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Astrodynamics
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Orbit Perturbations • Secular variations – langsomt, lineært • Short-period variations • Long-period variations
Element
Short Period Long Period
Orbit Time
Third-Body Perturbations
Right ascension of the ascending node
Moon 0.00338 ( cos i ) / n
Sun 0.00154 ( cos i ) / n
Argument of perigee 2 Moon 0.00169 ( 4 - 5 sin i ) / n 2 Sun 0.00077 ( 4 - 5 sin i ) / n
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Perturbations Because of a Non-spherical Earth
Right ascension of the ascending node
-2.064741014 a-7/2 ( cos i ) (1- e2 )2 J2 cos(90) = 0,0 Argument of perigee 1.032371014 a-7/2 ( 4 -5 sin 2 i ) (1- e2 )2 J2 sin²(63,43495) = 0,8
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Perturbations From Atmospheric Drag
Perturbations from Solar Radiation
6 aR 4.510 (1 r)A/m
r: Reflection factor (1: specular reflection, 0: absorption) A: Satellite cross-section (exposed to the Sun) – m² m: Satellite mass –kg a: 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 km P = 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 storakse e Ekscentriciteten i Inklinationen Den opstigende knudes længde (i forhold til forårspunktet Perifokus’ vinkelafstand fra den opstigende knude T Perifokustiden
Low Earth orbit (LEO)
Mir: 350km altitude, near circular a: 6730 km, e: 0.00 P: 91 minutes n: 15.725 omløb/døgn i: 51.6° Baikonur Launch site
Change in right ascension of the ascending node:
-5.1 deg/day
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Landsat 7 orbit (LEO)
Landsat 7 is an Earth resources spacecraft which images the Earth's surface in visible and infrared light. Near polar orbit of 700km altitude a: 7080 km P: 98 min. i: 98.8°
Change in right ascension of the ascending node:
+1 deg/day
Perturbations Because of a Non-spherical Earth
Right ascension of the ascending node
-2.064741014 a-7/2 ( cos i ) (1- e2 )2 J2
Argument of perigee 1.032371014 a-7/2 ( 4 -5 sin 2 i ) (1- e2 )2 J2
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Geosynchronous Orbits (GEO)
A geosynchronous orbit is an orbit which has an orbital period close to that of the Earths rotation. A geostationary orbit is a special case of the geosynchronous orbit where inclination = 0° and the period is equal to the rotation period of the earth (approx 1436 minutes).
a: 42160 km e: 0 i: 0 P: 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 the ascending 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 the ascending 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 the ascending 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, use highly eccentric orbits with apogee's of over 100,000km. The reason for using these orbits is generally to permit continues observations of celestial objects without the earth blocking the view every 30 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 the ascending 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
V 2 / 2 / r / 2a
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r r
V 2 / 2 / r / 2a
r r r
V 2 / 2 / r / 2a
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r r r
V 2 / 2 / r / 2a
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