117:. Because of the bulge of the central body, the gravitational force on a satellite is not directed toward the center of the central body, but is offset toward its equator. Whichever hemisphere of the central body the satellite lies over, it is preferentially pulled slightly toward the equator of the central body. This creates a torque on the satellite. This torque does not reduce the inclination; rather, it causes a torque-induced gyroscopic
764:
106:
525:
759:{\displaystyle {\begin{aligned}\omega _{\mathrm {p} }&=-{\frac {3}{2}}\cdot {\frac {6\,378\,137^{2}}{\left(7\,178\,137\left(1-0^{2}\right)\right)^{2}}}\cdot \left(1.082\,626\,68\times 10^{-3}\right)\cdot 0.001\,038\cdot \cos 56^{\circ }\\&=-7.44\times 10^{-7}{\text{ rad/s}}\end{aligned}}}
283:
498:
772:
The apparent motion of the sun is approximately +1° per day (360° per year / 365.2422 days per tropical year ≈ 0.9856473° per day), so apparent motion of the sun relative to the orbit plane is about 2.8° per day, resulting in a complete cycle in about 127 days. For retrograde orbits
781:
can be thought of as positive but the inclination is greater than 90°, so the cosine of the inclination is negative.) In this case it is possible to make the precession approximately match the apparent motion of the sun, resulting in a
150:
386:
900:
113:
A non-rotating body of planetary scale or larger would be pulled by gravity into a spherical shape. Virtually all bodies rotate, however. The centrifugal force deforms the body so that it has an
530:
391:
73:
The direction of precession is opposite the direction of revolution. For a typical prograde orbit around Earth (that is, in the direction of primary body's rotation), the
144:
around Earth, the precession is westward (nodal regression), that is, the node and satellite move in opposite directions. A good approximation of the precession rate is
814:
1003:
278:{\displaystyle \omega _{\mathrm {p} }=-{\frac {3}{2}}{\frac {{R_{\mathrm {E} }}^{2}}{\left(a\left(1-e^{2}\right)\right)^{2}}}J_{2}\omega \cos i}
493:{\displaystyle {\begin{aligned}R_{\mathrm {E} }&=6.378\,137\times 10^{6}{\text{ m}}\\J_{2}&=1.082\,626\,68\times 10^{-3}\end{aligned}}}
819:
376:
The nodal progression of low Earth orbits is typically a few degrees per day to the west (negative). For a satellite in a circular (
969:
70:. This bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the primary body.
51:
of artificial satellites, which have no measurable effect on the motion of Earth. The nodal precession of more massive,
769:
This is equivalent to −3.683° per day, so the orbit plane will make one complete turn (in inertial space) in 98 days.
979:
74:
78:
915:
370:
82:
43:. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform
24:
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62:
Around a spherical body, an orbital plane would remain fixed in space around the gravitational
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of the orbital plane to the equatorial plane, as well as the orbital eccentricity.
114:
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Equatorial bulge torques a satellite orbit, leading to nodal precession
94:
20:
89:, that is the node precesses eastward. This nodal precession enables
28:
105:
32:
895:{\displaystyle {\tilde {J_{2}}}=-{\frac {J_{2}}{GM_{E}R_{E}^{2}}}}
777:
is negative, so the precession becomes positive. (Alternatively,
380:= 0) 800 km altitude orbit at 56° inclination about Earth:
77:
decreases, that is the node precesses westward. If the orbit is
301:
40:
56:
924:, another kind of orbital precession (the change in the
1004:
Discussion of nodal regression from
Analytical Graphics
816:
used in this equation is the dimensionless coefficient
822:
795:
528:
389:
153:
348:
is the angular velocity of the satellite's motion (2
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277:
1010:
66:. However, most bodies rotate, which causes an
342:is the eccentricity of the satellite's orbit,
918:, or "precession of the equinoxes" for Earth
352:radians divided by its period in seconds),
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999:Nodal regression description from USENET
104:
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133:The rate of precession depends on the
47:. The following discussion relates to
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906:or gravity field model for the body.
13:
539:
400:
192:
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14:
1035:
992:
315:is the body's equatorial radius (
75:longitude of the ascending node
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519:. The precession is therefore
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93:to maintain a nearly constant
1:
971:Elements of spacecraft design
954:
938:on the lunistices depends on
511:, so the angular velocity is
7:
909:
300:is the precession rate (in
128:
10:
1040:
371:second dynamic form factor
336:of the satellite's orbit,
95:angle relative to the Sun
968:Brown, Charles (2002).
91:heliosynchronous orbits
934:, in which the Moon's
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784:heliosynchronous orbit
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503:The orbital period is
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926:argument of periapsis
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809:{\displaystyle J_{2}}
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140:For a satellite in a
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81:, this increases the
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125:to drift with time.
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358:is its inclination,
121:, which causes the
45:gravitational field
922:Apsidal precession
904:geopotential model
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53:natural satellites
944:its orbital nodes
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59:is more complex.
37:astronomical body
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932:Lunar standstill
916:Axial precession
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115:equatorial bulge
68:equatorial bulge
17:Nodal precession
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974:. p. 106.
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49:low Earth orbit
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993:External links
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940:the precession
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142:prograde orbit
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87:ascending node
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1019:Astrodynamics
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123:orbital nodes
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25:orbital plane
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64:primary body
61:
16:
15:
936:declination
749: rad/s
517: rad/s
326:for Earth),
135:inclination
101:Description
35:axis of an
31:around the
1024:Precession
1013:Categories
955:References
949:Lunar node
119:precession
79:retrograde
33:rotational
21:precession
902:from the
846:−
837:~
740:−
732:×
726:−
711:∘
703:
697:⋅
687:⋅
674:−
666:×
647:⋅
616:−
566:⋅
553:−
535:ω
509:.4 s
479:−
471:×
421:×
270:
264:ω
223:−
170:−
156:ω
83:longitude
55:like the
29:satellite
910:See also
129:Equation
39:such as
435: m
332:is the
324: m
85:of the
23:of the
19:is the
978:
288:where
690:0.001
655:1.082
513:0.001
460:1.082
414:6.378
41:Earth
27:of a
976:ISBN
789:The
729:7.44
304:/s),
57:Moon
942:of
700:cos
694:038
659:626
605:137
601:178
581:137
576:378
515:038
507:052
464:626
418:137
322:137
319:378
302:rad
267:cos
1015::
786:.
736:10
707:56
670:10
663:68
475:10
468:68
425:10
97:.
984:.
928:)
885:2
880:E
876:R
870:E
866:M
862:G
856:2
852:J
843:=
832:2
828:J
802:2
798:J
779:ω
775:ω
743:7
723:=
683:)
677:3
651:(
640:2
635:)
630:)
624:2
620:0
613:1
609:(
597:7
593:(
585:2
572:6
561:2
558:3
550:=
540:p
505:6
482:3
457:=
448:2
444:J
429:6
411:=
401:E
396:R
378:e
366:2
363:J
356:i
350:π
346:ω
340:e
330:a
317:6
312:E
309:R
297:p
294:ω
273:i
259:2
255:J
247:2
242:)
237:)
231:2
227:e
220:1
216:(
212:a
208:(
201:2
193:E
188:R
178:2
175:3
167:=
161:p
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