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Week 9 Notes

by: Austin Frownfelter

Week 9 Notes 0087

Austin Frownfelter

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About this Document

These are the notes for week 8. They are mostly a transcript of the important notes from the lectures this Tuesday and Thursday. Included are comprehensive equations, formulas, diagrams, images and...
Basics of Space Flight
Dr. Regina Schulte-Ladbeck
Class Notes
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This 4 page Class Notes was uploaded by Austin Frownfelter on Tuesday November 3, 2015. The Class Notes belongs to 0087 at University of Pittsburgh taught by Dr. Regina Schulte-Ladbeck in Summer 2015. Since its upload, it has received 25 views. For similar materials see Basics of Space Flight in Astronomy at University of Pittsburgh.


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Date Created: 11/03/15
Trajectories  ­ Flight paths through space  ­ Conic Sections          ­ Figure 8 (free return trajectories)          ­ Spiral (Electric propulsion ­ solar sails)          Sub­orbital trajectory  ­ Reach space, without completing a full orbit  ­ Example: For V2 with horizontal distance of 330 km,  Δv = 1.6 km ≈ 3,580mph  s   Orbital Trajectories  ­ Kepler and Newton  ­ v = 2πr  P ­ v = GM   √ r ­ GM = 4π 22  r2 4π2 3 ­ P = GM r   ­ Kepler’s 3rd law    Video:   ­ Planet is one of foci of the orbit  ­ Fastest point is at apogee, slowest point is at perigee  ­ Square of the Period of orbit is proportional to the cube of its semi­major axis  ­ Orbital Elements:  ­ a = semi­major axis = size  ­ e = eccentricity = shape  ­ i = inclination = tilt  ­ Ω = right ascension of ascending node = pin  ­ ω = argument of perigee = twist  ­ v = mean anomaly = current position in orbit  ­ Burns:  ­ Posigrade burn = orbit raised everywhere except at burn point  ­ retrograde burn = orbit lowered everywhere except at burn point  ­ Hohmann transfer orbit  ­ Perigee at one orbit  ­ Apogee at other  ­ Uses the least fuel, most efficient, but time consuming  ­ Molniya orbit  ­ Change the eccentricity to increase coverage time of a certain area  ­ Sun­synchronous orbit  ­ The craft sees the same amount of time every orbit  ­ Orbital Perturbations  ­ Earth’s non­spherical shade and other bodies can modify an orbit  ­ Too much of a change requires more burn, else the craft will fall    Post­video:  Characteristics  ­ Semi­major axis, or orbital altitude  ­ Low Earth Orbit  ­ Under 2000 km, or 1240 miles  ­ Medium Earth Orbit  ­ Between 2000 km and 35,786 km, or 122,236 miles  ­ High Earth Orbit  ­ Greater than 35,786 km  ­ Eccentricity  ­ Inclination  ­ Orbital Direction  ­ With spin of Earth (prograde orbit)  ­ Against spin of Earth (retrograde orbit)  ­ Synchronicity  ­ What multiple of the planet’s rotation period is the satellite’s orbital period  ­ 1:1 = synchronous, orbits once per day  ­ Special case:  ­ Geostationary orbit, satellite “hovers” over one point, always in  zenith of observer underneath    ­ Launch Window  ­ Time you can launch  ­ Affected by mission profile (all launch constraints)  ­ Time of day (sunlight)  ­ Weather/Visibility  ­ Launch Azimuth  ­ Direction of Launch  ­ Affected by mission profile  ­ Latitude of launch site (distance from equator)  ­ Safety constraints (cannot drop stages on land)  ­ Orbital inclination will always be greater than the latitude of the launch site,  Except if azimuth is exactly west/east, which the inclination will be equal    Orbital Maneuvers  ­ Need Δv ­ thrust, propellant = money  ­ Changing orbital altitude  ­ Apogee will increase, except at burn  point  ­ Orbital rendezvous ­ “Target” and “Chaser”  ­ Chaser and Target must have the  same inclination  ­ Must have the same altitude  ­ Chaser’s orbit must be synchronized  with the target’s orbit    ­ If every part of the orbit is the same, then the phase angle (angle between the 2) will  always stay the same.  How do they catch up?  ­ Put the chaser in a phasing orbit.    ­ Increase the apogee (Δv), so when the chaser returns to its burn point  (where the 2 orbits intersect), the angle is 0, and they meet.  ­ Requires 2 burns of the chaser, 1 to raise the phase orbit, the 2nd to  return the orbit back  ­ “Proximity Operations”  ­ How do we do this with the least fuel?  ­ Hohmann transfer orbit, minimal Δv  ­ Used to get one circular orbit to  another  ­ Used for Earth orbits and  Interplanetary travel    ­ For transferring planets, there is a  small window of opportunity to  make this transfer because of the  planetary alignment                Gravity Assist  ­ Add or subtract Δv using the gravity of a planet  ­ Because a planet is already in an orbit, you can use the  gravity to pull it along, giving it more velocity.  The same  works to slow it down  ­ Example: Jupiter slingshot  ­ Voyager space probes used gravity assists of the  planets to get farther in the solar system faster    Free­return trajectory  ­ Uses gravity to turn a spacecraft around  ­ “Free” meaning no burns required  ­ Analogy: Boomerang    Constant Thrust Trajectory  ­ Depart from Earth orbit using constant, low  thrust  ­ Engines:  ­ Ion engine  ­ Solar Sail  ­ Spiral orbit  ­ Example:  ­ Dawn to Vesta and Ceres 


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