Travelling at Light Speed

Date: 04/11/98 at 16:20:00
From: Mr. DEAN LOWELL CRUMMY
Subject: LIGHT TRAVEL

How long in time, not distance, would it take to go to Mars or 
Jupiter? At light speed?

Date: 04/13/98 at 09:48:19
From: Doctor Barrus
Subject: Re: LIGHT TRAVEL

Hi, Dean!

It depends on how far away from Mars or Jupiter the earth is. The 
earth, according to: 

     http://www.star.le.ac.uk/espace/Planets/relativep.html    

is located an average of 150 million kilometers away from the sun, and 
Jupiter and Mars are at average distances of 780 and 228 millions of 
kilometers away from the sun, respectively. But every planet is 
revolving around the sun, and at different rates, so the distance from 
planet to planet is constantly changing.

So, assuming that the sun, the Earth, and Mars were all lined up 
(which they're not), you could have Mars and Earth as close together 
as (228 - 150 =)78 million kilometers ...

     <---------------228---------->
     (Sun)               *        *
                       Earth     Mars
     <------150----------><---78-->

... or as far apart as (228 + 150 = )378 million kilometers:

     *                     (Sun)             *
     Mars                                   Earth
     <---------228-----------><----150------->


Similarly, distances between Earth and Jupiter could be anything from 
around 630 million kilometers to 930 million kilometers. Of course, 
these calculations aren't exact, because the two planets and the sun 
rarely line up like in the diagrams above, and the distances I used 
are just average distances -- the planets can be closer to or farther 
away from the sun. I just gave the example above so that you could see 
that the distances can really vary.

But let's suppose that we know the exact distance between the earth 
and another planet. Then to find out how long the trip would be, we'd 
use the formula

     distance = speed * time

to get
 
             distance  
     time = ----------
              speed

So, suppose the Earth and Mars are 200 million kilometers away from 
each other right now. Then a trip to Mars would take time t, where

     t = (200 million kilometers)/(speed of light)

       = (2 * 10^11 meters)/(3.0 * 10^8 meters per second)

[Here, I just converted the kilometers into meters (using the fact 
that there are 1000 meters in a kilometer), wrote the distance in 
scientific notation (so it's easier to calculate), and wrote out 
approximately what the speed of light is.]

So:
   
     t = 667 seconds (approximately) 

which translates to 11 minutes and 7 seconds.

(NOTE: This is how long someone on *earth* would see the trip as 
taking. A person actually on the ship to Mars, traveling at the speed 
of light, wouldn't be aware of ANY time passing. This would happen 
because of the phenomena that Einstein explained in his theory of 
relativity.)

So in summary, it isn't possible to answer your question exactly, 
because the distances between earth and Mars and Jupiter are always 
changing, and therefore the times required to travel to them at light 
speed also change. If we did know the exact distance, though, we could 
figure out approximately how long a journey of that kind would take.

-Doctor Barrus, The Math Forum
Check out our web site! http://mathforum.org/dr.math/