Transcript SLS-RFM_14-18 (Lunar Relay Satellite Orbits_v03_141021)

Fall Technical Meeting, London 11/10 – 11/14/2014
SLS-RFM_14-18
Orbital Considerations For A Lunar Comm
Relay
H. Garon, V. Sank - NASA/GSFC/ASRC
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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
(e)
Initially elliptical
Initially
circular
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
Initially circular
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10/9/14
Ely*: “New class of stable highaltitude 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. 301-316
 Ely, T.A. and Lieb, E., Constellations of Elliptical Inclined
Lunar Orbits Providing Polar and Global Coverage, AAS
05-343, AAS/AIAA Astrodynamics Specialists Conference,
August 7-11, 2005.
[http://trsnew.jpl.nasa.gov/dspace/bitstream/2014/37462/1/05-2140.pdf]
Proposal –
 3 satellites
 120° apart
 Ellipse with e~0.6 and i~51°
 Periapsis (North lunar pole) ~ 700km
(Note: figure directly from http://science.nasa.gov/sciencenews/science-at-nasa/2006/30nov_highorbit/ )
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10/9/14
Orbit of Moon around Earth
Moon North pole,
spin axis,
tipped 6.8º from
ecliptic normal.
Moon rotates on
axis once per month
Moon orbit period = 27. 317 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
Moon
Ecliptic
Earth
Plane of Earth orbit around Sun
Moon South pole
in view of Earth.
From south pole,
Earth appears at
elevation of 6.8º .
Moon
.
6.8º
Moon South pole
NOT in view of Earth.
From south pole,
Earth appears at
elevation of - 6.8º .
+ 6.8º
Elevation
to Earth center
from Moon
south pole
(degrees)
- 6.8º
Moon orbit plane inclined
~ 5.14º from ecliptic.
Varies from 4.98º to 5.30º
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.
0
14
28
42
56
12 days
Time (days)
.
5.14º
6.8º
Shackleton crater location:
89.6 S, 110 E
0.4 from south pole
From Shackleton crater,
Earth will appear to.
rise to elevation of 7.2º
and fall to - 6.4º
over a ~ 28 day period.
14 days
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12/10/05
Terminology from Kepler
For point on ellipse
x2 y2
+
=1
a2 b2
r=
Basic Orbit Dynamics
Y
x,y
p
1+ e cos
v = (
1
r
1
)
2a
Definition of terms (in plane only, 2D)
Q
a = semi major axis
b = semi minor axis
a2=b2+c2
t
Object
a
c = semi distance between foci
in orbit
e = eccentricity = c/a
b
r p
2
p = semi latus rectum = a(1-e )
ra = “radius” to apoapsis
E

perigee
a
apogee
Central
rp = “radius” to periapsis
body
c = ea
X
F
S x F
V
m = mass of central body
G = Newton's gravitational constant
 =Gm
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
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