Doubly averaged effect of the Moon and Sun on a high altitude Earth satellite orbit |
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Authors: | Ash Michael E |
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Institution: | (1) Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Mass., USA;(2) Present address: Charles Stark Draper Laboratory, Inc., Cambridge, Mass., USA |
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Abstract: | Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI
ab, whereI
b=180°–I
a andI
a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature
a
semi-major axis
-
A
lk
coefficient defined in Equation (11)
-
B
lk
coefficient defined in Equation (24)
-
C
km
coefficient defined in Equation (25)
-
D, E, F
coefficients in Equations (38), (39)
-
e
eccentricity
-
H
k
expression defined in Equation (34)
-
expression defined in Equation (35)
-
I
inclination of satellite orbit on lunar (or solar) ring plane
-
J
2
coefficient of second harmonic of Earth's gravitational potential (1082.637×10–6
R
E
2
)
-
K
k, Lk, Mk
expressions in Section 4
-
expressions in Section 4
-
p=a(1–e
2)
semi-latus rectum
-
P
l
Legendre polynomial of degreel
-
q
argument of Legendre polynomial
-
radial distance of satellite
-
R
E
Earth equatorial radius (6378.16 km)
-
R, S, W
perturbing accelerations in the radial, tangential and orbit normal directions
- syn
synchronous orbit radius (42 164.2 km=6.6107R
E)
-
t
time
-
T
satellite orbital period
-
T
orbital period of perturbing body (Moon)
-
T
e
period of long periodic oscillations ine for |I|<I
a
-
T
s
synodic period
-
U
gravitational potential of lunar (or solar) ring
-
x, y, z
Cartesian coordinates of a satellite with (x, y) being the ring plane
-
coefficient defined in Equation (20)
- ![Delta](/content/r213514u68t76g00/xxlarge916.gif)
average change in orbital element over one orbit ( =a, e, I, , )
- 1, 2 3
unit vectors in thex, y, z coordinate directions
-
r
,
s
,
w
unit vectors in the radial, tangential and orbit normal directions
- = +
angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite
-
angle around the ring
-
gravitational constant times mass of Earth (3.986 013×105 km s–2)
- ![mgr](/content/r213514u68t76g00/xxlarge956.gif)
gravitational constant times mass of Moon (or Sun)
-
m
gravitational constant times mass of Moon ( /81.301)
-
s
gravitational constant time mass of Sun (332 946 )
-
ratio of the circumference of a circle to its diameter
-
radius of lunar (or solar) ring
-
m
radius of lunar ring (60.2665R
E)
-
s
radius of solar ring (23455R
E)
-
true anomaly
-
argument of perigee
- 0
initial value of
-
i
critical value of in quadranti(i=1, 2, 3, 4)
-
longitude of ascending node on ring plane
This work was sponsored by the Department of the Air Force. |
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Keywords: | |
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