Question

A satellite has a central bus with a moment of inertia of 50 kg-m^2 about its solar array rotation axis. In addition, it has two solar arrays which each have a MOI of 25 kg-m^2 about that axis. If a worst-case, 1 second thruster burn causes an impulse which increases the rotation rate of the full system about this axis by 1 degree/sec, what minimum holding torque would you recommend for each solar array drive?

Answer 1

`\tau = 471.2 Nm`

Step-by-step explanation:

As we know that central bus has moment of inertia as

`I_1 = 50 kg m^2`

also the solar array has moment of inertia given as

`I_2 = 25 kg m^2`

total moment of inertia of the satellite is given as

`I = I_1 + I_2`

`I = 50 + 25 = 75 kg m^2`

now the rotation rate is given as

`\omega = 1 degree/s`

`\omega = 2\pi rad/s`

now the angular acceleration is given as

`\alpha = (\Delta \omega)/(\Delta t)`

`\alpha = (2\pi - 0)/(1)`

`\alpha = 2\pi rad/s^2`

now torque is given as

`\tau = I\alpha`

`\tau = (75)(2\pi)`

`\tau = 471.2 Nm`