0.00064734
0
0.00064734
Problem 7.13 A space station is in circular orbit 2 of radius R. A spacecraft is in coplanar circular orbit
1 of radius
R
r
. At
t0
the spacecraft executes an impulsive maneuver to rendezvous with the space
station at time
tf
= one-half the period
T0
of the space station. If
u0
0
, find
(a) the initial position of the spacecraft relative to the space station, and
(b) the relative velocity of the spacecraft when it arrives at the target. Sketch the rendezvous tra-
jectory relative to the target.
฀
=
0 0 nsin nt
0 0 0
X
Y
1
2
r
R
t = 0
t = T0/2
cos nt 2 sin nt 0
1 0 0
0
4n
0
4n
0
2
T0
0
0
y
x
t = 0
3
4
r
r
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 7
Problem 7.14 If
u0
0
, calculate the total delta-v required for rendezvous if
r
0
y0
ˆ
j
,
v0
0
and
tf
= the period of the circular target orbit. Sketch the rendezvous trajectory relative to the target.
0
n
y0




6
6
3
3T
Problem 7.15 A GEO satellite strikes some orbiting debris and is found 2 hours afterwards to have
drifted to the position
r 10ˆ
i10ˆ
jkm
 
relative to its original location. At that time the only slightly
damaged satellite initiates a two-impulse maneuver to return to its original location in 6 hours. Find the
total delta-v for this maneuver.
฀
3694 5895
10
0.00177
0.000587
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 7
v2
 vr
r
0
 vv
v0
 
0
Problem 7.16 Design problem.
Problem 7.17 The target A is in a circular earth orbit with mean motion n. The chaser B is directly
above A in a slightly larger circular orbit having the same plane as A’s. What relative initial velocity
v0
is required so that B arrives at the target A at time
tf
= one-half the target’s period?
x
y
B
A
xo
CW frame
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 7
04
n
4
n9.425
n
v0
 7
x0
18.85
x0
04
n
1
7
x0
Problem 7.18 The space station is in a circular earth orbit of radius 6600 km. The space shuttle is also in
a circular orbit in the same plane as the space station. At the instant that the position of the shuttle rela-
tive to the space station, in Clohessy-Wiltshire coordinates, is
r5ˆ
ikm
 
. What is the relative velocity
v
of the space shuttle in m/s?
2n
20.001177 5 50.0088311 km s 8.8311 m s
Problem 7.19 The Space Shuttle and the International Space Station are in coplanar circular orbits. The
space station has an orbital radius R and a mean motion n. The shuttle’s radius is
Rd
d R
 
. If a
two-impulse rendezvous maneuver with
tf  4n
 
is initiated with zero relative velocity in the x–
direction
u0
0
 
, calculate the total delta-v.
0
0.5858
v0
n
 
Problem 7.20 The chaser and the target are in close-proximity, coplanar circular orbits. At
t0
, the
position of the chaser relative to the target is
r
0aˆ
i
. Use the Clohessy-Wiltshire equations to find the
total delta-v required for the chaser to end up in circular orbit 2 at
rf aˆ
i
when
t
n
, where n is
the mean motion of the target.
4
n3
n
0
7 0
6
1
0
3
16 n
n
4
a
2na 1
2na na