Where do the missing minutes in a live feed from a spaceship to Mars go?

[John_melb]

Hi, I've just discovered this site, and I'm hoping someone can give a lay answer to the following question:

Imagine I'm watching a constant live feed from a camera on a spaceship that's next to me, and this spaceship then takes off to Mars. When the spaceship reaches Mars, the video feed that I'll be watching will be minutes in the past due to the time it takes for the signal to reach Earth. However, if I'm watching a constant feed, then where did these missing minutes go, or rather, where did the extra minutes of footage come from, and how was it introduced into my constant stream? Does it have something to do with this?



Thanks in advance.

 

[sophiecentaur]

Hi, I've just discovered this site,

Welcome to PF - well spotted!
A great piece of what we could now call 'old fashioned' TV and there is no doubt that it was genuine. The same thing could have been in a Hollywood movie and we could doubt what it shows. Sandra Bullock looks very nice in the film Gravity but that's not real Physics! Clunky bits of wood and metal are more reliable than the dreaded 'simulations' that we so often see on TV or on our computers.
To answer your question, the message in the movie needs to be extended a bit. (It is not necessary to include Special Relativity or anything fancy for a simple answer. ) When the spaceship crew are moving away from you, the distance to the on-board ticking clock is gradually increasing so a TV signal of that clock that you receive will show those ticks, equally spaced in time but each tick takes (very slightly) longer to reach you than the last. Their apparent frequency will be lower than when the clock was back on Earth. This is the well known Doppler Shift effect. Over the whole journey, these time differences or phases (between the Ship and Earth frames) add up to minutes of delay that you describe. Half way there, the delay (in the Earth's reference frame) will be half what it is from Mars. On a simple model, it doesn't matter how fast the ship has been travelling. A slow journey will involve many more ticks with very little extra delay each whilst a fast journey will involve fewer ticks with larger delay each.
The total time delay (phase) is proportional to the frequency difference times the transit time.

 

[fresh_42]

Just to add a simple example. If you're listening to a radio that constantly is driven away from your position, you will have the same delays. At a few hundred meters you will hear the effect. In former times when the starting pistol of a 100 m run hadn't been connected to the electronic system, one could hear, that the bang has been always a little late compared to what we saw on the TV screen when the runners started, because the microphones have been somewhere else in the stadium.

 

[John_melb]

Thanks all for the explanation! So, is it fair to say that if the video on the spaceship was of people playing basketball, then the further away the spaceship travels from me, then the more they will be seen to play in slow motion?

 

[sophiecentaur]

If you look at the movie, carefully, at the beginning, whilst he's in the upside down chair, the smoke form his pipe moves slightly 'downwards', despite the fact that he blows it sideways.

 

[Nugatory]

However, if I'm watching a constant feed, then where did these missing minutes go, or rather, where did the extra minutes of footage come from, and how was it introduced into my constant stream?

there are no extra minutes.

This will make more sense if you consider that a "live video feed" is actually a series of still frames being transmitted one after the next. Suppose the ship sends 100 frames per second, and suppose the ship is moving at 30 km/sec. The first frame leaves the ship at time zero just as it launches, so it's also received at time zero. The second frame is sent at time 10 msecs; the ship is 300 meters away so that frame is received at time 10.000001 msecs. By then the ship has moved a bit farther along so we haven't actually lost any time; the ship is exactly where it is supposed to be at 10.000001 msecs. The third frame is sent at time 20 msecs when the ship is 600 meters away, and it's received at time 20.000002 msecs...

The ship is transmitting at 100 frames per second, one frame every 10 msecs, but we're receiving one frame every 10.000001 msecs - the feed is slowed by one part in one million. A trip to Mars takes long enough for that to add up to eight minutes.

 

[sophiecentaur]

Thanks all for the explanation! So, is it fair to say that if the video on the spaceship was of people playing basketball, then the further away the spaceship travels from me, then the more they will be seen to play in slow motion?

Their motion (rate of waving arms and legs etc) will be 'slowed down by a constant amount - depending on the speed of recession but not on where they are. The delay but not the frequency will change along the journey.

I wonder if your idea is based on how the Doppler effect is experienced with passing vehicles. This is because the path of the vehicle is to one side of the observer and the relative velocity is not constant, due to the trigonometry of the situation. We assume here that the path of the ship is directly away from the observer (distances being much greater than for traffic on a road).

 

[Nugatory]

Thanks all for the explanation! So, is it fair to say that if the video on the spaceship was of people playing basketball, then the further away the spaceship travels from me, then the more they will be seen to play in slow motion?

Almost. The faster the ship is moving, the more they will appear to be in slow motion. The distance doesn't affect the slow motion.

You might want to google for "Doppler effect"... It's related.

 

[sophiecentaur]

This will make more sense if you consider that a "live video feed" is actually a series of still frames being transmitted one after the next.

That's an interesting way of putting it. If the TV display sync is locked to Earth Frame, what you would see would be a picture of a basketball game which rolls slowly downward and to the right (just like in the bad old days where sync was the first thing to be lost when the signal was dodgy.)

 

[John_melb]

Excellent--I think I get it now! Yeah, I was referring to speed of recession rather than the distance from the observer. sophiecentaur, I guess your "frequency" reference is analogous to Nugatory's "frame" reference.

 

[sophiecentaur]

I guess your "frequency" reference is analogous to Nugatory's "frame" reference.

Yes. A continuous change of distance (relative shift of reference frame) causes a frequency change of the frames per second.