###### Orbital Mechanics For Engineering Students

114 SOLVED PROBLEMS

1 SOLVED PROBLEMS

Question: 5.11

## A tracking station is located at Φ = 40° north latitude at an altitude of H = 1 km. Three observations of an earth satellite yield the values for the topocentric right ascension and declination listed in the following table, which also shows the local sidereal time θ of the observation site. Use ...

Data for Example 5.11 Observation Time (second...
Question: 10.9

## Use Equation 10.136 to obtain the equations of motion of a torque-free, axisymmetric, dual-spin satellite, such as the one shown in Figure 10.21. ...

M_{G_{net}}=\left[\frac{dH^{(v)}_{G}}{dt})_...
Question: 11.4

## (a) Find the extrema of the function z = −x² − y². (b) Find the extrema of the same function under the constraint y = 2x + 3. ...

(a) To find the extrema we must use Equations 11.6...
Question: 10.14

## The uniform, monolithic 10 000 kg slab, having the dimensions shown in Figure 10.30, is in a circular LEO. Determine the orientation of the satellite in its orbit for gravity gradient stabilization, and compute the periods of the pitch and yaw/roll oscillations in terms of the orbital period T. ...

According to Figure 9.9(c), the principal moments ...
Question: 10.13

## A satellite is in torque-free motion. A control moment gyro, spinning at the constant rate ωs, is gimbaled about the spacecraft y and z axes, with φ = 0 and θ = 90° (cf.Figure 10.25). The spacecraft angula velocity is ω = ωzk. If the spin axis of the gyro, initially along the x direction, is ...

Substituting \omega_{x} ={\omega}_{y}=\dot{...
Question: 10.12

## A satellite is in torque-free motion (MGnet = 0).A non-gimbaled gyro (momentum wheel) is aligned with the vehicle’s x axis and is spinning at the rate ωs0. The spacecraft angular velocity is ω = ωxˆi. If the spin of the gyro is increased at the rate ω˙s,find the angular acceleration of the ...

Using Figure 10.25 as a guide, we set  \phi...
Question: 10.11

## The communications satellite is in a circular earth orbit of period T. The body z axis always points towards the earth, so the angular velocity about the body y axis is 2π/T. The angular velocities about the body x and z axes are zero. The attitude control system consists of three momentum wheels ...

The absolute angular velocity of the xyz frame is ...
Question: 10.10

## A spacecraft in torque-free motion has three identical momentum wheels with their spin axes aligned with the vehicle’s principal body axes. The spin axes of momentum wheels 1, 2 and 3 are aligned with the x, y and z axes, respectively. The inertia tensors of the rotationally symmetric momentum ...

The absolute angular velocity ω of the spacecraft ...
Question: 10.8

## A satellite is to be completely despun using a two-mass yo-yo device with tangential release. Assume the spin axis of moment of inertia of the satellite is C = 200 kg · m² and the initial spin rate is ω0 = 5 rad/s. The total yo-yo mass is 4 kg, and the radius of the spacecraft is 1 meter. Find (a) ...

(a) From Equation 10.104, K=1+\frac{C}{mR^{...
Question: 10.7

## A spacecraft of mass m and with the dimensions shown in Figure 10.15 is spinning without precession at the rate ω0 about the z axis of the principal body frame. At the instant shown in part (a) of the figure, the spacecraft initiates a coning maneuver to swing its spin axis through 90°, so that at ...

From Tables A.1 and A.2 we have \begin{alig...