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### 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.)

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/
```
Associated Topics:
High School Physics/Chemistry

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