= Solution
Interpret the one-light-day separation $D$ as measured in the station frame at capsule launch, and retain the ship's initial inertial <rest frame> until reception at the station. The phrase does not explicitly name a frame; an alternative is given below. The ship-frame simultaneous separation is $D'=D/\gamma_s$. The capsule moves at $0.9c$ towards a station approaching at $0.85c$, so their separation decreases at $1.75c$ in this frame. This is a separation rate, not either object's <speed>. Hence the elapsed ship-frame coordinate <time> is
$$
\boxed{\Delta t_s=\frac{D}{\gamma_s(0.9+0.85)c}\simeq0.301018\,\mathrm{day}\simeq7.2244\,\mathrm h.}
$$
It is the interval assigned using synchronized clocks in the ship frame to the launch and remote arrival. A single onboard clock does not directly mark the remote arrival event; observing its arrival signal would add a light-travel delay. If the stated one-light-day separation were instead measured in the ship frame, the answer would be $\Delta t_s=(1/1.75)\,\mathrm{day}=0.571429\,\mathrm{day}$.
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