period of revolution around the Earth is exactly
equal to its period of rotation on its axis, so it always keeps
the same face turned toward Earth. The Moon requires 27.32
_18
( 4 ) days (siderealmonth) to make a complete 360" rotation of
Ot="x;xor
the Earth and return to the same place relative to the stars.
During that time, the Earth is revolving around the sun at
where
about 1o per day (360'/365.25days).With referenceto the
sun, the Moon takes 29.53 days (synodic month) to go from
K is a nondimensional number expressing the degree to
which correlation can be achievedwith a stereoimage full Moon to full Moon or to complete one full lunar cycle.
The synodic month is the time basis for Moonsat's orbits'
(for example,K : 0.50 means a correlation error of
The Moon rotates very slowly compared to the Earth's rotaabout one-half pixel);
tion. The rate ofrotation is 0.549'/hour or 13.176oldayor
B is the basedistancebetween sensorpositions when
one complete rotation in inertial spaceevery 27.32 days. The
(0.6
pixels
0.9
is
are
detected
<
BIH
<
typithe stereo
rotation iate is one twenty-seventh that of the Earth's, and
cal for spacesystems);
the Moon's orbital plane is inclined about 5" I'with respe-ct
H is the orbital height of the sensor above the mean
to the ecliptic (plane of Earth's orbit). These parameters afradius of the Moon:
fect the sbategy for obtaining full global imagery coverage'
or, :0.3 x CI as stated in the NtvtRs;
The approach in this conceptual design is to image the Moon
(Example:assumeBlH :0.7 and CI : 10 m as given
as it rotates every 29.53 days underneath the orbiting sensor,
in Table 2);
'1.
which is essentiallyfixed in inertial space(Krueger,1965;
X 0.7x 0.3X 10m;and
tr :
personal communication, 1988; Batson,
A.P. Colvocoresses,
O1990).
and
Batson,
1987;
Greely
Ps = 4.2m.
Recognizingthat both methods yield the same 4.2-m
pixel size, it can be concluded that imagery with a 4-m spatial resolution will provide 1:50,000-scale
topographic prodPE&RS
Satellites
furLunar
06italChancteristics
For satellite lunar mapping and reconnaissancemissions,
near-polar, near-circular orbits are desired because of the
L423
I'olar orbit plane
l-ine of nodes
for Nloonsat's
orbit plane aa
end oI mission
(14.765days after
best geome(ry.,
orbit plane
Litre of nodes
for N,loonsat's
orbit plane at
(14.765 days before
Dest geometw)
therefore, provide sun-synchronous orbits attractive for many
Earth-sensingmissions.
For example, to obtain a4 exact sun-synchronous
-'
orbit
for 100 km abbve the Moon, O"ro"l*U"
o: (#H
3Go:26.e26.
[#.""tt-*]
and, for o : 1862.63km and e: 0, Equation6 givesi:
1,43.745".This is not an acceptable o.bit"l inclin"ation
for -lu_
Sidereal: :7.J? drts
nar mapping, becausethe orbit does not pass sufEcieniiy
near the poles.
d =26.e273degrees
i:";::::::tX
4t=ldegrees
ro.229'qegrees
, The geometry shown in Figure 1 is a view from above
F=
me ecliptic plane. The sketch is useful for orbit design
be_
Figure1. Lunargeometry-Onelunar day.
cause it shows the line of nodes of Moonsat's orbit. ihe or_
bital plane can be allowed to precess due to lunar oblateness
tqgugh a sidereal angle of z{ while the moon moves in its
orbit one sidereal lunir day (e : za.sza6;i. This allows
use
need for global coverage,yet the orbits must have sufficient
of the p-erturbation to as^suiesunlight conditioor,
d
sceneillumination from the sun. Sceneillumination must re_ is less than the i{eal,
"ftfr""gh
0/2 : 13.46{g..For example,
if 6': ["
constant as possible throughout the imaging cycle.
is selected,then,fl: 26 : B" per lunar day, and substitutine
Tui" :r
the precessionof Moonsat'sorbitil plane is
jll"_Iqyation 6 gives the resulting n;;-pol;;;;il;;'tt,,?
_unlortunately,
thir
y_"1{,rlotvas compared to the Moon's rotational .atie.Impor_
i : 103.862'.SelectingQ : 4" leads tJ an inilination j l
rng the sun-synchronouscondition for lunar orbits, as can
104', which leans the_brbitalplane toward the sun, but is
be
oone tor.Earth orbits, is
feasible for producing near_polar,
near enough polar to be considereda near_polarmission.
'
^not
't
sun-.synchronousorbits for the
he above is basedupon the mission lasting one sidereal
-Moon. It is suggest"edthai an
inclination of 104'is a reasonabl,e
compromii-: it i" nealrpo_
o!"21.!?.d"ys. In order to create theipportunity to
lar and accommodatesthe need for solir iliumination.
Tllrll alt ot the Moon
map
with consideration for *riri tigt ti.rg, it is
necessarythat the mapping mission last at least oile syiodic
--Precesslon
of l,ineof Nodes
pi 2s l.? days.-rhtJnecessitates
starting
inJ
The pr-ecession
of a satellitesline of nodes due to oblateness l1ll1, late with
respect to the geometry of Fig-ure
"*lyf . fhe
:1d,"9,
of the body is given by Battin (rgez): i.e.,
properry
moditied mission duration is 2.27 days longer, be']".*ty'l
glllilg 1.10bdays
aad ending 1.105days ,,i"t",;
wrth.respect
to
the
sidereal
day. If tht1O4" orbiial inclina_
o: - t" (i)"
=
i, p a(t-e,),
(5) tion is retained and, t_herefore,
;
"cos
the corresponding t"toonJ
":S
rgtg gf B' per lunar month, then it is "apparentthat
q.::Tlo"
@oI Frgure1 is increasedby (29.53+ 22.32)(4.06i= 4.g2g6"
where
at the beginning and ending oi thi, lo.rge.-1Zs.seauys)
mir_/, = coefficient pertaining to oblatenessof the Moon
sion. In Figure t, B :
Using the synodic values in
(0.000207108),
:- {.
=
:
Figure
the
lunar.gravifational
7,
7O.2292o.
(4gOZ.7BO
&
Therefore,1.O.2292o
mass
B
km"/secz),
will be the lare_
'
.r = mean radius of the lunar sphere (I7J2.63 km),
_estangular displacementof the sun above o. l"fo- tfr"-*'
M.oonsatorbit plane. This results in the Sun alwavs beine
H = orbital height above the mean radius of the Moon
(100 km for Moonsat),
wrthrn 1,0.2292"of the sun_synchronouscase.The orbital"
analysis was done by f. Junkins (personal communication,
a = radius of the orbit above the Moon's center of mass
=(r+Fl,
1ee2).
e = eccentricity o^ftheorbit (zero for circular orbits), and
11 summa-ry,the computations for a compromise awav
"
i = inclination of the orbital plane to the equator.
sun-synchronous orbit and toward tire near polai
IT q9
lnclrnarlon
[rJ yields i - 104". If the imaging missionis to be
substituting
one syaodic lunar month"to Zcquire global
and
o
into
Equation
]2,
\
lL,
b,
it
can
.
_No*,
:Tl:d_gr.1for
be shown that
coverage,
the sun will lie. in the orbital plane is.ZOd days af_
-the.mission. Aligning_Moorrr"t,, orbital pl;;;j:L:tgj"g
wltn Ure sun ttre mirllroint of the mission is open
o: -40.61s(j)'",r-",,-, cosi
to ques_
(6) tion. Optimal atilluminatibn
is clearly terrain_d"p6.rdent.it
[r""", *-4*u=]
bu that selecting i : 90owould be adequate,and it cer_
3g{
The Moon's oblatenessis much less than the Earth,s.The
optimum geometric coverage.More analysis
rather extreme oblatenessof the Earth arises due to the fact
I:t_Lll
-llqy\des
Is wa-rranted
on the O"999L, of selectinginclination. Regard_
that the Earth rotates at the high angular velocity of eOO.l
ing sun angle, Kruger (1965) showed tha"t
eood sun lishtlns
d.aV,in contrastto the Moon, ;hicfrotates at tlie ."t,oti""ty
occurs at sun altitudes of 15oto 4so.It mai be best to"run "
slow angular_rateof J6O"/(27.s2.days).
