Astronauts Did This To The Moon. Scientists Are Thankful For It.

The Apollo 11 astronauts did not leave the moon unchanged. Besides some footprints and a flag, there was some equipment left on the moon, including a mirror pointed towards the earth. Earth-based scientists can measure the distance to the moon by firing a laser pulse at the mirror and measuring the time it takes for the laser pulse to return to earth.

How long does it take in seconds for a short laser pulse to bounce off the moon and come back?

Image credit: Neil Armstrong/NASA/Corbis

Details and assumptions

  • The moon is, on average, 385 , 000 km 385,000~\mbox{km} away from the earth
  • The speed of light is approximately 3 × 1 0 8 m/s 3 \times 10^8~\mbox{m/s} ,
  • Note: This experiment, the Lunar Laser Ranging Experiment, is one of the most accurate distance measurements ever made. For example, one can determine that the moon is moving away from the earth at a rate of 3.8 centimeters per year.
  • Note: Although the Ancient Greeks were able to rationally estimate the size of the earth using rudimentary mathematics, their calculations were hopelessly off for the size of the moon. Find out why.


The answer is 2.57.

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28 solutions

Amlan Mishra
Jan 7, 2014
  • Distance travelled by the light = d = 385000+385000 = 770000 km

  • Speed of light = v = 300000 km/s

  • So time taken = d/v = 770000/300000 seconds = 2.566667 seconds

The Big Bang Theory

The lunar laser ranging experiment is featured in this episode of The Big Bang Theory. Its a pretty funny episode.

Cole Coupland - 7 years, 5 months ago

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NOW THIS IS A GOOD QUESTION - Sheldon!

Aniruddh Mishra - 7 years, 3 months ago

At first I was thinking about including relativistic effects, but then ruled it out because a photon technically doesn't have mass, but I don't know for sure.

Does anybody know the relativistic effects on a photon is such a case?

Milly Choochoo - 7 years, 5 months ago

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the path of a photon relativistic is not effected unless acted on by gravitational forces.

Matthew Ferguson - 7 years, 4 months ago

easy

Aunie Abdul Mutalib - 7 years, 5 months ago

t=d/v so the ans is 2.57

Anupam Tripathi - 7 years, 5 months ago

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t=2d/c is right

Jeya Subramanian - 7 years, 4 months ago

2.566667 seconds APPROX

RAHUL PARMAR - 7 years, 5 months ago

if the moon is basically 400,000 from earth and l/s is 300,000 then the answer is 1.3

Matthew Ferguson - 7 years, 4 months ago

The question was how much time the laser takes to reach us after it bounces from the moon. The answer is for the round trip taken by the laser.

Ramachandran Nagarajan - 7 years, 3 months ago

oh noooo....... I forgot to multiply the distance by 2. :/

puzzle seeker - 7 years, 1 month ago

speed of light is 3800000000....ur answer is incorrect

Mohammad Ahmed - 7 years, 4 months ago

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it is in m/s. but the distance is given in km. hope u got ur mistake

Sarthak Rapartiwar - 7 years, 3 months ago

we can use the formula

t= s v \frac {s}{v}

which t is time s is distance and v is velocity based from the problem , the distance is 385,000 km or 385,000,000 m and the velocity are 3 × 1 0 8 3 \times\ 10^{8} m/s or 300,000,000 m/s to obtain the time, we will use the formula above , and thus we obtain

385 , 000 , 000 300 , 000 , 000 \frac {385,000,000}{300,000,000} = 1.283 and because it is still the time needed by the laser to reach the moon to know the time it needed back and forth is

1.283 × 2 1.283 \times 2 = 2.566 and with decimal approach we will obtain 2.570 \boxed{2.570}

I thought there was not any decimal approaching cause I entered 2.566 back then but it said that my answer was wrong haha

Sem David Sitanggang - 7 years, 6 months ago

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well, i wrote 2.569 and it's correct, oh well :-)

Elizabeth Maria Clarissa - 7 years, 6 months ago

YOUR METHOD OF EXPLAING IS DIFFICULT

Harsh Shrivastava - 7 years, 6 months ago
Reeshabh Ranjan
Jan 7, 2014

The distance of moon from earth is 385000 km or 385000000 metre. The speed of the laser pulse= speed of light = 3 x 10^8 metre/s. So, one way time= 385000000/ 300000000 = 1.283 and two way time = 2.566 seconds or 2.57 seconds.

