Question

A drum-shaped Earth orbiting spacecraft of radius 1 m is spin stabilized with H=2000 Nms and has a spin-axis moment of inertia Iz=500 kg m2. It is nominally aligned with thr spin axis along either the positive or negative orbit normal direction, depending on the following considerations: the spacecraft is designed to radiate heat to dark space out of the “bottom” side. Because of the nodal regression of the orbit, and the consequent time-varying angle between the sun vector and the orbit plane, it is necessary several times per year to “invert” the spacecraft, i.e., to precess the spin axis around to the opposite orbit normal direction, so that the sun does not shine into the bottom side. Four 50-N thrusters mounted on the rim of the spacecraft control the spin axis attitude. The thrusters are operated in pulse mode, with a pulse width of 40 ms, followed by a 60-ms off-period. How many thruster pulses are required to accomplish this? How long does the process take? Because of the short pulse, we may ignore any cosine losses associated with finite pulse width.

Answer 1

Using a formula, we have

= I

where, = angular momentum = 2000 kg.m²/s

I = spin axis moment of inertia = 500 kg.m²

THEN, we get

= (2000 kg.m²/s) / (500 kg.m²)

= 4 rad/s

A torque is defined by a formula as -

= I

r F sin = I

(1 m) (4 x 50 N) sin 90⁰ = (500 kg.m²)

= (200 N.m) / (500 kg.m²)

= 0.4 rad/s²

We know that,   = / t

t = (4 rad/s) / (0.4 rad/s²)

t = 10 sec

(a) How many thruster pulses are required to accomplish this?

N = (10 sec) / (20 x 10^-3 sec)

N = 500 pulses