978-0078112829 Chapter 5 Solution Manual Part 3

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5

Problem 5.19 A sea-level tracking station at latitude +29 makes the following observations of a satel-

lite at the given times.

Topocentric Topocentric

Time Local sidereal time Right ascension Declination

(min) (degrees) (degrees) (degrees)

0.0 90 15.0394 20.7487

1.0 90.2507 25.7539 30.1410

2.0 90.5014 48.6055 43.8910

Use the Gauss method without iterative improvement to estimate the state vector of the satellite.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5

Problem 5.20 Refine the estimate in the previous problem using iterative improvement.

Problem 5.21 Calculate the orbital elements from the state vector obtained in the previous problem.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5

Problem 5.22 The position vector

R

of a tracking station and the direction cosine vector

ˆ



of a satellite

relative to the tracking station at three times are as follows:

t10 min

R1 1825.96ˆ

I3583.66ˆ

J4933.54 ˆ

K km

 

ˆ



1 0.301687ˆ

I0.200673ˆ

J0.932049 ˆ

K

t21 min

R2 1816.30ˆ

I3575.63ˆ

J4933.54 ˆ

K km

 

ˆ

2 0.793090ˆ

I0.210324ˆ

J0.571640 ˆ

K

t32 min

R3 1857.25ˆ

I3567.54ˆ

J4933.54 ˆ

K km

 

ˆ



3 0.873085ˆ

I0.362969ˆ

J0.325539 ˆ

K

Use the Gauss method without iterative improvement to estimate the state vector of the satellite at the

central observation time.

฀

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5

Problem 5.23 Refine the estimate in the previous problem using iterative improvement.

Problem 5.24 Calculate the orbital elements from the state vector obtained in the previous problem.

Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 5

Problem 5.25 A tracking station at latitude 60°N and 500m elevation obtains the following data:

Topocentric Topocentric

Time Local sidereal time Right ascension Declination

(min) (degrees) (degrees) (degrees)

0.0 150 157.783 24.2403

5.0 151.253 159.221 27.2993

10.0 152.507 160.526 29.8982

Use the Gauss method without iterative improvement to estimate the state vector of the satellite.

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