1. SLS-RFM_14-18 Orbital Considerations For A Lunar Comm Relay
Fall Technical Meeting, London 11/10 – 11/14/2014
SLS-RFM_ Orbital Considerations For A Lunar Comm Relay
H. Garon, V. Sank - NASA/GSFC/ASRC
RFM-PCOM 12 Nov 2014

2. Lunar Satellite Comm Relay Problem Statement
Potential lunar base placement where Earth may be below lunar horizon majority portion of a month (slide 4)
Due to Earth’s gravitational pull, high-altitude (>1200km) orbits regardless of eccentricity are inherently unstable while circular orbits at lower altitudes will not remain circular for very long. Time scales associated with substantive perturbation may be on the order of weeks.
Crash into
Moon
Initially elliptical
a semi major axis
Angle from X axis to
line of nodes
Angle from line of nodes
to periapsis
M mean anomaly
e = c/a
(e)
Initially
circular
Initially circular
RFM-PCOM 12 Nov 2014
10/9/14

3. Ely*: “New class of stable high-altitude lunar orbits”
Ely, T.A., Stable Constellations of Frozen Elliptical Inclined Lunar Orbits, Journal of the Astronautical Sciences, vol. 53, No. 3, July-Sept 2005, pp
Ely, T.A. and Lieb, E., Constellations of Elliptical Inclined Lunar Orbits Providing Polar and Global Coverage, AAS , AAS/AIAA Astrodynamics Specialists Conference, August 7-11, [ *
Proposal –
3 satellites
120° apart
Ellipse with e~0.6 and i~51°
Periapsis (North lunar pole) ~ 700km
(Note: figure directly from )
RFM-PCOM 12 Nov 2014
10/9/14

4. . . Orbit of Moon around Earth Ecliptic Earth Moon Moon 4
Moon North pole,
spin axis,
tipped 6.8º from
ecliptic normal.
Moon rotates on
axis once per month
Moon orbit period = days,
(360º /27.3 = 13.2º / day)
but during that time Earth rotates
27º around Sun so period appears
to be ~ 29 days.
Moon spin axis
orientation fixed due to
conservation of
angular momentum
6.8º
Moon .
6.8º
Moon .
Ecliptic
Plane of Earth orbit around Sun
Earth
5.14º
Moon South pole
in view of Earth.
From south pole,
Earth appears at
elevation of 6.8º .
Moon South pole
NOT in view of Earth.
From south pole,
Earth appears at
elevation of - 6.8º .
Moon orbit plane inclined
~ 5.14º from ecliptic.
Varies from 4.98º to 5.30º
Shackleton crater location:
89.6 S, 110 E
0.4 from south pole
Earth will be at least 1º above
Horizon for about 12 days out
of ~ 28 day cycle.
From Moon South pole,
Earth will appear to.
rise to elevation of 6.8º
and fall over a ~ 28 day period.
From Shackleton crater,
Earth will appear to.
rise to elevation of 7.2º
and fall to - 6.4º
over a ~ 28 day period.
Elevation
to Earth center
from Moon
south pole
(degrees)
+ 6.8º 14 28 42 56
12 days
- 6.8º
Time (days)
14 days
RFM-PCOM 12 Nov 2014 4
12/10/05

5. Terminology from Kepler
1+ e cos x2 a2 y2 b2
= 1
For point on ellipse
Basic Orbit Dynamics . X Y  a b p Q V S t F E r
Object
in orbit
perigee
apogee
c = ea
x,y
v = ( )
r a
Definition of terms (in plane only, 2D)
a = semi major axis
b = semi minor axis a2=b2+c2
c = semi distance between foci
e = eccentricity = c/a
p = semi latus rectum = a(1-e2)
ra = “radius” to apoapsis
rp = “radius” to periapsis
m = mass of central body
G = Newton's gravitational constant
 = G m
T = orbit period = 2 a3/2 /
= True anomaly = angle centered at focus, from perigee to object
E = Eccentric anomaly = angle at center of superimposed circle, from perigee to object line
M = Mean anomaly = E - e sin E = 2 (time fraction of orbit)
n = Mean Motion = 2  /T = “”
Area of ellipse =  a b
Central
body x
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