As far as I know there is great speculation about the pictures as can be seen because of the presence of multiple light sources and the presence of the shadow of a third person....probably they never went there

Santanu Banerjee - 7 years, 5 months ago

yeah t=d/s so 1.28*2=2.56 is answer.....because the total distance is 2 times of the one way ........

Vishav Sharma - 7 years, 4 months ago

You are my hero I only measured the pulse going one way not two. Thank You.

Matthew Ferguson - 7 years, 4 months ago
Shubham Sawaiker
Dec 8, 2013

Total distance=385,000 * 2=770000km=770000000m=7.7 * 10^8 Time=Distance/speed=7.7 * 10^8/3*10^8 =7.7/3=2.566666666... =2.57

Rahma Anggraeni
May 6, 2014

s = v × t 2 s=\frac{v \times t}{2}

t = 2 s v t=\frac{2s}{v}

t = 2 × 385 , 000 , 000 300 , 000 , 000 t=\frac{2 \times 385,000,000}{300,000,000}

t = 2.566667 t=\boxed{2.566667}

Distance travelled by the laser light= 385000 x 2 (Because the light has to travel to the moon and come back) speed of the light = 3 x 10^8 m/s time = distance / velocity So the answer is 2.566 (approx) seconds

Satya Siddharth
Mar 21, 2014

VELOCITY=DISTANCE/TIME SO, TIME=DISTANCE/VELOCITY SO t=2 385000/3 1O^8 (2 IS MULTIPLIED BECAUSE OF THE LASER PULSE RETURN BACK TO EARTH) t=2.5666667

Swapnil Rajawat
Mar 1, 2014

what will happen if moon goes on forever.

Shweta Rai
Feb 28, 2014

time taken in seconds for a short laser pulse to bounce off the moon and come back=speed of laser pulse total distance travelled by the short laser =2 (385000*1000)/300000000 =2.567

Yogesh Ghadge
Feb 25, 2014

distance from the earth to moon is 385000km we should covert it in meters we get 385000000m ,speed=300000000m/s , using time formula t=d/s=385000000/300000000=1.28sec. now the time of ray coming back to earth 2*1.28=2.57sec

Vaisakh Vrindavan
Feb 14, 2014

velocity of light =3E10 distance of moon from earth =385000km =385E6 m time=distance/speed =385E6/3E10 =1.283 s therefore distance from earth to moon and return =1.283 s * 2=2.56

Vitasta Jain
Feb 11, 2014

Distance=Speed Time Time = Distance/Speed = 385000 km *2/3 10^8 (since the laser will have to come back after reflection the distance traveled will be two times) =385000000 2 m s/3 10^8 m =2.57 sec

Atiq Ur Rehman
Jan 27, 2014

Total distance = 385000 km x 2; or 385000000 meters x 2 = 7.7E8 meters; Velocity of light = 3E8 m/s; As we know that; speed (v) = distance(d)/time(t); or time (t) = distance(d)/speed(v) time(t )= 7.7E8/3E8 = 2.57 seconds

Ammar Aziz
Jan 26, 2014

Actually the universally accepted value of speed of light is 3 lac kilometers per seond. By applying the unitry method if found that it takes almost 1.28 sec for a pulse of light to reach the moon. If the minute variation in distance due to moving away of moon is neglected then the time taken by light to reach back the earth is also 1.28 sec. So the double of 1.28 is the time in seconds taken by the pulse of light in this experiment

