Week 9 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: https://www.youtube.com/watch?v=Am7EwmxBAW8 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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