Assume that the moon and Earth are the same distance from the sun. How long, to the nearest second, does it take for sunlight to reach the moon and reflect to Earth?

1 Answer
A. S. Adikesavan
May 30, 2016

#(d+2d sin (theta/2))/299792.458# seconds, where d km is the common distance and #theta# is the angular spacing between Moon and Sun, as observed from Earth..

Explanation:

If Moon (M)_Earth (E) distance = d = Sun(S)-Earth distance and the

angular spacing between Moon and the Sun, as observed from the

Earth, is #theta#,the answer is

#(d+2d sin (theta/2))/299793458# seconds.

Here, ES = MS = d km.

#angleSEM=theta. EM=2d sin(theta/2).#.

i light second = 299792.458 km

Total distance for light to travel = (d +2d sin(theta/2) km.

Time taken = distance /speed = #(d+2d sin (theta/2))/299792.458# seconds.

In mathematical exactitude, this event might be a rare event. Yet, it is likely to occur about mid time, in between Full Moon and New Moon.

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