# If an object moves towards you at light speed, what would you see?

1. Mar 7, 2012

### Albertgauss

Hi all,

I just want to check my qualitativie understanding of what I would see if a ship approached me at the speed of light. Is the following correct:

Let's say a light-radiating ship travelling near "c" a long distance off approaches Earth. The light it emits will travel at "c", so the image of the ship will travel at "c". The image of the ship will arrive well before the actual ship arrives. At first, when the ship is far away, the image of the ship will reach Earth a long time before the actual ship does. However, as the ship approaches closer to Earth, the image of the ship won't be as far ahead as the actual ship.

Is the above thought correct?

2. Mar 7, 2012

### ghwellsjr

The closer the ship is to the speed of light, the shorter the time before it arrives that you will start to see it approach you. Let's say that it has been stationary at its far away location for as many years as it is light years away so that you can actually see it not moving. Then suppose that it accelerates toward you and quickly achieves its final speed near c. You won't see this happen for almost as many years as it is light years away. Then when you do see it approach you, it will be very much blue-shifted and in a rather short period of time you will see it make its entire trip toward you. The exact details depend on the distance away and its speed.

3. Mar 7, 2012

### Albertgauss

Okay, I think I got it. I know that effects such as Doppler-shifts, aberattion, distortion, and such exist, but I want to avoid them so that I can understand this aspect of Relativity.

Part 1: The ship is far away from Earth and at rest. It emits an image of itself. Earth will not recieve this first image--and thus not know about---the ship for a long time. The ship starts to go in motion.

Part 2. The ship starts to accelerate. It emits images of itself. Each image has information about the ship when it departed from the ship. The ship is closer behind these images than the images emitted during the beginning stage of its journey.

Part 3. The ship hits 0.999c, its final. constant cruising speed. It is right behind any images it emits now.

Part 4. Earth recieves the first images of the ship, the images emitted during Part 1. Earth sees the ship only as it was at the beginning of its journey, far away in a more primitive stage. The actual ship, is of course, almost to the Earth. Then, its like somone hits a "fast-forward" button on the ship's journey. The more recent images come in faster than the earlier ones. Earth learns about the end of the ship's journey faster at the end of the trip than the beginning. The ship finally lands.

This is consistent with seeing the whole journey of the ship only near the conclusion of the ship's journey.

How am I doing?

Also, I did not understand:

"The closer the ship is to the speed of light, the shorter the time before it arrives that you will start to see it approach you."

Let ship A be at rest, X Au's away (Astro units), and B is incoming, cruising towards Earth at 0.999c. Suppose that when B gets to X, both A and B emit images of themselves at the same time. Wouldn't the images of A and B reach Earth at the same time?

4. Mar 7, 2012

### PAllen

Yes, of course, but B will arrive a very short time after you first see it (pass A). If there is a C passing at .99999C, it will arrive an even shorter time after you see it passing A. The faster the ship, the shorter the time interval between when you see it and when it arrives. Maybe you interpreted this statement some other way?

5. Mar 7, 2012

Perfect.

6. Mar 7, 2012

### ghwellsjr

You're doing great. I like the way you partitioned the emission aspect of the scenario and associated that with the reception at earth but you didn't follow through, so I'm not sure what you would have said. You indicated that the images come in faster at the end than at the beginning but this is only true if you are associating this with the emissions during part 2. I presume that part 2 doesn't last very long and the vast majority of the trip is during part 3. Once earth starts seeing these emissions, there is no further speeding up of the images. Hopefully, this is what you had in mind.
Yeah, that does sound confusing. I'm really just stating what you said in part 3, that the ship is right behind its images, the faster it is going, the closer it is to its images.
Yes.

7. Mar 8, 2012

### Albertgauss

Great! PAllen said it best about "The closer the ship is to the speed of light, the shorter the time before it arrives that you will start to see it approach you." I got that down now.

Okay, last thing. Suppose now that my ship is at coordinate X away from Earth. It emits images of itself but does not move. Earth receives these images well before the ship leaves its coordinate. Thus, Earth knows the ship is X away well before it departs.

The ship departs now, moving slowly at first, emitting images of itself throughout the whole journey. As far as the actual journey is concerned, it will be the same as above. That is, Earth wonâ€™t know the ship has even taken a journey until the ship almost gets to Earth. The ship will be much closer to Earth than what the images from any stage of the journey imply. Earth will learn about the journey in the same fast-forward manner as above. The ship will arrive on the heels of its most recent emitted images.

Also, it seems this scenario would be hold qualitatively for any scenario similar to the one above. Whether the ship starts out light years away, or only kilometers away, the same scenario would play out. Events would certainly happen on much shorter timescales for a ship starting kilometers away than light years away, and accelerations could be different, but the overall picture should remain the same. Is this correct?

8. Mar 8, 2012

### ghwellsjr

Yes.

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