On the Moon's surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round$-$trip time. Assume the distance to the Moon is precisely $\backslash (3\mathrm{.}84\backslash$times $10^\{8\}\backslash$mathrm$\{$~m$\}\backslash ),$ and the Earth's atmosphere $($which varies in density with altitude$)$ is equivalent to a layer $30\mathrm{.}0$ km thick with a constant index of refraction $\backslash ($ n$=1\mathrm{.}000293\backslash ).$ What percent correction is needed to account for the delay in time due to the slowing of light in the Earth's atmosphere?

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