Time it Takes Light to Travel Halfway Around Earth

[IsaacAsimov]

Here's a problem I thought of that I found a solution for:

 

Problem:

 

How long does it take for a person on the surface of the Earth to communicate with someone else on a different point on the Earth, assuming a fibre optic link and using circles with circumscribed polygons?

 

Or: How long does it take light to travel 1/2 way around the Earth?

 

Solution:

 

Find: t in s

Given: c=3E8 m/s, mean r_E=6.37E6 m

s=vt, t=s/v

C_E=2(pi)r_E, 1/2 C_E=1/2(2)pi(r_E)

t=s/v=(1/2)C_E/c=pi(r_E)/c=3.14(6.37E6 m)/3.00E8 m/s=0.07 s = 7/100 s

[swansont]

If you go in for a more precise answer, it will depend on which way you send the light. The speed of light is constant — in an inertial frame of reference. The earth is rotating, which means that it's not an inertial reference system. If you send the light west it will make the trip about 100 ns faster than if the earth were not rotating, and 100 ns slower if it goes east. i.e. in the time it takes light to go that far, the earth will have moved around 30 meters, either toward or away from the source.

[Joatmon]

I realise what you are asking (and that I'm nit picking) - but I'll just mention that light travels slower in a fibre optic cable than it does through air.

• 
  "It's actually a light signal that travels through a fibre optic cable. The speed is the speed of light divided by the refractive index of the material. This works out to around 200 million metres per second."
   
  h

ttp://wiki.answers.com/Q/What_is_the_speed_of_electrical_signal_in_optical_fiber_cable

Edited April 25, 2012 by Joatmon

[IsaacAsimov]

Thank you for correcting me, however I was just giving the general solution.

 

If you like, try inputting your values for the speed of light and see what the travel time would be.

 

Isaac

[IsaacAsimov]

Here's a problem I thought of that I found a solution for:

 

How long does it take 2 people to communicate with each other at any 2 points on the Earth using 4 communications satellites?

 

Or: How long does it take light to travel 1/2 way around a square circumscribed around a circle (Earth)?

 

Solution:

 

Find: t in s

Given: c=3E8 m/s, mean radius of Earth r_E=6.37E6 m

Let a=1/8 distance around square=r_E

s=vt, t=s/v

circumference of square C_s=8a, 1/2 C_s=(1/2)(8a)=4a=4r_E

t=s/v=4r_E/c=4(6.37E6 m)/3E8 m/s=0.08 s = 8/100 s

[IsaacAsimov]

Here is a problem I thought of that I found a solution for:

 

Problem: How long does it take light to travel 1/2 way around the Earth using 6 communications satellites that form a circumscribed hexagon?

 

Solution:

 

Find: t in s

Given: distance from center of Earth to a side =a=r_E=6.37E6 m_, distance from center of Earth to a vertex =r, n=6 sides, c=3E8 m/s

r=a/[cos(pi/n)]=r_E/cos(pi/6)=6.37E6 m/0.866=7.36E6 m

3r=2.21E7 m

s=vt

t=s/v=2.21E7 m/3E8 m/s=0.07 s = 7/100 s