Problem 5.1 The geocentric equatorial position vectors of a satellite at three separate times are
r
15887ˆ
I3520ˆ
J1204 ˆ
K (km)
r25572ˆ
I3457ˆ
J2376 ˆ
K (km)
r
35088ˆ
I3289ˆ
J3480 ˆ
K (km)
.
Use Gibbs’ method to find
v2
.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5
Problem 5.2 Calculate the orbital elements and perigee altitude of the space object in the previous
problem.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5
Problem 5.3 At a given instant the altitude of an earth satellite is 600 km. Thirty minutes later the alti-
tude is 1000 km and the true anomaly has increased by 120. Find the perigee altitude.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5
Problem 5.4 At a given instant, the geocentric equatorial position vector of an earth satellite is
r
13600ˆ
I4600ˆ
J3600 ˆ
K (km)
.
Thirty minutes later the position is
r
2 5500ˆ
I6240ˆ
J5200 ˆ
K (km)
.
Calculate
v1
and
v2
.
398,600 1110.356 s
Problem 5.5 Compute the perigee altitude and inclination for the previous problem.
h
59970.52
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5
Problem 5.6 At a given instant, the geocentric equatorial position vector of an earth satellite is
r
15644ˆ
I2830ˆ
J4170 ˆ
K (km)
.
Twenty minutes later the position is
r
2 2240ˆ
I7320ˆ
J4980 ˆ
K (km)
.
Calculate
v1
and
v2
.
v2
Problem 5.7 Compute the orbital elements and perigee altitude for the previous problem.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5
Problem 5.8 Calculate the Julian day (JD) number for the following epochs:
(a) 5:30 UT on August 14, 1914.
(b) 14:00 UT on April 18, 1946.
(c) 0:00 UT on September 1, 2010.
(d) 12:00 UT on October 16, 2007.
Problem 5.9 Calculate the number of days from 12:00 UT on your date of birth to 12:00 UT on today’s
date.
Problem 5.10 Calculate the local sidereal time (in degrees) at:
(a) Stockholm, Sweden (east longitude 18°03) at 12:00 UT on January 1, 2008.
(b) Melbourne, Australia (east longitude 144°58) at 10:00 UT on December 21, 2007.
(c) Los Angeles, California (west longitude 118°15) at 20:00 UT on July 4, 2005.
(d) Rio de Janeiro, Brazil (west longitude 43°06) at 3:00 UT on February 15, 2006.
(e) Vladivostok, Russia (east longitude 131°56) at 8:00 UT on March 21, 2006.