Nitish Dubey
Jan 18, 2014
  • Net Distance to be covered by the Laser Light is,
    2 times the total Distance Between Earth And Moon i.e, 2 × 385 1 0 6 2 \times 385*10^{6} m.
  • Speed of Light = 3 × 1 0 8 3 \times 10^{8} m/sec.
  • as time = Distance/velocity
  • therefore, time taken by Laser = 2 × 385 1 0 6 2 \times 385*10^{6} / 3 × 1 0 8 3 \times 10^{8} = 2.567
Deddy Wirata
Jan 15, 2014

t = (S+S)/v = 2S/v = 2(385 x 10^6)/(3 x 10^8) = 2.5666666666666666666666.. seconds

Sourav Modak
Jan 13, 2014

t= twice the distance/ velocity

Joseph Mordeno
Jan 13, 2014

the distance is 385,000 km, making it up to 385,000,000 meters. since the laser needs to be bounced back to the earth, it makes the distance doubled up to 770,000,000 m.

distance (d) = 770,000,000 m

speed (s) = 3 x 10^8 m/s = 300,000,000 m/s

time (t) = ?

t = d/s = (770,000,000 m) / (300,000,000 m/s) = 2.56666666...., 2.567 or 2.57 seconds

Mrugesh Joshi
Jan 11, 2014

It will be 2x(distance between moon and earth)/(speed of light)=2.5666 seconds

Irfan Wahyudin
Jan 11, 2014

t = 2s/v ,...t=2(385000000 m)/300000000 m/s = 2.567 s

Prashant Chauhan
Jan 11, 2014

It's two times the time taken for the laser pulse to reach the moon which is (distance between moon and earth/speed of the pulse).

Umakant Mane
Jan 10, 2014

total distance travelled ba pulse = 385000 *2 km and speed of the pulse = 3E8 m/s so time= distance/speed

Kumaran Ramu
Jan 10, 2014

Light can travel 300,000 km/s.

Moon is away by 385,000 km.

Distance to be traveled by LASER to return to the Earth = 385,000 x 2 = 770,000 km

Therefore total traveling time by LASER light to a distance of 770,000 km is = 770,000/300,000 = 2.567

Salil Bhonsle
Jan 9, 2014

Velocity = displacement / time .. Therefore time taken for the 1-way trip is 385,000/3X10*5 = 1.28 seconds Therefore time taken for the entire trip is 2X 1.28 =2.56 seconds

Rui-Xian Siew
Jan 9, 2014

Since speed=distance/time, time=distance/speed. Distance from earth to moon=385000000m. Therefore if the laser pulse start from earth to moon and back to earth again, time taken=2x385000000/300000000=2.566s

The solution is simple. We just use the formula ----------> Time = Distance/speed

Distance from the earth to the moon in metres = 385000000 m Time = 3*10^8 seconds = 300000000 s

Time = 385000000/300000000 = 1.28333333333 seconds = Time taken for beam to reach the moon

The question wants us to find the time taken for the beam to reach the moon and return to earth ------------------> 1.28333333333 * 2 = 2.56666666667 seconds = Answer

i forgot that it go and come back i did not multiply it by 2 ):

Jalawi Saud - 7 years, 5 months ago

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Join the club.

Matthew Ferguson - 7 years, 4 months ago

Let the distance between the earth and the moon be d The laser pulse goes and comes back, thus covering a total of 2d Let the speed of light be c

Time taken by light = 2d/c

Substituting d by 385000 km and c by 300000 kms^-1,

we get, t= 2.5667

Catherine Guillen
Dec 11, 2013

r=d/t but in this problem we need to find for time(t) so

t=d/r

d= 385000 x 2 * double the distance since the laser pulse will do a sort of a *round-trip as it bounces off the mirror back to the Earth**

d=770000km

r= 3 x 10^8 m/s = 300000000 m/s note that the given unit for d is km so convert this to km

r= 3 x 10^5= 300000 km/s

Finally:

t= d / r

t=770000 km / 300000km/s

t= 2.57 s

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