1. (Re) Orientation 1 - Introduction 2 - Propulsion & ∆V
3 - Attitude Control & instruments
4 - Orbits & Orbit Determination
LEO, MEO, GTO, GEO
Special LEO orbits
Orbit Transfer
Getting to Orbit
GPS
5 - Launch Vehicles
6 - Power & Mechanisms
7 - Radio & Comms
8 - Thermal / Mechanical Design. FEA
9 - Reliability
10 - Digital & Software
11 - Project Management Cost / Schedule
12 - Getting Designs Done
13 - Design Presentations
Another night of F=MA?
Education is the process of realizing that you don’t know what you thought you knew...
Sporadic Events:
•Mixers
•Guest Speakers
•Working on Designs
•Teleconferencing
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2. Review of Last time Attitude Determination & Control Design Activity
Feedback Control
Systems description
Simple simulation
Attitude Strategies
The simple life
Eight other approaches and variations
Disturbance and Control forces
Design build & test an Attitude Control System
Or in a word, F=MA
Design Activity
Team designations
Mission selections
Homework - ACS for mission
Plant (satellite)
Set point
Error
Control Algorithm
Sensor
Disturbances
Actuator
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3. LEO vs. GEO Orbit LEO: 1000 km GEO: 36,000 km Low launch cost/risk
Short range
Global coverage (not real time)
Easy thermal environment
Magnetic ACS
Multiple small satellites / financial “chunks”
Minimal propulsion
GEO: 36,000 km
Fixed GS Antenna
Constant visibility from 1 satellite
Nearly constant sunlight
Zero doppler
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4. LEO & GEO Pros / Cons Pros Cons LEO GEO Low launch cost
High launch reliability
Low radiation (except poles and SAA)
Short slant range
RF, imaging, probes
Global coverage from polar
Doppler ranging & GPS
Easy thermal for 0°C < T < 20°C
Financial small chunks
Atmospheric drag
Tracking antennas
Doppler compensation
Short, infrequent, irregular contacts
Requires autonomy
No global perspective
Lots of clutter
Frequent battery cycling
Except sun-synch
Low temp hard to achieve
LEO
Large Fixed Antennas are cheap
Constant visibility from 1 satellite
Nearly constant solar illumination
Zero Doppler
Need large antenna
1/3 second R/T delay
Large orbit maintenance ∆V
Large insertion ∆V;
complex launch
Thermal Averaging difficult
Exposure to solar weather
Poor Polar Visibility
Finances chunky
GEO
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5. Orbit Ground Rules #1: Orbits are Dynamic.
There are no “stationary” orbits. They are a dynamic balance of kinetic and potential energy - centripetal acceleration vs. gravitational acceleration. I.e. w2r + Mg/r2 = constant and w a v/r so v2 a l/r => w a l/ r3/2 => t a r3/2 also, v = perigee, apogee
#2: Orbit plane bisects earth because gravity is radial and it must balance centripetal acceleration.
#3: Orbits are not tracks - knowing instantaneous position and velocity fully determines orbit
#4: Orbit plane wrt sun changes slowly if at all.
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6. Orbits are Dynamic.
Ground Rule #1 means...
Orbit period is shorter for lower orbits since: w2r + Mg/r2 = constant and w a v/r so v2 a 1/r => w a 1/ r3/2 => t a r3/2
For an eliptic orbit, V is maximum @ perigee, apogee
Geosynchs don’t just “hang” there
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7. Ground Rule #2 means... Must be geosynch @ the equator
Orbit plane bisects earth
Ground Rule #2 means...
Must be the equator
Orbit planes & inclination are fixed
Orbits are not tracks - knowing instantaneous position + velocity fully determines the orbit
Orbit plane wrt sun changes slowly
Launch “windows”: the orbit plane always includes the launch site and the earth’s center. These might need to have an orientation wrt e.g. the sun or have a specific time of day at launch, or be aligned to a target
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8. Orbits are not tracks
Ground Rule #3 means...
Changing Orbit: where new & old orbit intersect, change V to that appropriate to new orbit
If present and desired orbit don’t intersect: join them via an intermediate that does
Do V changes where V is a minimum (at apogee)
Orbit determination: requires a single simultaneous measurement of position + velocity. GPS and / or ground radar can do this. A 1 2 3 B + =
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9. Orbit plane wrt sun changes slowly
Ground Rule #4 means...
Polar, sun synch dawn - dusk orbit… isn’t, after a few months.
Geosynch satellites… don’t remain geosynch on their own.
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10. Getting to (LEO) Orbit
#1: Raise altitude from 0 to 300 km (this is the easy part)
Energy = mgh = 100kg x 9.8 m/s2 x 300,000 m = x 108 kg m2/ s2 [=W-s = J] = 82 kw-hr = x 106 m2/s2 per kg ∆V = (E)1/2 = m/s
#2: Accelerate to orbital velocity, 7 km/s (the harder part)
∆V (velocity) = m/s (80% of V, 94% of energy)
∆V (altitude) = 1715 m/s
∆V (total) = 8715 m/s
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11. Getting to (LEO) Orbit - from an airplane
Airplane is at 10 km altitude and 200 m/s airspeed
#1: Raise altitude from 10 to 300 km
Energy = mgh = 100kg x 9.8 m/s2 x (300,000 m - 10,000 m) ∆V = (E)1/2 = m/s (98% of ground based launch ∆V) (or 99% of ground based launch energy)
#2: Accelerate to orbital velocity, 7 km/s from 0.2 km/s airplane
∆V (velocity) = m/s (97% of ground ∆V, 99% of energy)
∆V (∆H) = m/s (98% of ground ∆V, 99% of energy)
∆V (total, with airplane) = 8486 m/s
∆V (total, from ground) = 8715 m/s
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12. Common µspacecraft Orbits
Remote Sensing:
Favors polar, LEO, 2x daily coverage (lower inclinations = more frequent coverage).
