Question #42832

A deep-space rocket is traveling at a constant velocity $v = \frac{\sqrt{3}}{2}c$ relative to an inertial space station. At $t=0$, the rocket begins to accelerate with a constant proper acceleration $a$ along its direction of motion ($+x$-axis). Inside the rocket, a rigid electric dipole is pivoted frictionlessly at its negative charge $-q$. The positive charge $+q$ has a rest mass $m_0$ and is at a distance $2l$ from the pivot. A uniform static electric field $\vec{E} = E_0 \hat{i}$ and a uniform photon beam of intensity $I$ propagating along the $+y$-axis exist inside the rocket (both measured in the rocket's frame). A perfectly absorbing flat disk of area $A$ is attached to the $+q$ charge, rigidly fixed such that its surface normal is always parallel to the dipole axis (directed from $-q$ to $+q$). The $-q$ charge and the connecting rod do not interact with the radiation. Assuming the dipole reaches a steady-state equilibrium angle $\theta \in (0, \pi/2)$ with respect to the $+x$-axis, which of the following expressions correctly gives $\cos\theta$?