As
Moonsat over several cycles and take advJnta!" of Uurililfrt_
oi
this and the fact that the Moon has no o""".rr,
" "orrr"qrr".r""
ing as it occurs in each cycle.
the lr4oon has
a much more spherical shape.Therefore,the oblateness_in_
3yced.orbltal precessionis much Iess.This perturbation has
Moonsgt's
06ltal Tracepattem
hrstorically been dependedupon for Earth_c-entered
orbits to
Perhapsthe most important factor in sizing Moonsat,s
orbit
causenear-polarorbits to preiess about a degree/dayand,
rs the spacecraft'ssubsatellitetrace on theiurface of
the roSypodic: f9.53 days
L424
PE&RS
tating Moon. The criterion is that illumination changes as little as possible between adjacent swaths and the height must
be appropriateto the requirements:i.e.,
s :360'/Q
where
T :2'U57'392
7 "..
362-1,
: 7O67.2o96sec/orbit
777.78683min/orbit
v)
S : trace shift-distance(longitudinal) between
two successiveequatorial crossings
repetition parameters,I K and N trace
Q:
Orbits/lunar day
Given the period (7J and assuming circular orbits, an
equation to solve for the orbital height (.FI)above the mean
radius (r) of the Moon is
In this case,S : 360' + 361 orbits : 0.997"per orbit.
In generalQ can have the form Q = I - KIN
a--r+"--1.(E)']*
(8)
where 1 : integer number of orbits in a lunar day and l sets
the height H, and KIN -- a rational fraction reduced to lowest terms.
If Q is an integer with no K/N fraction, Q results in a
trace pattern which repeatsitself every lunar day. Otherwise,
the denominator of the fraction, N, definesthe number of lunar days it takes the ground trace to repeai itself. This is
called the repeat cycle. The numerator K is related to the
number P, where P is the number of integral segmentsbetween traceslaid down on successivelunar days. Each trace
shift (S) is divided into fi integral segments;where fl : (M
- K (Gerdingand fenkin, 1971; Light, 1990).
I-f- {N -<21 . t h e n P : K b u t ,
..K. 1
tf t t,then P: N - K.
i
06it PedodandHelghttur Moonsat
A cartographer's preference is an orbit that provides global
coveragein a sequentialmanner; that is, a swath is collected
on orbit 1 and then orbit 2 collects the next adjacentswath,
thus providing contiguousswathing coveragearound the lunar globe. A lunar orbit of 100 km is high enough to be
above the mountains and low enough to permit high spatial
resolution with reasonablysized optics. With an orbital
height of 100 km, the satellite will cover the Moon in aPproximately 361 orbits, and the lunar rotation per orbital peiiod is on the order of 30 km, which leads to a reasonable
swath width.
If orbits in the neighborhoodof 100 km altitude (54 nautical miles) are selected,the orbit period (7) must satisfy the
relation
(10)
(11)
Therefore, from Equation 11,
r + H:1837.3541 km
H: 7837.35km - 1737.63km
: 99.72 km : 100 km
Also, from Equation B, the number of orbits (fl) in the repeat
cycle (Q) to cover the Moon in one lunar synodic day (29.53
days) is
n:1(N) - K.
For Moonsat,
R:362(1)-1
: 361 orbits to cover the Moon in one lunar synodic
d"y.
Sensor
SwathWidth
Considering the Moon as a sphere, the circumference (C) of
the Moon at the equator is
C : 2n (1737.63km)
: 10,917.851km
Then, due to the Moon's rotation per each Moonsat orbit, the
width (114of each orbital pass is
w:
2o"i!,i
km/orbit
361 orbits
_ 10,917.851km (sin 103.862degrees)
361 orbits
: 29.363km/orbit at the equator
(72)
The actual sensor swath width (sw) must be some comfortable amount larger than W to provide image sidelap and allow
some variation in the orbit due to various perturbations. Expanding the 29.363km to 35 km yields a sensorswath width
that is small compared to Earth satellites,but the 3s-km
swath width will allow a reasonable data rate for transmitting data back to Earth.
2,557,392sec/lunar synodic daY
Florensky et aL (1.97'1.)
defined appropriate scalesand
/^\
t:T
L Y r map sheet sizesfor mapping the Moon. Table 4 presents
their recommendations.In Table 4, the dimensions for a 1:
50,000-scalemap of a lunar area is 0"40' by 1'00', which is
where
20.5 km latitude by 30.5 km longitude. Therefore,a scene
2,55'1,392: number of secondsin one lunar synodic day
size of 25 km along track and 35 km wide is more than ade(29.53Earth days/lunar day x 86,400 sec/
quate to cover one map sheet at 1:50,000scale and allow for
Earth day),
: number of lunar synodic days in the repeat
some orbital perturbation.Also, Inge and Batson (1992) proN
vide an excellent documentation of indexes for the Moon
cvcle.
