978-0078112829 Chapter 4 Solution Manual Part 2

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 4

Problem 4.15 For a spacecraft, the following orbital parameters are given:

e1.5

perigee altitude = 300 km

i35



130



115

Calculate

r

and

v

at perigee relative to (a) the perifocal reference frame and (b) the geocentric equatorial

frame.

Problem 4.16 For the spacecraft of Problem 4.15 calculate

r

and

v

at two hours past perigee relative to

(a) the perifocal reference frame, and; (b) the geocentric equatorial frame.

Problem 4.17 Calculate

r

and

v

for the satellite in Problem 4.5 at time

t050 minutes

. (

t00!

)

Eesin EM

Problem 4.18 For a spacecraft, the following orbital parameters are given:

e1.2

perigee altitude = 200 km

i50



75



80

Calculate

r

and

v

at perigee relative to (a) the perifocal reference frame and (b) the geocentric equatorial

frame.

Problem 4.19 For the spacecraft of Problem 4.18 calculate

r

and

v

at two hours past perigee relative

to (a) the perifocal reference frame and (b) the geocentric equatorial frame.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 4

Problem 4.20 Given that

e0.7

,

h75 000 km2s

, and



25

, calculate the components of velocity

in the geocentric equatorial frame if:

Q

 Xx

0.83204 0.13114 0.53899

0.02741 0.98019 0.19617

0.55403 0.14845 0.81915













Problem 4.21 The apse line of the elliptical orbit lies in the XY plane of the geocentric equatorial frame,

whose Z-axis lies in the plane of the orbit. At B (for which



140

) the perifocal velocity vector is

v

 

x 3.208 0.8288 0





Tkm sec

 

. Calculate the geocentric-equatorial components of the velocity at

B.

฀

Problem 4.22 A satellite in earth orbit has the following orbital parameters:

a7016 km

e0.05

i45



0



20



10

Find the position vector in the geocentric-equatorial frame.

Problem 4.23 Calculate the orbital inclination required to place an earth satellite in a 300 km by 600 km

sun-synchronous orbit.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 4

Problem 4.24 A satellite in a circular, sun-synchronous low earth orbit passes over the same point on

the equator once each day, at 12 o’clock noon. Calculate the inclination, altitude and period of the orbit.

Problem 4.25 The orbit of a satellite around an unspecified planet has an inclination of 45°, and its per-

igee advances at the rate of 6 degrees per day. At what rate does the node line regress?

Problem 4.26 At a given time, the position and velocity of an earth satellite in the geocentric equatorial

frame are

r 2429.1ˆ

I4555.1ˆ

J4577.0 ˆ

K km

 

and

v 4.7689ˆ

I5.6113ˆ

J3.0535 ˆ

K km/ s

 

. Find

r

and

v

precisely 72 hours later, taking into consideration the node line regression and the advance of per-

igee.

39 

1&

Update the transformation matrix between perifocal and geocentric equatorial coordinates:

Problem 4.27 The space shuttle is in a circular orbit of 180 km altitude and inclination 30°. What is the

spacing, in kilometers, between successive ground tracks at the equator, including the effect of earth’s

oblateness?

The change in east longitude of the ascending node after 1 orbit of the satellite is: