Orbital Mechanics for Engineering Students 3rd. Edition by Howard D. Curtis | 9780080977478 | 0080977472

Mechanical Engineering

Orbital Mechanics for Engineering Students

2 SOLVED PROBLEMS

157 SOLVED PROBLEMS

Question: 8.1

Calculate the synodic period of Mars relative to that of the earth. ...

Verified Answer:

In Table A.1 we find the orbital periods of earth ...

Question: 8.3

Calculate the radius of the earth’s sphere of influence. ...

Verified Answer:

In Table A.1 we find

m_{\text {earth }}=5.9...

Question: 9.11

Calculate the principal moments of inertia about the center of mass and the corresponding principal directions for the bent rod in Figure 9.16. Its mass is uniformly distributed at 2 kg/m. ...

Verified Answer:

The mass of each of the rod segments is

m_1...

Question: 8.10

In Example 8.8, calculate the delta-v required to place the spacecraft in an elliptical capture orbit around Mars with a periapsis altitude of 300 km and a period of 48 h. Sketch the approach hyperbola. ...

Verified Answer:

From Tables A.1 and A.2, we know that

\begi...

Question: 8.9

In Example 8.8, calculate the delta-v required to launch the spacecraft onto its cruise trajectory from a 180 km circular parking orbit. Sketch the departure trajectory. ...

Verified Answer:

Recall that

\begin{aligned}& r_{\text {...

Question: 8.8

A spacecraft departs earth’s sphere of influence on November 7, 1996 (0 h UT), on a prograde coasting flight to Mars, arriving at Mars’ sphere of influence on September, 12, 1997 (0 h UT). Use Algorithm 8.2 to determine the trajectory and then compute the hyperbolic excess velocities at departure ...

Verified Answer:

Step 1: Algorithm 8.1 yields the state vectors for...

Question: 6.4

Spacecraft at A and B are in the same orbit (1). At the instant shown in Figure 6.11 the chaser vehicle at A executes a phasing maneuver so as to catch the target spacecraft back at A after just one revolution of the chaser’s phasing orbit (2). What is the required total delta-v? ...

Verified Answer:

We must find the angular momenta of orbits 1 and 2...

Question: 9.9

Find the principal moments of inertia and the principal axes of inertia of the inertia tensor. [I] = [ 100 -20 -100 -20 300 -50 -100 -50 500] kg.m² ...

Verified Answer:

We seek the nontrivial solutions of the system [la...

Question: 9.21

(a) Write down the quaternion for a rotation about the x-axis through an angle θ. (b) Obtain the corresponding direction cosine matrix. ...

Verified Answer:

(a) According to Eqn (9.146),

q =\sin \cfra...

Question: 9.20

Figure 9.24 shows a rotating platform on which is mounted a rectangular parallelepiped shaft (with dimensions b, h, and l ) spinning about the inclined axis DE. If the mass of the shaft is m, and the angular velocities ωp and ωs are constant, calculate the bearing forces at D and E as a function of ...

Verified Answer:

The inertial XYZ frame is centered at O on the pla...

Question: 9.12

Calculate the net moment on the solar panel of Examples 9.2 and 9.8 (Figure 9.17). ...

Verified Answer:

Since the comoving frame is rigidly attached to th...

Question: 9.8

For the satellite of Example 9.2, which is reproduced in Figure 9.13, the data are as follows: N = 0.1 rad/s and θ = 0.01 rad/s, in the directions shown: θ = 40° and d0 = 1.5 m. The length, width, and thickness of the panel are l = 6 m, w = 2 m, and t = 0.025 m. The uniformly distributed mass of ...

Verified Answer:

We can treat the panel as a thin parallelepiped. T...