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

RFM-PCOM 12 Nov 20141

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.

RFM-PCOM 12 Nov 20142

a semi major axisAngle from X axis to line of nodesAngle from line of nodes to periapsisM mean anomalye = c/a

Initially circular

Initiallycircular

Crash intoMoon

10/9/14

(e)

Initially elliptical

Ely*: “New class of stable high-altitude lunar orbits”

3

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 satellites120° apartEllipse with e~0.6 and i~51°Periapsis (North lunar pole) ~ 700km

(Note: figure directly from http://science.nasa.gov/science-news/science-at-nasa/2006/30nov_highorbit/ )

RFM-PCOM 12 Nov 2014

10/9/14

*

Orbit of Moon around Earth

EclipticPlane of Earth orbit around Sun

Moon North pole,spin axis,

tipped 6.8º fromecliptic normal.Moon rotates on

axis once per month

Earth

Moon orbit plane inclined ~ 5.14º from ecliptic. Varies from 4.98º to 5.30º

5.14º

Moon South polein view of Earth.From south pole,Earth appears at

elevation of 6.8º .

Moon South poleNOT in view of Earth.

From south pole,Earth appears at

elevation of - 6.8º . Shackleton crater location: 89.6 S, 110 E

0.4 from south pole

0 14 28 42 56

Time (days)

Elevationto Earth center

from Moonsouth pole (degrees)

+ 6.8º

- 6.8º

From Moon South pole,Earth will appear to.

rise to elevation of 6.8ºand fall over a ~ 28 day period.

From Shackleton crater,Earth will appear to.

rise to elevation of 7.2ºand fall to - 6.4º

over a ~ 28 day period.

Moon orbit period = 27. 317 days,(360º /27.3 = 13.2º / day)

but during that time Earth rotates27º around Sun so period appears

to be ~ 29 days.

Earth will be at least 1º aboveHorizon for about 12 days out

of ~ 28 day cycle.

12 days

14 days

12/10/05

6.8º

Moon

.6.8º

Moon

.

Moon spin axisorientation fixed due to

conservation of angular momentum

4RFM-PCOM 12 Nov 2014

Terminology from Kepler

Definition of terms (in plane only, 2D)a = semi major axisb = semi minor axis a2=b2+c2

c = semi distance between focie = eccentricity = c/ap = 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 mT = orbit period = 2 a3/2 / = True anomaly = angle centered at focus, from perigee to objectE = 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

.

X

Y

a

b p

Q

VS

t

FF

E

r

Object in orbit

a

perigeeapogee

c = ea

Basic Orbit Dynamicsr =

p1+ e cos

Centralbodyx

x,y

x2

a2

y2

b2+ = 1

For point on ellipse

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2/6/10

v = ( )1 1 r 2a