Since distance is equal to speed multiplied by time
(I want to review that), we can
make some simple conclusions about how far the ship
travels as it travels from earth to Alpha Centuri:
We know the speed of
light and we know from the reference frame of the
earth, light takes about 4 years to travel the distance.
Since there are 31,557,600 seconds in one year (I
want to see that calculation), according to the
earth's reference frame, Alpha Centuri is:
Therefore, if we see the space ship travel at 50%
c, according to us, it
should take the space ship 8 years to get to Alpha
Centuri.
Link below to its own page.
This would be different for the mover in the space
ship, because the mover would measure a different time
predicted by the time dilation
equation.Would this time measured for the mover by
the mover be more than, less than or the same as the time
measured for the mover by the stationary frame?
In fact the time would be about 6.9 years. So
according to the mover, the distance traveled was only
3.46 light years (I want to see
that calculation), not 4 light years as was
registered by the stationary frame. Therefore, space has
been contracted for the mover.
In general, distance is calculated by knowing time and
velocity.
d = vt
Here we will refer to the distance measured for the
mover by the stationary frame as length, l_{o}.
Consider a 3 x 10^{8} meter stick traveling
past us at half the speed of light (50% c).
We want to measure the length of this stick in the
mover's frame of reference and the stationary frame of
reference.
To accomplish this, we will time how long it takes the
3.0 x 10^{8} meter stick to pass a set point in
space.
According to the mover for the mover, the meter stick
is 3 x 10^{8} metes long. Since it is traveling
at 50% c, the mover
measures a time of 2.0 seconds (I
want to see that calculation) to pass by the time
both ends of the meter stick pass the point in space.
See animation. (add animation and link)
According to the stationary frame, the mover's stick
takes a longer time to pass the point. Instead of 2
seconds, the stick, traveling at 50% c,
takes 2.3094 seconds to pass the point in space.
Since the mover was moving at 50% c,
and the stationary frame timed the stick to take 2.3094
seconds to pass the point in space, the stationary frame
calculates the stick's length to be 3.5 x 108 meters.
Here, we need to make some distinctions. The stick is
3.0 x 108 meters in the frame that sees it at rest, its
own. In the frame that sees it moving, it is longer!
The above is wrong! Check out how to say it correclty
and break this page up into parts b, c, and d for lesson
3. Also remember to consider calling this Level 3 and
remember the game is a game of hunting for a ship headed
toward different stars with a convict...you are a bounty
hunter and you must arrive before convict to collect your
bounty.
Also remember to set of a table of contents for this
site.