: number of swaths skipped on adjacent lunar
and Planets.
K
synodic days, and
: integer number of orbits per lunar synodic
Geometdc
Configuration
ofSensorc
I
: 36? scalesthe height (FI)to
panchromatic
band (seeFigure 2), is conBand
t,
Moonsat's
day.
Setting
.
I
figured in convergentstereomode. The Z-coordinates(elevaapproximately 100 km.
tions) are the intersectionsof the convergedsensor'srays at
Using Equation 9, the approximateorbital period (7) for
the lunar surface. The vertical, down-looking sensor in the
one repeat cycle to cover the lunar globe is
PE&RS
L425
TeaLe4.
(rnou Fr-oRetsxv
LurunnMnpScnlesllo DtMENsroNs
Er al., 1971)
Frame dimensions
Lat
Long
Frame dimension
at maps
scale (cm)
16"00'
go00'
4"00'
1"20'
0'40'
o"20'
0010'
49
4S
49
40
4T
40
50
Map Scale
Frame
dimensions
(in km)
aI
1:1,000,000
1:500,000
1:250,000
1:100,000
1:50,000
1:25,000
1:10,000
20'00'
10'00'
5'00'
2'00'
1"OO'
0'30'
0'10'
490.0
245.O
722.5
40.0
20.5
10.0
5.0
61
61
61
61
61
61
50
610.0
305.0
752.5
61.0
30.5
15.2
5.0
Sheets:
number in the
preceding scale
I
4
4
720
4
4
6
Sheets:
number in preceding
1:1.000.000
scale
7
4
16
L20
480
1,520
77.520
middle of Figure 2 represents the other five multispectral images(not in stereo).The two rectangulararray sensorslooking out to the celestial sphere are for sensing stars from
which precise attitude can be determined.Becausethe suggested104" orbit is 14" off the poles, the sensormay be designed to tilt off-nadir for imaging at the poles.
compute attitude. The attitude orientation matrix computed
in the right ascension,declination system has to be transformed into the lunar coordinate system. The transformed attitude can be related to the stereoground-looking sensors.
This star derived attitude becomes the orientation for the
stereomodels.
AttltudeSensor
A preferred way of sensing attitude is by using star sensors.
Star cameraswere used in the Apollo 15, 16, and 17 missions. Star sensorsare available off-the-shelffrom the electrooptical industry. Assume that a rectangular anay CCDsensor
can detect star light of magnitude five or lower and that
there are approximately 5,400 such stars distributed uniformly over the celestial sphere, the calculated star density
(P) is
TenalnSensor
The proposed configuration for Moonsat's convergent stereo
sensorsis basedupon a number of scientific requirements:
a 4-metrespatialresolution,
o in-orbit stereocapability,
. scenesizesufficientto covera 1:50,000-scale
imagemap
sheet.and
. geomebicquality sufficientfor digital elevationmodelsaccurateto +3 m.
Solid state linear arrays with detector size of 13 pcmwould
require 8,750 detectors with a 20' angular field of view to
cover the 35-km swath width. The focal length required for
sensing 4-m pixels on the lunar surface with convergent
stereo-sensorsis approximately 0.4 m. These parameters €ue
all well within the state-of-the-artfor the sensor industry.
The high resolution stereocameraproposed as a candidate
for the mission to the Moon by Neukum (1SSO)specifiesa
detector size of 7 pm. lf 7-g,m detectors are sufficient, the focal length of the sensor would be reduced by about 50 percent.
P=
5,4OOstars/sphere
41,,253square degrees/sphere
0.13 stars
square oegree
'
(rJ,
For a rectangularstar sensorfield of view,7" X 9o : 63
square degrees,one can expect an averageof 8.2 stars in the
sensor's field of view at any time (Junkins and Strikwerda,
1981).Light (1SOO)
showed that typical sensorattitudes of
+ 2 to 4 Errcsecondsare possible;this star-derivedattitude
can be related to the Moon-looking panchromaticsensors
employing precalibration of the sensor geometric configuration and synchronizedtiming. As a star transits acrossthe
rectangular arrays, a continuous estimating function can
Star and
Termin Sensors
Scene Size
25Knx35Km
Swath Width
35 Km
Orbit
Orbit
l97o Sidelap
at Equator
Near Polar Orbit
i = 104"
Altitude
100 Km
.
