= Solution
With metric convention $(+---)$, the invariant interval is $c^2\Delta\tau^2=c^2\Delta t^2-|\Delta\mathbf r|^2$ along an inertially moving clock. For constant <speed> $v$ in the ground frame, $|\Delta\mathbf r|=v\Delta t$, so
$$
\boxed{\Delta t=\gamma\Delta\tau,\qquad\gamma=(1-v^2/c^2)^{-1/2}.}
$$
The aircraft records <proper time> $\Delta\tau=1000\,\mathrm s$. The ground duration is measured by a network of <clocks> at rest in the ideal ground frame, with <Einstein synchronisation>. Its excess is
$$
\Delta t-\Delta\tau=1000(\gamma-1)\,\mathrm s
\simeq1000\frac{300^2}{2c^2}\,\mathrm s
\simeq5.0\times10^{-10}\,\mathrm s.
$$
Thus \b[the ground-frame duration is longer by about $0.50\,\mathrm{ns}$]. This is the special-relativistic <time dilation> contribution under the stated constant-speed assumptions; gravitational potential differences and Earth's rotation are outside this model.
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