The Speed of Light


Introduction

Remember:
distance = speed x time

Light travels very fast

It takes light very little time to cross a room, but can take years to cross the gap between stars.

Examples

How long does it take light to cross a lecture hall measuring 50 feet from front to back? speed = 1 foot/billionth of a second
distance = 50 feet
and so time = distance/speed = 50/1 = 50 billionths of a second
How long does it take light to get to us from the Sun? (The Sun is 93 million miles away) distance = 93,000,000 miles
speed = 186,000 miles/second
and so time = distance/speed = 93,000,000/186,000 = 500 seconds (equal to 8 minutes 20 seconds)
How far is a light year? (A light year is defined as the distance light travels in one year. It is a convenient unit for distance in astronomy where interstellar and intergalactic distances are too large to be conveniently expressed in miles.) speed = 186,000 miles/second
time = 1 year = 365 x 24 x 60 x 60 = 31,500,000 seconds
so distance = 186,000 x 31,500,000 = 5,859,000,000,000 miles (a little less than 6 trillion miles)
How far is it to the nearest star? The nearest star is about 4 light years away, so taking the result of the previous calculation 

distance = 4 x 5,859,000,000,000 miles = 23,436,000,000,000 miles (a long way!)

How long would it take you to get to the Andromeda Galaxy (2.7 million light years away) if you had a spaceship capable of traveling 100,000 mph? This is a harder problem. We have to first find out how far it is and then calculate the time. 
  • To find the distance in miles

  • From the definition of a light year, the distance to the Andromeda Galaxy is 2,700,000 light years = 2,700,000 x 5,859,000,000,000 miles = 1.58 x 1019 miles (that is 158 followed by 17 zeroes!)
  • To find the time

  • distance = 1.58 x 1019 miles
    speed = 100,000 miles/hour
    time = distance/speed = 1.58 x 1019/100000 = 1.58 x 1014 hours (158 trillion hours, or about 18 billion years)