Period:
.
Orbits / lunar synodic day: 361
.
Repeat Coverage: 29.53 days (361 Orbits)
ll7.?87 Min
Figure2. Moonsat.
Multlspectlal
Senson
Table 3 shows the spectral wavelengths and spatial resolution of 10 m for each of the five sensors. These sensors are
nadir looking with 3,500 detectorsto cover the 35 km swath
width. The focal lengths for the sensorswill range from 0.13
m to 0.23 m.
Sengor
Posltlon
on0illt
The preferred methbd for tracking satellites over the years
has been doppler radar backing. Doppler was successfully
used in the Apollo program during the 1960s. Now that the
Global Positioning System (cps) is about complete, satellite
positioning around the Earth may resort to using the GPS
constellation where feasible. cPS range accuracy for a satellite inside the constellation is o: -r8 metres.Becausethe
Moon is, on average,at least 20 times further away than an
Earth satellite, the moon orbiting receiver to GPSsatellite geometry would be weak. The result is position dilution of precision (enoe). Unfortunately, both doppler tracking and the
GPShave this similar drawback. In either case, tracking can
be used as a constraint on the 3D behavior of the Moonsat,
but, because of the small subtended angle between Moonsat
TreLe5.
nto Rrre ron Sceles 25 ev 35 xi/
Drn Volut*,te
Ps Pixels in Pixels x I Bands to Bits per
(m) scene bits/Dixel transmit scene
4 5.47y.70? 4.38X108
1 0 8.75X106 T.OOX.IO?
5
Compressed Data rate
(Mbps)
8 to 4 bits
4.38X108
1.75X108
8.75X108
3.50X108
*stereopanchromatic
27
17
Total data rate 38
and the GPSconstellation,a computed X,Y,Z-cootdinatemay
have a large PDoP,and may be difficult to obtain. This depends on cps transmitting outward as well as inward which
may not be the case. In fact, an experiment or simulation
study is warranted to determine GPS'sapplication to satellite
positioning outside its constellation.For Moonsat, sensorpoSitiotrr as i function of precise time (0.0001sec) for each line
of detectors is needed. This position integrated with the star
and terrain sensorsall synchlonized with precise time form
the basis for knowing both position and attitude of Moonsat.
These position and attitude data would serve as vital inputs
to computing a unified lunar control point network (Brown,
1968).
ttloongat
Summary
In summary, Moonsat ptoposes six essential characteristics
that shoulci meet data iequirements for 1:50,000-scaletopographic products (including DEMs)and image map-data suitable-for cts applications. These data would be an ideal set for
lunar modeling and research useful for the entire international community. The six essential Moonsat characteristics
are as follows:
. 4-m groundpixel size in stereoto supporttopographicmapping at 1:50,000
scale;
o itereoscopiccoveragewith the panchromaticband in the
sameorbit;
. precisesatelliteposition,attitude,and calibration;
o broad area coverage(25 by 35 km scene);
o contiguous global coverageevery lunar month; and
o multiipectril bands nearly equivalent to those used by the
Landsat ru and spot and applicable to lunar science'
Specifications for Moonsat are as follows:
Mission: Imaging the Moon for topographic GIs, mapping,
and lunar science applications at 1:50,000 scale
and smaller.
Orbit:
andRate
DataVolume
The two convergent stereo terrain sensorswill sample on 4m centers acrosJ track for the panchromatic stereo bands,
and the nadir-looking sensorswill sample on 10-m centers
for bands 2,3,4,5, and 6 as shown in Table 3. Datavolumes are computed by Equation 16 and are shown in Table
5.
06lts
Clrcular
ObltalVeloclty:
For calculating data rates,it is essentialto know the satellite
velocity (4), and the velocity of the satellite'strack on the
surface(Vr).
-:[+.
J"',*,,""
Velocity (V")
Ground velocity
(v)
Terrain
sensor:
(14)
Substituting the appropriate values defined in Equation 5,
% : 1.63 km/sec
Then
(15)
",:l#)km/sec
: 1..54km/sec
DataRatelor Moonsat
: (4+*=)
pixersperscene
(9!{;=)
ttut
where ps : pixel size.
The satellite velocity on the lunar surface(V") is 1.54
km/sec. The time to image one 25-km scene;25 kn + 1'54
km/sec : 1.6.24sec. Data compressionrates going from 8 to
4 bits are well within industry capabilities.The final data
rate : compresseddata + 16.24 sec, which yields 38 Mbps
for all sensorstransmitting.
