Orbital Mechanics for Engineering Students 4th. Edition by Howard D. Curtis | 9780081021330 | 008102133X

Mechanical Engineering

Orbital Mechanics for Engineering Students

166 SOLVED PROBLEMS

1 SOLVED PROBLEMS

Question: 8.6

A spacecraft departs earth with a velocity perpendicular to the sun line on a flyby mission to Venus. Encounter occurs at a true anomaly in the approach trajectory of 30°. Periapsis altitude is to be 300 km. (a) For an approach from the dark side of the planet, show that the postflyby orbit is as ...

Verified Answer:

The following data are found in Tables A.1 and A.2...

Question: 8.5

After a Hohmann transfer from earth to Mars, calculate (a) the minimum delta-v required to place a spacecraft in orbit with a period of 7 h (b) the periapsis radius (c) the aiming radius (d) the angle between periapsis and Mars’ velocity vector. ...

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The following data are required from Tables A.1 an...

Question: 11.12

Calculate the net moment on the solar panel of Examples 11.2 and 11.8 (Fig. 11.17). ...

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

Question: 11.11

Calculate the principal moments of inertia about the center of mass and the corresponding principal directions for the bent rod in Fig. 11.16. Its mass is uniformly distributed at 2 kg/m. ...

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The mass of each of the four slender rod segments ...

Question: 11.10

Find the moments of inertia of the rod in Example 11.5 (Fig. 11.15) about its center of mass G. ...

Verified Answer:

From Example 11.5,

\left[ I _A\right]=\left...

Question: 11.9

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 [I]...

Question: 8.7

Find the distance between earth and Mars at 12 h UT on August 27, 2003. Use Algorithm 8.1. ...

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Step 1: According to Eq. (5.48), the Julian day nu...

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 ...

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

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

r_{\t...

Question: 8.4

A spacecraft is launched on a mission to Mars starting from a 300-km circular parking orbit. Calculate (a) the delta-v required, (b) the location of perigee of the departure hyperbola, and (c) the amount of propellant required as a percentage of the spacecraft mass before the delta-v burn, assuming ...

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From Tables A.1 and A.2, we obtain the gravitation...

Question: 8.2

Calculate the minimum wait time for initiating a return trip from Mars to earth. ...

Verified Answer:

From Tables A.1 and A.2 we have

\begin{alig...