At a given point in its orbit, the moon is 2.4 x 10^5 miles from the earth.

Question

At a given point in its orbit, the moon is 2.4 x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. Please show work using dimensional analysis.

Answer 1

Hi Connie,

 

From our problem, we can see that we need to convert miles to meters. so that we can compute the required time in seconds.

 

So let's apply our necessary conversion ratios to cancel out all the distance units via dimensional analysis to allow us to compute the required time in seconds:

 

(2.4 x 10⁵ mi.)(1 km. / 0.625 mi.) = 3.84 x 10⁵ km.

(3.84 x 10⁵ km.)(1.0 x 10³ m. / 1 km.) = 3.84 x 10⁸ m.

(3.84 x 10⁸ m.)(1 sec. / 3.0 x 10⁸ m.) = 1.28 sec.  

 

In the above three calculations, we went from miles to km. and then to meters, so that we could use the given speed of light measured in m./sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 10⁵ miles).

 

Thanks for submitting this problem and glad to have been of help.

 

God bless, Jordan.