BALLISTIC TRAJECTORIES

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THE ESCAPE VELOCITY • A vehicle will escape earth if it has a parabolic (e=1) or hyperbolic (e>1) trajectory • In the case of a parabolic trajectory, the kinetic and potential energies are equal • The escape velocity is larger than orbital velocity by a factor of 2 1/2 • If at burnout V b Km/sec the vehicle will escape earth independent of the direction of motion
Ballistic Missile Trajectory Satellite Orbit THE ELLIPTICAL ORBIT GEOMETRICAL RELATIONS
Page 1 and 2: BALLISTIC TRAJECTORIES It’s time
Page 3 and 4: THE TWO BODY PROBLEM (1)
Page 5 and 6: CONSTANTS OF MOTION (1) SPECIFIC AN
Page 7 and 8: CONSTANTS OF MOTION (3) SPECIFIC EN
Page 9 and 10: Trajectory Equation (2)
Page 11 and 12: Trajectory Equation (4)
Page 13 and 14: SPACE VEHICLE TRAJECTORIES Example:
Page 15 and 16: SOLUTIONS OF THE TWO BODY PROBLEM (
Page 17 and 18: THE ORBITAL VELOCITY (1) = 0
Page 19: GEOSYNCHRONOUS MISSION DESIGN
Page 23 and 24: THE LINK BETWEEN GEOMETRICAL AND PH
Page 25 and 26: • At the end of a rocket launch o
Page 27 and 28: SOLUTION OF EXAMPLE 1
Page 29 and 30: BALLISTIC MISSILE S ! " !
Page 31 and 32: THE HIT EQUATION • Hit equation c
Page 33 and 34: MINIMUM ENERGY TRAJECTORIES
Page 35 and 36: ERROR ANALYSIS
Page 37 and 38: COORDINATES FOR ANALYSIS OF PLANAR
Page 39 and 40: RANGE SENSITIVITY TO BURNOUT TRAJEC
Page 41 and 42: RANGE SENSITIVITY TO BURNOUT VELOCI
Page 43 and 44: TIME OF FLIGHT (AND OTHER PARAMETER
Page 45 and 46: BALLISTIC MISSILE DISPERSION RANGE
Page 47 and 48: BALLISTIC MISSILE DISPERSION SIDE D
Page 49 and 50: # % # " $ # # % # Example: Sigma_R=
Page 51 and 52: TRAJECTORY TYPES Lofted Minimum Ene
Page 53 and 54: LOFTED AND DEPRESSED TRAJ. • RANG
Page 55 and 56: DEPRESSED TRAJECTORIES • Late det
Page 57 and 58: ICBM 9000 KM TRAJECTORIES FOR: 15 d
Page 59 and 60: ! " " & " # $ %
Page 61 and 62: BURN-OUT TIME VS RANGE
Page 63 and 64: AN APPROXIMATE METHOD FOR ESTIMATIN
Page 65 and 66: AN APPROXIMATE METHOD FOR ESTIMATIN
Page 67 and 68: EXAMPLE: 1360 KM TBM • Design a T
Page 69 and 70: LAUNCH MASS(KG) 60000 50000 40000 3
Page 71 and 72:
DOUBLE STAGE TBM
Page 73 and 74:
TWO IDENTICAL STAGES TBM RANGE: 200
Page 75 and 76:
EFFECTS OF EARTH ROTATION Example :
Page 77 and 78:
HITING A MOVING TARGET (EARTH ROTAT
Page 79 and 80:
HITTING A MOVING TARGET FLAT TRAJEC
Page 81 and 82:
HITTING A MOVING TARGET (4) SPACE T
Page 83:
HITTING A MOVING TARGET (6) SPACE T
Page 86 and 87:
EARTH ROTATION EFFECT: VELOCITY REL
Page 88 and 89:
SOLVING THE ROTATING HIT PROBLEM (2
Page 90 and 91:
SOLVING THE ROTATING HIT PROBLEM (4
Page 92 and 93:
IMPORTANT! IMPOTRANT!
Page 94 and 95:
• A missile is fired from: North
Page 96 and 97:
REFERENCES • Free flight of a bal
Page 98 and 99:
• The Two Body Problem 3-24 • E
Page 100:
) 920 150 1000 26 B & & & & & " ' '
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BALLISTIC TRAJECTORIES

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