Harmonic orbit: period x n = 24 hours
LEO Comms:
Same! - multiple satellites reduce contact latency. Best if not in same plane.
Equatorial:
Single satellite provides latency < 100 minutes
• Sun Synch:
Dawn/Dusk offers Constant thermal environment & constant illumination (but may require ∆V to stay sun synch)
Elliptical:
Long dwell at apogee, short pass through radiation belts and perigee...
Molniya. Low E way to achieve max distance from earth.
MEO:
Typically 10,000 km. TRW Odyssee comms cluster, GPS.
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13. ∆V Directory Shuttle to 500 km circular: 300 m/s LEO to GTO: 2000+ m/s
GTO to GEO: m/s
LEO Inclination change: 7000 m/s x sin (∆angle)
Typical orbit maintenance: 100 to 300 m/s (sun synch or geosynch, per year) + =
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14. Orbit Description*
Sir Isaac Newton used his Second Law of Motion combined with his Law of Gravitation to describe the motion of a small body orbiting about a much larger body. The 2-body equation of motion (∑E=constant) is:
r + (m /r3) r = 0
where m = km3 / sec2 (gravitational parameter for Earth)
r = rE + h (mean radius of Earth plus altitude)
rE = km (mean radius of Earth)
To solve for the position vector, r, we need 6 constants of integration (second order equation in 3 dimensional space). Therefore, we can find the current position and velocity based on a previous known position and velocity.
* Thanks to Rob Baltrum
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15. Orbit Description - 2
A solution to the 2-body equation of motion is a polar equation of a conic section given by:
r = a(1-e2) / (1 + e cos n)
The position in the orbital plane, r, depends on the values of a (semi-major axis), e(eccentricity), and n (polar angle or true anomaly). The conic section equation describes 4 major type of orbits:
circle e = 0 a = radius
ellipse 0< e < 1 a > 0
parabola e = 1 a = ∞
hyperbola e > 1 a < 0
Therefore, if the polar equation for a conic section can be used to describe a spacecraft position in the orbital plane (3 terms - a, e, n) we then only need to describe the orientation of the orbit about the Earth (or central body).
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16. The 6 Classical Orbital Elements
Orbit Description - 3
The 6 Classical Orbital Elements
The first 3 elements describe the type of conic section the orbit represents. The second 3 elements describe the orientation of the orbit with respect to the Earth (or central body).
a, semi-major axis - a constant distance ( in kilometers) which describes the size of the orbit.
e, eccentricity - a dimensionless constant which describes the shape of the orbit.
(elliptical, circular, parabolic, hyperbolic)
n, true anomaly - the angle in degrees, measured in the direction and plane of the spacecraft’s motion, between the perigee point to the position vector of the spacecraft at any time. This determines where in the orbit the S/C is at a specific time.
i, inclination - the angle in degrees between the angular momentum vector and the unit vector in the Z-direction. This is a measure of how the orbit plane is ‘tilted’ with respect to the Equator.
Ω, longitude or right ascension of the ascending node - the angle in degrees from the Vernal Equinox (line from the center of the Earth to the Sun on the first day of autumn in the Northern Hemisphere) to the ascending node along the Equator. This determines where the orbital plane intersects the Equator (depends on the time of year and day when launched).
w, argument of perigee - the angle in degrees, measured in the direction and plane of the spacecraft’s motion, between the ascending node and the perigee point. This determines where the perigee point is located and therefore how the orbit is rotated in the orbital plane.
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17. Orbital Characteristics
Orbit Description - 4
Orbital Characteristics
From the 6 orbital elements other characteristics about the spacecraft orbit can be derived.
Perigee radius (closest approach), rp = a (1-e)
Apogee radius (farthest distance), ra = a (1+e)
Orbital period, T = 2π (a3 / m) 1/2
For a circular orbit,
rp = ra = rcir
The constant orbital velocity can be found as:
Vcir = (m / rcir)1/2
Beta angle is the angle in degrees between the Sun vector and the normal to the orbital plane. This angle is critical for power and thermal analysis to determine the amount of time in the the Sun and in eclipse behind the Earth.
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18. Orbit Description - 5
Example - A Shuttle Orbit (LEO / low inclination)
Shuttle generally launches directly into a circular orbit from Kennedy Space Center (Latitude 28.4°). to an altitude of h=300 km (~ 162 nmi).
Since the Shuttle goes directly into its orbit, the inclination is equal to the launch facility latitude, i = 28.4°. The orbit is circular, therefore the eccentricity is zero, e = 0. The altitude is the same throughout the orbit since it is circular (perigee and apogee radius are equal).
rcir = rE + h = km
rcir = km
The circular radius is also the semi-major axis,
a = rcir = km
The orbital period is
T = 2π (a3/µ)1/2
T = 2π[ ( km)3/ ( km3/s2) ]1/2
T = s = minutes
The circular velocity is
Vcir = (µ / rcir) 1/2 = [ ( km3/s2) / ( km) ] 1/2
= km/s (~ mph)
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