Question

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?

The answer should be 0.466 and 0.093 rad/hr.

Answer 1

Solution:-

Given :-

               M = 3500Ibf = 1587.6kg

                r = 8feet = 1.22m

Using the formula ,

      Ma = 2/5 m*r²

Where,

M = satellite weight

r = distance between chamber axes

3500Ibf = 1587.6kg , 8feet = 1.22m

Ma = 2/5 * 1587.6*(1.22)²

Ma = 645.2kg/m²

Or

M = 697.14 slug/ft²

Using the below formula

T = FI = Ma * angle

1. = 697.14*a

A = 1.43*10^-6 degree/s²

W = a*t

W = 0.00000143 *3600 = 0.0052degree /s =

W = 0.327rad/s

0.00005 = 697.14a

Angle = 7.2*10^-6 deg/s²

W = a*t

W = 7.2*10^-7*8600

W =0.00026deg/s

W= 0.016rad/hr