00:01
In this problem, you want to know what observer on a rocket measures for the speed of light from light coming from the sun.
00:09
So we have the sun frame, which is at rest, and the rocket moving relative to the sun.
00:15
This is the light, or i call it particle for a second.
00:17
I'm going to just deal with it as a particle for a moment, then worry about the speed.
00:21
So we know that speed of light from the sun is c.
00:25
We want to know what is it relative to the rocket.
00:27
And the rocket is moving 0 .95c relative to the sun.
00:31
Notice rocket, this is the v, the velocity of rocket relative to the sun.
00:38
This is the velocity of the particle relative to the sun.
00:41
This is the velocity of the particle relative to the rocket.
00:44
That's the notation.
00:46
Now, let's go back.
00:49
You may have done these problems in your chapter back in mechanics on two -dimensional motion.
00:56
This would have been relativistic, i mean, it should have been two -dimensional, two -dimensional relative motion.
01:04
So non -relativistically, you would have found this, or you would have done, use this.
01:09
Vps, say you have a person on a boat, and the person's moving relative to the boat, and the boats moving relative to the shore.
01:16
And you want to know what the person's motion is, velocity is relative to the shore.
01:23
So what you would do is you would add up those two, the motion of the boat and the motion of the person, as vectors.
01:30
So here would be the person relative to the boat.
01:33
I'll use r for the boat because of notation.
01:36
This is the person relative to the boat plus the boat relative to the shore.
01:41
That's, you add it up as vectors and that would give you the person relative to the shore.
01:46
That's the non -relativistic form.
01:48
And if you do it in one dimension, in, you know, one dimension, one dimensional case, just x, say, v, p .s.
02:00
These are still got pluses and minuses.
02:02
So if something's moving to positive x, you've got a plus, negative x, it's got a minus.
02:05
But it doesn't have the two -dimensional aspect, because that's all we care about in our problem.
02:11
So that'd be the one -dimensional form of it, of this vector relation.
02:18
But that's the idea behind it.
02:20
That's the notation.
02:23
Now, before we get into the relativistic one, let's look at this.
02:27
So we're looking for pr.
02:30
So that would give me pr is vps minus vrs.
02:39
So let's put in our values and see what we get.
02:43
Vps is c minus rs 0 .95c.
02:49
So that is 0 .05c.
02:53
You're in a way almost outracing it.
02:56
So you're not you're attributing it relative to a to not much speed because of your great.
03:04
Great motion.
03:06
So 0 .05c.
03:08
Think about it in any one second.
03:10
It's gaining on you, but only this amount.
03:14
So that's why your tribute.
03:15
That's why you attribute such a slow speed because of your high speed.
03:19
So that's what you'd get non -routivistically.
03:24
Now, before we do this, let me look at another case here.
03:28
Let's say, let's say i had the situation.
03:40
Same thing there.
03:41
Rocket, sun.
03:43
And here's my.
03:44
But this time, vps, that's what we want to know.
03:50
And vpr, we know.
03:54
We've, on a rocket ship, we turn on our lights, turn on headlights.
03:59
We turn on a flashlight and send it forward.
04:03
And we say, that's the speed of light c.
04:05
We grant that for at rest, the speed of light is c.
04:10
We're granting that.
04:13
So what would be, in this case, vpr? or actually not vps...