morehead state university morehead, ky prof. bob twiggs rjtwiggs@gmail
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Understanding Orbits Orbit Facts. Morehead State University Morehead, KY Prof. Bob Twiggs [email protected]. Understanding Orbits. This aircraft is flying across the country. - PowerPoint PPT PresentationTRANSCRIPT
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• Longitude• Latitude• Altitude• Horizontal velocity• Heading ( north, south, etc.)• Velocity (ascending or descending)
This aircraft is flying across the country.The ground controller radios the pilot and wants to get all of the parameters that determine it’s flight, what are they?
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Greenwich, UK
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Greenwich, UK
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Understanding Longitude and Latitude
Morehead ~= W 840, N 37.50
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Satellite Launch Ports
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Launch directions from launch ports
Vandenberg AFB
Cape Kennedy
French GuianaPolar
Polar
57.50
Near Equatorial
Polar
28.50
ISS 51.60
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r = 6378 km
What additional orbit launch velocity would be needed to
launch to 500 km circular orbit from the equator to the east?
What additional orbit launch velocity would be needed to
launch to 500 km circular orbit from the equator to the west?
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q
r = 6378 km
2010
0
4030
50
r’r’ = 6378*cos (q)
Now can calculate throw velocity at any
latitude
Q = 300
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Altitude - h
Altitude - h
Orbital Velocity - v
What must be the velocity of the launch vehicle to put a spacecraft into a given orbit?
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What determines the velocity of spacecraft in a circular orbit?
v
Fg
Fc
Velocity of spacecraft
Altitude: given
Orbit Period
Vcir = 631.3481 r-1/2 km/sec r - is from center of the earth – 6378 + alt km
Vesc = 892.8611 r-1/2 km/sec
Circumference = 2pr
Orbit
Time to orbit = distance/velocityOrbit Period = Time to orbit (minutes)
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Orbital Eclipse Vcir = 631.3481(r+h)-1/2 km/secAltitude Velocity Circum Period Time %
km km/sec km Min Min Eclipse r = 6378 km300 7.726 41958 90.51 36.59 40.4% h = altitude350 7.697 42272 91.53 36.33 39.7%400 7.669 42586 92.55 36.11 39.0% Circumference = 2pi(r+h)450 7.641 42900 93.58 35.92 38.4%500 7.613 43214 94.61 35.75 37.8% Period = (Circum/velocity)/60550 7.585 43529 95.64 35.61 37.2%600 7.558 43843 96.68 35.49 36.7% Eclipse time = (2*(90-ACOS(r/(r+h))*(180/3.1415))/360)*Period650 7.531 44157 97.72 35.38 36.2%700 7.504 44471 98.77 35.28 35.7%750 7.478 44785 99.82 35.20 35.3%800 7.452 45099 100.87 35.13 34.8%
Orbit CalculationsEclipse Time for Noon-Midnight Orbit
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Eccentricity
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Relationship between conic sectionsConic Sections Eccentricity
Circle e = 0
Ellipse 0 < e < 1
Parabola e =1
Hyperbola e >1
e = 2c/2a
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• Orbital size, use the semimajor axis, a• Orbital shape, is defined by eccentricity, e• Orientation of the plane in space, uses
inclination, i right ascension of the ascending node, Ω
• Orientation of the orbit within the plane is defined by the argument of perigee, v
• Spacecraft’s location in the orbit is represented by true anomaly, u
Spacecraft orbit definition
XX
X
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XXX
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Classic Orbital Elements (COEs) Checklist
• Orbit’s size• Orbit’s shape• Orbit’s orientation
Orbit plane in spaceOrbit within the plane
• Spacecraft’s location
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r
h
dFor a zenith pass.
1. What is the distance d in km?
2. What is the time it takes the spacecraft to go from A to B?
BA
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What is maximum latitude that a geostationary spacecraft can be seen?
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Assessment Time
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