PE&RS
Type
Inclination
Altitude
Period
Orbits per synodic lunar day
Repeatcycle
Attitude
sensor:
Circular
N e a r p o l a r ,i - 1 O 4 "
100 km
71,7.787minutes
361
29.53 days, one slmodic
lunar month
1.63 km/sec
1.54 km/sec
Number of orbits 3 6 1
to cover lunar
globe
Linear array pushbroom
Types
each band
35 km (coversone 1:
Swath width
50,000-scalemaP)
4 m for panchromatic
Pixel size
band
l0mfor5multispectral
bands
>0.4m
Focal length
Convergent stereosensor
Array Scan
configuration (panchromatic) Vertical sensor
configuration (multispectral)
20" for 35 km swath
Field of view
Approximately 30" deConvergence
pending on B/H ratio
angle
8,750 for panchromatic
Detectorsin
band
array
3,500 for multispectral
bands
cPs, if feasible, or EarthSensor
positioning
based tracking
Rectangular arrays (2),
Type
time synchronized
Measures stars magnitude
Stars
5 or lower traversing array realtime
Attitude as a function of
Output
time
(t), 9, ,(
!2 to 4 arc seconds
L427
Sensitivity:
Band No.
1.
2.
3.
4.
5.
6.
Quantization:
Level:
SpectralBand/
Centers
Color
0.40-0.80
Panchromatic for
stereomapping
0.40
0.56
o.70
0.95
7.20
Blue
Green
Red
NIR
NIR
Scenesize:
B bits per
pixel
25 bv 35 km
Data rate:
38 Mbps
Sensortiming:
0.0001 sec
256 shadesof gray
Scenecovers a 1:50.000scale map sheet which is
0040'bv 1000'
Downlink compressedB to
4 bits (5o percent)
Relative timing
Acknowledgments
The author is indebted to ]ohn L. Junkins, Texas A&M University, for orbit inclination analysis (Figure 1). Also, Larry
Rowan of the U.S. GeologicalSurvey provided information
on spectralsensing,and Ray Batson and Frederick Doyle (retired) of the U.S. GeologicalSurvey offered constructivesuggestions on an early draft of this paper.
References
Asker, J.R.,1992.U.S. Draws Blueprints for First Lunar Base,.Aviation Weekand Space Technology,August 3I,7992, pp. 4Z-S1.
Battin, R.H., 1987.An Introduction to the Mathematicsand Methods
of Astrodynamics, American Institute of Aeronautics and Astronautics, Inc., New York, New York, 504 p.
Brown, D.C., 1968.A Unified Lunar Control Network, Photogrammetric Engineering, 34(72):7272-1292.
Batson,R.M., 1987.Digital Cartographyof the Planets:New
Methods, its Statesand its Future, Photogrammetric Engineering
& Remote Sensing,53(9):7277-7278.
Charette,M.P., T.B. McCord, C. Pieters,and l.B. Adams, 7924. Application of Remote Spectral ReflectanceMeasurementsto Lunar
Geology Classification and Determination of Titanium Content of
Lunar Soils, lournal of Geophysicol Research,79(11):1605-161g.
Colvocoresses,
A.P., 1982.An Automated Mapping Satellite System
(Mapsat), Photogrammetric Engineering & Remote Sensing,
48(10):1585-1591.
Doyle, F.J.,1970.PhotographicSystemsfor Apollo, Photogrammetric
Engineering,
36(10):1039-1044.
1992. Report of the Planetary Cartography Working Group,
Presentation to Congressof the International Society of Photogrammetryand RemoteSensing,Washington,D.C., z-14 August
7992.
Florensky,K.P., A.A. Gurshtein,V.I. Korablev,L.M. Bougaevsky,and
K.B. Shingareva,797l.Classiffcation,ScalesSequenceand Nomenclature of Lunar Maps, ?fte Moon, D. Reidel Publishing
Company/Dordrecht-Holland,
3:78-89.
Gerding,R.B.,and K.R. fenkin, 1971.OceanColor Measurements
Utilizing a Noon Orbit for Earth ResourcesSatellite Applications, Proceedingsof the SPIE Seminar: Remote Sensingof Earth
Resourcesand the Environment, November 1971, Palo Alto, California, 27:7O1-7O9.
Greeley, R., and R.M. Batson, 799O.Planetary Mapping, Cambridge
University Press,Cambridge,New York.
