EAS 4510
HW #3
Spring 11
1. Develop the DCM that transforms representations in the ECI frame to an SEZ frame located
longitude Lo and latitude LA .
2. The period of a circular orbit was developed as TP
2
n
2
R
3
2
R3
which can be expressed as a function
Test #1
EAS 4300 Aero Propulsion
February 13, 2004
Two hours, open book/notes.
Problem 1 (40).
1
2
3
The thrust nozzle for a highspeed airbreathing engine is shown. At State 1, the flow is
subsonic, the stagnation pressure is 2 atm, and the stagnation te
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A Review of the Evolution of Aircraft Piston Engines
Volume 1, N umber 4 (End of Vol
EAS 4510
HW #9
Spring 08
1. Prob. 7.5 (Prussing & Conway)
2. The position and velocity vectors of the Shuttle (STS63) at t=38:14:34:59.99 GMT are
ECI
ECI
R = 0.8566 I + 0.8195 J + 0.8976 K DU ,
v = 0.2138 I 0.6757 J + 0.4196 K DU/TU .
In order to rendezv
EAS 4510
HW #10
1.
Spring 08
(a) Show that the Lagrange parameters for the minimum energy trajectory between P and
1
P2 satisfy min = and min = 0 .
(b) Show that if f = , the time of flight associated with the minimum energy orbit is
TOF =
nmin
where nmin
EAS 4510
HW #7
Spring 08
14. Augment the MATLAB program developed in HW #6 to perform orbit propagation.
(a)
First, using the orbital elements, develop the new position and velocity vectors
PQW
PQW
coordinatized in the PQWframe (i.e.,
r and
v ) and then
EAS 4510
HW #8
Spring 08
1. Show that circularization of an elliptical orbit is more fuel efficient if performed at the
apoapsis (i.e., vcirA < vcirP )
2. Show that escape from an elliptical orbit is more fuel efficient if performed at the periapsis
(i.e.
EAS 4510
HW #6
Spring 08
15. Develop a Matlab program that computes the orbital elements ( a , e , i , , , f 0 ) given
(i) position and velocity vectors or (ii) three position vectors (Gibbs method). The output
from you program should CLEARLY display the
EAS 4510
HW #4
1.
The trajectory equation developed in class has the form
e= e =
1
Spring 08
r=
p
1 + e cos f
where
B and f (true anomaly) is the angle between the position vector r and the
reference direction B . Using differential calculus, mathematical
EAS 4510
HW #3
Spring 08
1. If Ri = xi i + yi + zi k denotes the inertial position (i.e., position wrt O) of body mi , then
j
the position of m j with respect to mi is r ij = R j Ri . Since the gravitational force field is
conservative, then there exists
f
Apoapsis
e
1
Periapsis
Line of apsides
Line of nodes
Descending node
Position of
orbiting body
Z
X
i
Classical Orbital Elements
Y
Reference direction
Vernal Equinox
(First point of Aries)
n
Ascending node
orb_elements
Geocentric orbits Equatorial
Helioc
EAS 4510
HW #1
Spring '08
1. What are free vectors? What are bound vectors? Give an example of each.
2. Given four vectors a , b , c , and d , without using component definitions for each vector,
validate the identity: ( a b ) ( c d ) = ( a c ) ( d b ) (
EAS 4510 Final Exam
ClosedBook Section (100pts.)
Spring '06
NAME: _
INSTRUCTIONS
Complete all questions in the space provided. If additional space is required, use a separate sheet
of paper. Work as neatly as possible. Whenever possible, show all work fo
EAS 4510 Exam #2
OpenBook Section (50pts.)
Spring '07
NAME: _
INSTRUCTIONS: For maximum credit work as neatly as possible and show all relevant work.
Use only ONE SIDE of your answer sheets with each question beginning on a new page. The
order of your an
EAS 4510 Exam #1
OpenBook Section (50pts.)
Spring '07
NAME: _
INSTRUCTIONS: For maximum credit work as neatly as possible and show all relevant work.
Use only ONE SIDE of your answer sheets with each question beginning on a new page. The
order of your an
EAS 4510 Final Exam
ClosedBook Section (100pts.)
Spring '07
NAME: _
INSTRUCTIONS
Complete all questions in the space provided. If additional space is required, use a separate sheet
of paper. Work as neatly as possible. Whenever possible, show all work fo
EAS 4510
Astrodynamics
Patched Conic 1
Planet Size Perspective
FitzCoy
University of Florida
EAS 4510
Astrodynamics
EarthMars Hohmann Transfer
Velocity conditions at transition between
conics (i.e., at planets sphere of influence)
r1 = 1.000AU
v Helio
Lamberts Problem
EAS 4510
Astrodynamics
Problem Statement:
Given two points in space (P1 and P2) defined by the geometry below and the time of
flight between these point, determine the trajectory connecting the points (i.e.,
determine the semimajor axis
EAS 4510
Astrodynamics
Impulsive Maneuvers
Problem Statement:
Often times, it is necessary to modify an existing orbit to change either its size, shape,
and/or orientation. This is due either to errors in the orbit parameters of the insertion
orbit from t
Time/Position Relationships
Keplers Equation:
a (t T) = E e sin E
(t T) = e sinh F F
M = n( t T ) =
a
M = n( t T ) =
(Elliptic)
3
(Hyperbolic)
3
t = r x + r 0 v 0 C(x2)x 2 + (1 r 0)S(x2)x 3
0
a
a
a
(Universal)
y sin y , y > 0
y
y
y2
S(y) = 1 + =
3! 5!
EAS 4510 Final Exam
ClosedBook Section (100pts.)
Spring '05
NAME: _
INSTRUCTIONS
Complete all questions in the space provided. If additional space is required, use a separate sheet
of paper. Work as neatly as possible. Whenever possible, show all work fo
EAS 4510 Final Exam
Spring 03
ClosedBook (100pts.)
NAME: _
INSTRUCTIONS
Complete all questions in the space provided. If additional space is required, use a separate sheet of
paper. Work as neatly as possible. Whenever possible, show all work for maximum
d = m r cos f
r
, e = r =
d
m r cos f
p
em
r=
=
1 + e cos f
1 + e cos f
Apoapsis
2
2
e= a b
a
F*
a
b
C
Definition:
A conic section is the loci of points whose distance from a fixed
point F and a from a fixed line DD have a constant positive ratio.
(i.e.,
Orbit Mechanics Parameters & Units
EAS 4510
Astrodynamics
Canonical Units:
A set of normalized units (distance and/or time) defined with respect to the
central reference body. For all planetocentic orbits, the normalization is done
such that the distance
EAS 4510
Astrodynamics
Patched Conic 1
Miscellaneous Planetary Information
FitzCoy
University of Florida
EAS 4510
Astrodynamics
Planet Orbits (partial)
RMercury 0.3871 AU
RVenus 0.7233 AU
REarth 1.0000 AU
RMars 1.5237 AU
AU
RJupiter 5.2028 AU
Mercury
Ve
EAS 4510
HW #4
Spring 11
1. For a particle on mass m moving with constant rectilinear motion, show that its angular
momentum about an arbitrary fixed point O is conserved. Provide a geometric interpretation.
2. Two masses are in a repulsive central force
EAS 4510
HW #1 & 2
Spring 11
Due: 1/21/11
1. What is free vector? What is a bound vector? Give an example of each.
2. Prove the Triangle Inequality: If a b c , then a b c .
3. Prove the Schwartz Inequality: a b a b .
4. Given three vectors a , b , and c ,