128:. 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
775:
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770:{\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}}}
294:
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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
792:
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
161:
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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
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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
155:
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
825:
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289:{\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}
504:{\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}}}
830:
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387:
The nodal progression of low Earth orbits is typically a few degrees per day to the west (negative). For a satellite in a circular (
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81:. This bulge creates a gravitational effect that causes orbits to precess around the rotational axis of the primary body.
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62:
of artificial satellites, which have no measurable effect on the motion of Earth. The nodal precession of more massive,
780:
This is equivalent to −3.683° per day, so the orbit plane will make one complete turn (in inertial space) in 98 days.
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54:. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform
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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.
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Equatorial bulge torques a satellite orbit, leading to nodal precession
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906:{\displaystyle {\tilde {J_{2}}}=-{\frac {J_{2}}{GM_{E}R_{E}^{2}}}}
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51:
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is negative, so the precession becomes positive. (Alternatively,
391:= 0) 800 km altitude orbit at 56° inclination about Earth:
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decreases, that is the node precesses westward. If the orbit is
67:
935:, another kind of orbital precession (the change in the
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Discussion of nodal regression from
Analytical Graphics
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used in this equation is the dimensionless coefficient
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is the angular velocity of the satellite's motion (2
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77:. However, most bodies rotate, which causes an
353:is the eccentricity of the satellite's orbit,
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929:, or "precession of the equinoxes" for Earth
363:radians divided by its period in seconds),
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1010:Nodal regression description from USENET
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144:The rate of precession depends on the
58:. The following discussion relates to
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326:is the body's equatorial radius (
86:longitude of the ascending node
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530:. The precession is therefore
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982:Elements of spacecraft design
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382:second dynamic form factor
347:of the satellite's orbit,
106:angle relative to the Sun
979:Brown, Charles (2002).
102:heliosynchronous orbits
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795:heliosynchronous orbit
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514:The orbital period is
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937:argument of periapsis
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820:{\displaystyle J_{2}}
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151:For a satellite in a
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136:to drift with time.
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369:is its inclination,
132:, which causes the
56:gravitational field
933:Apsidal precession
915:geopotential model
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64:natural satellites
955:its orbital nodes
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70:is more complex.
48:astronomical body
16:(Redirected from
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126:equatorial bulge
79:equatorial bulge
28:Nodal precession
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18:Nodal regression
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60:low Earth orbit
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153:prograde orbit
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1030:Astrodynamics
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36:orbital plane
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75:primary body
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947:declination
760: rad/s
528: rad/s
337:for Earth),
146:inclination
112:Description
46:axis of an
42:around the
1035:Precession
1024:Categories
966:References
960:Lunar node
130:precession
90:retrograde
44:rotational
32:precession
913:from the
857:−
848:~
751:−
743:×
737:−
722:∘
714:
708:⋅
698:⋅
685:−
677:×
658:⋅
627:−
577:⋅
564:−
546:ω
520:.4 s
490:−
482:×
432:×
281:
275:ω
234:−
181:−
167:ω
94:longitude
66:like the
40:satellite
921:See also
140:Equation
50:such as
446: m
343:is the
335: m
96:of the
34:of the
30:is the
989:
299:where
701:0.001
666:1.082
524:0.001
471:1.082
425:6.378
52:Earth
38:of a
987:ISBN
800:The
740:7.44
315:/s),
68:Moon
953:of
711:cos
705:038
670:626
616:137
612:178
592:137
587:378
526:038
518:052
475:626
429:137
333:137
330:378
313:rad
278:cos
1026::
797:.
747:10
718:56
681:10
674:68
486:10
479:68
436:10
108:.
995:.
939:)
896:2
891:E
887:R
881:E
877:M
873:G
867:2
863:J
854:=
843:2
839:J
813:2
809:J
790:ω
786:ω
754:7
734:=
694:)
688:3
662:(
651:2
646:)
641:)
635:2
631:0
624:1
620:(
608:7
604:(
596:2
583:6
572:2
569:3
561:=
551:p
516:6
493:3
468:=
459:2
455:J
440:6
422:=
412:E
407:R
389:e
377:2
374:J
367:i
361:π
357:ω
351:e
341:a
328:6
323:E
320:R
308:p
305:ω
284:i
270:2
266:J
258:2
253:)
248:)
242:2
238:e
231:1
227:(
223:a
219:(
212:2
204:E
199:R
189:2
186:3
178:=
172:p
20:)
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