A CubeSat in a circular equatorial orbit at altitude uses a rigid magnetic torque rod…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A 2.0kg CubeSat in a circular equatorial orbit at altitude 600km uses a rigid magnetic torque rod of magnetic moment magnitude μ=5.0A⋅m2 to align one of its body axes with Earth’s local magnetic field. At Earth’s surface on the magnetic equator the field magnitude is B0=30μT. Assume the field of Earth’s dipole decreases with the inverse cube of the distance from the planet’s center and remains tangent to the surface at the equator.
(a) Calculate the magnitude of Earth’s magnetic field at the satellite’s orbital altitude on the equator.
(b) Determine the maximum torque the torque rod can exert on the satellite at that location.
(c) If the satellite’s principal moment of inertia about the controlled axis is 0.15kgm2, estimate the minimum time required to rotate the satellite through 90∘ from an initially perpendicular orientation, assuming the torque from part (b) is constant and always applied in the optimal direction.
(d) Discuss two limitations of using magnetic torque rods for attitude control at higher-latitude orbits and propose a complementary control method to overcome each limitation.