Head, J.W.,C. Pieters,T. McCord, I. Adams, and S. Zisk, 1978.DefiL42A
nition and Detailed Characterization of Lunar Surface Units Using Remote Observations, Icarus, 33i745-772.
Inge, J.L., and R.M. Batson, 7992. Indexes of Maps of the Planets and
Satellites,NASA Technical Manual 4395, August 1992,NASA
Code l-fT, Washington,D.C.
funkins, f.L., and T.E. Strikwerda, 1981. Star Pattern Recognition
and Spacecraft Attitude Determination, Virginia Polpechnic Institute and State University Report for Engineer Topographic
Laboratories,ETL-0260,Ft. Belvoir, Virginia.
Krueger,M.W., 1965.Some Design Considerationsfor Lunar Orbital
Photographic Systems,Proceedings of Semi-annual Convention,
American Society of Photogrammetry, Dayton, Ohio, 22-24 September, pp. 139-166.
Light, D.L., 1970. Extraterrestrial Photogrammetry at TOPOCOM,
Photogrammetric Engineering, 36(3):260-272.
1972. Photo GeodesyFrom Apollo, Photogrammetfic Engineering & Remote Sensing,38(6):574-587.
1980. Satellite Photogrammetry, Manual of Photogrammetry,
Foufth Edition (C. Slama, editor), American Society of Photogrammetry, Falls Church, Virginia, pp. 899-923.
1990. Characteristics of Remote Sensorsfor Mapping and
Earth Science Applications, Photogrammetric Engineering & Remote Sensing,56(12):1,61
3-1,623.
NASA, 1973. Apollo 17 Preliminary Science Report, NASA SP-330,
U.S. GovernmentPrinting Office, Washington,D.C., pp. 2-3.
Nash, D.B., and J.E.Conel, 1974. SpectralReflectanceSystematicsfor
Mixtures of Powdered Hypersthene, Labradorite, and Ilmenite,
lownal of GeophysicaI Research,79(11):1615-1621.
Neukam, Gerhard, 1990. HffSC: High Resolution StereoCamera,
Mars 94 Mission, German Aerospace ResearchEstablishment,
DLR, OE-PE,Part B.
1992. Planetary Remote Sensing with the Galileo Space
Probe, DZR-Nachrichten, (66):32-37.
Paine, T.O., 1986. Tlre Report of the National Space Commission, PioneeringThe SpaceFrontier, Bantam Books,Inc.,666 Fifth
Avenue, New York, pp. 138-140.
Soderblom,L.A., and l.M. Boyce, 1976.Distribution and Evolution of
Global Color Provinces on the Moon. Lunar Science. T:822-824.
Stafford, T.P., 1991. Report of the Synthesis Group on America's
Spoce Exploration Initiative, Superintendent of Documents, U.S.
Government Printing Office, Washington, D.C., p. iv.
Star, f., and f. Estes, 799O.Geographic Information Systems,An Introduction, Prentice Hall, Englewood Cliffs, New Jersey, pp. 1213.
(Received5 fanuary 1993:accepted2 June 1993)
Donald L. Light
Don Light has a BS Degree in Geodetic and Cartographic Science from The GeorgeWashington
University and a masters level diploma in Strategy and Management from the U.S. Naval War
College.Don served in the U.S. Army 30th Engineer Topographic Battalion (2 years),the DefenseMapping
Agency (25 years),and the U.S. GeologicalSurvey (uscs)
since 1980. His years of experiencehave spanned nearly all
phases of topographic mapping, photogrammetry, remote
sensing, and systems development for automating mapping
systems. Significant assignmentshave been Chief, Advanced
Technology Division, DefenseMapping Agency, rnc; Technical Director, DefenseMapping School; SpaceApplications
Studies,CongressionalOfEce of Technology Assessment;
Chief, Branch of SystemsDevelopment,uscs, National Mapping Division; and currently as Chief, Branch of Contract
Management,where he managesthe National Aerial Photography Program. Don has published numerous articles on remote sensing systems for the Earth and Moon and is the
author editor of Chapter 17, Satellite Photogrammetry in the
ASPRSMonuaI of Photogrammetry. In 1992, Don was
awarded the Department of the Interior's Meritorious Service
Award. He also teaches photogrammetry part time at the
GeorgeMason University, Fairfax, Virginia, and is a graduate
of the FederalExecutive DevelopmentProgram,1980.
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