Understanding Orbits
Orbit Facts
Morehead State University
Morehead, KY
Prof. Bob Twiggs
RJTwiggs@gmail.com
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Understanding Orbits
• Longitude
• Latitude
• Altitude
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?
• Horizontal velocity
• Heading ( north, south, etc.)
• Velocity (ascending or descending)
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Understanding Longitude and Latitude
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Greenwich, UK
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Greenwich, UK
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Morehead ~= W 840, N 37.50
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Satellite Launch Ports
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Launch directions from launch ports
57.50
Vandenberg AFB
ISS 51.60
Cape Kennedy
28.50
Polar
Polar
French Guiana
Polar
Near Equatorial
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Understanding Orbits
Understanding Longitude and Latitude
r = 6378 km
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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What additional orbit launch
velocity would be needed to
launch to 500 km circular orbit
from the equator to the east?
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Understanding Orbits
Understanding Longitude and Latitude
r = 6378 km
50
40
30
20
10
q
Q = 300
0
r’
r’ = 6378*cos (q)
Now can calculate
throw velocity at any
latitude
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Understanding Orbits
What must be the velocity of the launch vehicle to put a
spacecraft into a given orbit?
Orbital Velocity - v
Altitude - h
Altitude - h
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What determines the velocity of spacecraft in a circular orbit?
Altitude:
given
Velocity of spacecraft
Fc
v
Vcir = 631.3481 r-1/2 km/sec
r
Orbit
- is from center of the earth – 6378 + alt km
Vesc = 892.8611 r-1/2 km/sec
Fg
Orbit Period
Circumference = 2pr
Time to orbit = distance/velocity
Orbit Period = Time to orbit (minutes)
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Understanding Orbits
Understanding Longitude and Latitude
Orbit Calculations
Eclipse Time for Noon-Midnight Orbit
Orbital
Altitude Velocity
km
300
350
400
450
500
550
600
650
700
750
800
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km/sec
7.726
7.697
7.669
7.641
7.613
7.585
7.558
7.531
7.504
7.478
7.452
Circum
Period
Eclipse
Time
km
Min
Min
41958
42272
42586
42900
43214
43529
43843
44157
44471
44785
45099
90.51
91.53
92.55
93.58
94.61
95.64
96.68
97.72
98.77
99.82
100.87
36.59
36.33
36.11
35.92
35.75
35.61
35.49
35.38
35.28
35.20
35.13
Vcir = 631.3481(r+h)-1/2 km/sec
%
Eclipse
40.4%
39.7%
39.0%
38.4%
37.8%
37.2%
36.7%
36.2%
35.7%
35.3%
34.8%
r = 6378 km
h = altitude
Circumference = 2pi(r+h)
Period = (Circum/velocity)/60
Eclipse time = (2*(90-ACOS(r/(r+h))*(180/3.1415))/360)*Period
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Understanding Orbits
Eccentricity
e = 2c/2a
Relationship between conic sections
Conic Sections
Eccentricity
Circle
e=0
Ellipse
0<e<1
Parabola
e =1
Hyperbola
e >1
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Understanding Orbits
Spacecraft orbit definition
• 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
X
X• Orientation of the orbit within the plane is defined by the
argument of perigee, v
X• Spacecraft’s location in the orbit is represented by true
anomaly, u
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X
X
X
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Classic Orbital Elements (COEs) Checklist
• Orbit’s size
• Orbit’s shape
• Orbit’s orientation
 Orbit plane in space
 Orbit within the plane
• Spacecraft’s location
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For a zenith pass.
A
d
B
1.
What is the distance d in km?
2.
What is the time it takes
the spacecraft to go from
A to B?
r
h
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Understanding Orbits
What is maximum latitude that a geostationary spacecraft
can be seen?
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Understanding Orbits
Assessment Time
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