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Astrodynamics
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Orbit Perturbations• Secular variations – langsomt, lineært
• Short-period variations
• Long-period variations
Element
TimeOrbit
Short PeriodLong Period
Third-Body Perturbations
n i
n i
n i
n i
/ ) sin 5 - 4 ( 0.00077
/ ) sin 5 - 4 ( 0.00169
/ ) cos ( 00154.0
/ ) cos ( 00338.0
2Sun
2Moon
Sun
Moon
Right ascension of the ascending node
Argument of perigee
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Perturbations Because ofa Non-spherical Earth
Right ascension of the ascending node
Argument of perigee
2227/2-14J
22-7/214J
)e-(1 ) sin 5-4 ( 101.03237
)e-(1 ) cos ( 10-2.06474
2
2
ia
ia
sin²(63,43495) = 0,8
cos(90) = 0,0
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Perturbations From Atmospheric Drag
Perturbations from Solar Radiation
A/mraR )1(105.4 6
r: Reflection factor (1: specular reflection, 0: absorption)A: Satellite cross-section (exposed to the Sun) – m²m: Satellite mass – kga: m/s²
Perturbations From Atmospheric Drag
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Perturbations From Atmospheric Drag
Perturbations From Atmospheric Drag
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Perturbations From Atmospheric Drag
Ørsted
H = 700 kmP = 100 min
T = 30-40 years
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http://www.heavens-above.com/
Astrodynamics II
• Orbital elements• Orbit Maneuvering• Launch Windows• Orbit Maintenance• Earth Coverage
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a Den halve storaksee Ekscentriciteteni Inklinationen
Den opstigende knudes længde (i forhold til forårspunktetPerifokus’ vinkelafstand fra den opstigende knude
T Perifokustiden
Low Earth orbit (LEO)
Mir: 350km altitude, near circular a: 6730 km, e: 0.00P: 91 minutes n: 15.725 omløb/døgni: 51.6°Baikonur Launch site
Change in right ascension of theascending node:
-5.1 deg/day
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Landsat 7 orbit (LEO)
Landsat 7 is an Earth resources spacecraft which images the Earth'ssurface in visible and infrared light. Near polar orbit of 700km altitudea: 7080 km P: 98 min.i: 98.8°
Change in right ascension of theascending node:
+1 deg/day
Perturbations Because ofa Non-spherical Earth
Right ascension of the ascending node
Argument of perigee
2227/2-14J
22-7/214J
)e-(1 ) sin 5-4 ( 101.03237
)e-(1 ) cos ( 10-2.06474
2
2
ia
ia
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Geosynchronous Orbits (GEO)
A geosynchronous orbit is an orbit which has an orbital period close to thatof the Earths rotation. A geostationary orbit is a special case of thegeosynchronous orbit where inclination = 0° and the period is equal to therotation period of the earth (approx 1436 minutes).
a: 42160 kme: 0i: 0P: 1436 min
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TDRS (USA)
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Geosynchronous Transfer Orbits (GTO)
This is a 600 x 35,700km 28° inclination
a = 24530 km i = 28 e=0.71
Change in right ascension of theascending node:
-0.31 deg/day
Change in argument of perigee:
+0.53 deg/day
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Molniya orbits
This is a 400 x 40,000km 63.4° inclination
a = 26600 km i = 63.4 e=0.75 P=11.967 hrs.
Change in right ascension of theascending node:
-0.030 deg/day
Change in argument of perigee:
0.000 deg/day
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Mid Earth Orbit (MEO or GPS)
Circular orbit 60.0° inclination
a = 26600 km i = 60 e=0.00 P=11.967 hrs
Change in right ascension of theascending node:
-0.033 deg/day
Change in argument of perigee:
+0.008 deg/day
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Highly Eccentric Orbits (HEO)
A number of scientific satellites, particularly orbiting observatories, usehighly eccentric orbits with apogee's of over 100,000km.The reason for using these orbits is generally to permit continuesobservations of celestial objects without the earth blocking the view every30 to 40 minutes.The orbit of the Chandra X-ray observatory is a 9600 x 139000km,28.4° inclination orbit of 3809 minute period (63.5h orbit).
a = 80700 km i = 28.4 e=0.80 P=63.5 hrs
Change in right ascension of theascending node:
-0.009 deg/day
Change in argument of perigee:
+0.015 deg/day
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Orbit Transfer
Coplanar transfer
Modify the velocity vector
arV 2//2/2
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rr
arV 2//2/2
rr
r
arV 2//2/2
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rr
r
arV 2//2/2
