Answer to Question #279556 in Atomic and Nuclear Physics for byiringiro selever

Question

On 20 July 1969, the astronauts of Apollo 11 placed a reflector on the surface of the moon that with the telescope and electronic equipment on earth allows measurements of the time of flight of laser pulses from earth to the moon and back. Scientists are able to measure the time of flight of laser pulse from earth to the moon and back with an accuracy of one nanosecond. What is the accuracy of the distance to the moon distance? 

Answer 1

Given:

$\Delta t=10^{-9}\:\rm s$

$L=384\: 400 \:\rm km$

The time of light movement from the Earth to the Moon

$$t=\frac{L}{c}=\frac{384\: 400\:\rm km}{300\: 000\:\rm km/s}=1.28\: \rm s$$

The accuracy of the distance

$$\Delta L=L\frac{\Delta t}{t}\\ =\rm 384\: 400\: km*\frac{10^{-9}\: s}{1.28\: s}=0.0003\: km=30\: cm$$