A spherical satellite has 12 identical monopropellant thrust chambers for attitude

control with the following performance characteristics: thrust (each unit): 5 lbf; Is
(steady state or more than 2 sec): 240 sec; Is (pulsing duration 20 msec): 150 sec;
Is (pulsing duration 100 msec): 200 sec; satellite weight: 3500 lbf; satellite diameter:
8 ft; satellite internal density distribution is essentially uniform; disturbing torques,
Y and Z axes: 0.00005 ft-lbf average; disturbing torque, for X axis: 0.001 ft-lbf
average; distance between thrust chamber axes: 8 ft; maximum allowable satellite
pointing position error: ±1◦. Time interval between pulses is 0.030 sec.
(a) What would be the maximum and minimum vehicle angular drift per hour if no
correction torque were applied?

good

To find the maximum and minimum vehicle angular drift per hour, we need to calculate the torque exerted by the thrust chambers and the resulting angular drift.

The torque exerted by each thrust chamber can be calculated using the equation:

Torque = Thrust * Distance between thrust chamber axes

Given that the thrust of each unit is 5 lbf, and the distance between thrust chamber axes is 8 ft, we can calculate the torque exerted by each thrust chamber:

Torque = 5 lbf * 8 ft = 40 ft-lbf

Since there are 12 identical thrust chambers, the total torque exerted by all the thrust chambers would be:

Total Torque = 40 ft-lbf * 12 = 480 ft-lbf

Now, we can calculate the resulting angular drift using the equation:

Angular Drift = Torque / (Satellite Weight * Satellite Diameter)

Given that the satellite weight is 3500 lbf and the satellite diameter is 8 ft, we can calculate the angular drift:

Angular Drift = 480 ft-lbf / (3500 lbf * 8 ft) = 0.017 radians

To convert the angular drift to degrees per hour, we multiply by the conversion factor:

Degrees per Hour = 0.017 radians * (180 degrees / pi radians) * (3600 seconds / 1 hour) = 584.3 degrees per hour

Therefore, the maximum and minimum vehicle angular drift per hour, if no correction torque is applied, is approximately ±584.3 degrees per hour.

To calculate the maximum and minimum vehicle angular drift per hour, we need to consider the disturbing torques and the performance characteristics of the satellite's thrust chambers.

First, let's calculate the total torque acting on the satellite due to the disturbing torques.

The average disturbing torque for the Y and Z axes is given as 0.00005 ft-lbf. Since the satellite has 12 identical monopropellant thrust chambers, the total torque caused by the disturbing torques in the Y and Z axes is:

Total Torque (Y and Z axes) = 0.00005 ft-lbf * 12 = 0.0006 ft-lbf

The average disturbing torque for the X axis is given as 0.001 ft-lbf. Hence, the total torque caused by the disturbing torque in the X axis is:

Total Torque (X axis) = 0.001 ft-lbf

Next, let's calculate the maximum and minimum angular drift per pulse.

The time interval between pulses is given as 0.030 sec. For a pulsing duration of 20 msec (0.02 sec), the specific impulse Is is given as 150 sec. Using this information, we can calculate the maximum and minimum angular drift per pulse:

Maximum angular drift per pulse = (Total Torque * Is) / (satellite weight) = ((0.001 ft-lbf * 150 sec) / 3500 lbf) = 0.043°

Similarly, for a pulsing duration of 100 msec (0.1 sec), the specific impulse Is is given as 200 sec. Using this information, we can calculate the maximum and minimum angular drift per pulse:

Minimum angular drift per pulse = (Total Torque * Is) / (satellite weight) = ((0.001 ft-lbf * 200 sec) / 3500 lbf) = 0.057°

Now, let's calculate the maximum and minimum vehicle angular drift per hour.

There are 3600 seconds in an hour. Therefore, for a pulsing duration of 20 msec, the maximum and minimum vehicle angular drift per hour are:

Maximum vehicle angular drift per hour (20 msec) = (3600 sec / 0.03 sec) * 0.043° = 5160°

Similarly, for a pulsing duration of 100 msec, the maximum and minimum vehicle angular drift per hour are:

Minimum vehicle angular drift per hour (100 msec) = (3600 sec / 0.03 sec) * 0.057° = 6840°

So, the maximum vehicle angular drift per hour (without correction torque) is 5160°, and the minimum vehicle angular drift per hour is 6840°.