AA 4362 Astrodynamics

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AA 4362 Astrodynamics
Out-of-Plane Orbital Maneuvering
Week 8 Vallado Chapter 6 Sections 6.4
-6.6
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Orbital Maneuvering inThree Dimensions
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Why Plane Changes?
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Launch?
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Launch?
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Launch?
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Achieved Orbit Inclinations
0? Launch Azimuth 87.4?
Inclination 60? Launch Azimuth
39.5? Inclination 90? Launch Azimuth
28.5? Inclination 120? Launch Azimuth
39.5? Inclination 180? Launch Azimuth
87.4? Inclination
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OK, Lets prove this rigorously
Launch Initial Conditions
Position l, Latitude W,
Longitude (Inertial) h,
Altitude
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Launch Initial Conditions
Launch Initial Conditions (Inertial
Coordinates)
Sidereal hour angle
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Sidereal Hour Angle
Ignore for now!
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Computing the Hour Angle
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Earth Radius
Earth radius as Function of Latitude
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Initial Velocity Vectorafter the rocket turns
the corner
V0
Launch Initial Conditions
Velocity Vo (earth relative vel.)
g (flight path angle)
f (launch azimuth)
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Initial Velocity Vectorafter the rocket turns
the corner
Launch Initial Conditions
rotational velocity of earth
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Earth Boost
Launch Initial Conditions
(earth)
V boost acts due east
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Angular Velocity of Earth
Launch Initial Conditions
(earth)
V boost acts due east
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Initial Velocity Vectorafter the rocket turns
the corner
Launch Initial Conditions
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Inertial Velocity (Initial condition)
Rotate Through Latitude First
2-rotation

No 1 (X-axis) rotation Needed Why? z already
points Towards center of earth
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Inertial Velocity (Initial condition)
Rotate Through Longitude Next
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Inertial Velocity (Initial condition)
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Initial Conditions In Inertial Coordinates
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Out-of-plane orbital elements (contd)
l R x V
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Or you can use spherical geometry to get an
approximation (ignores earth rotation)
A good approximation is
cos(i) sin(?) cos(l)
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Spherical
A good approximation is
cos(i) sin(?) cos(l)
Approximate Orbit Inclinations
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Achieved Orbit Inclinations
0? Launch Azimuth 87.4?
Inclination 60? Launch Azimuth
39.5? Inclination 90? Launch Azimuth
28.5? Inclination 120? Launch Azimuth
39.5? Inclination 180? Launch Azimuth
87.4? Inclination
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Achievable Direct Launch Inclination Angles
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Achievable
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Bottom Line
So thats why we have to change Orbital planes
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Where do we Change Orbital Planes?
You can only change planes When the planes at
your orbits cross i.e. at the ascending
and Descending nodes of the orbit
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Simple Plane Change
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Simple Plane Change (contd)
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Simple Plane Change (contd)
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Simple Plane Change (contd)
DV can be expressed in polar form also
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Simple Plane Change (contd)
Evaluate magnitude of DV
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Simple Plane Change (contd)
Why no Vr component?
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Simple Plane Change (contd)
Define Flight path angle
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Simple Plane Change (contd)
Define Flight path angle
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Simple Plane Change (contd)
In-Plane Velocity Vector
perifocal
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Simple Plane Change (contd)
Circular orbit
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Example Geo-synchronousTransfer
iii) Hohmann transfer To geo-synchronous orbit
Calculate required DV
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Orbital Speed
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Gravity Losses
Equivalent specific energy required to lift
unit mass to Orbital altitude
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Vboost Due to Earths Rotation
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Plane Change DV
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Total Delta V required to Reach Equatorial Leo
Orbit from KSC
than what is required just to obtain orbit!
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How About Transfer to Geo-Stationary Orbit
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Hohmann transfer
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KSC Launch example Option 1
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OK, lets try another approach
where V is smaller
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Option 2
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Plane Change at Apogee


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KSC Launch Option 2
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KSC Launch Option 2
Better . But can we still do better than this?
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Combined Plane Change
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Combined Plane Change (contd)
Angle between vectors
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Combined Plane Change (contd)
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Combined Plane Change (contd)
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Combined Plane Change (contd)
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Option 3
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Option 3 (concluded)
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Option 4
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Cost to get to GEO from Equatorial Launch
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Cost to get to GEO from Equatorial Launch
Thats the bottom Line get a satellite to
GEO-stationary Orbit from KSC costs you gt3 DV
Compared to Equatorial LAUNCH
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