On the Moon's surface, lunar astronauts placed a corner reflector, off of which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time.
The Earth's atmosphere slows down light. Assume the distance to the Moon is precisely $3.84 \times 10^6$ m, and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer 40.0 km thick with a constant index of refraction $n = 1.000293$.
What is the difference $\Delta t$ in travel time between light that travels only through space to the Moon and back and light that travels through the atmosphere and space?
$\Delta t = $