How far away for observer to see speed of light travel?

[Banshii]

To clarify the title,

 

How far away from an object, and how big must the object be, for you to see it travel at the speed of light for at least 30 seconds?

 

As an example, when you are standing on the ground, you can easily see an airplane traveling faster than the speed of sound for a long while as it goes across the sky.

 

But, for an object traveling the speed of light.... if you were in a space ship relatively staying still, what's the closest you can be in order to see an object traveling at the speed of light for 20-30 seconds, before it gets too far away (and tiny) to see? And, how big would the object need to be for you to clearly see it, as in the airplane example above?

 

 

[Delta1212]

The distance at which something is visible depends on how big it is and how much light it gives off/reflects. How big it needs to be to see it depends on how far away it is and how much light is coming from it.

 

There's no single value for either of those things because they each depend upon the other, plus illumination.

[Banshii]

The distance at which something is visible depends on how big it is and how much light it gives off/reflects. How big it needs to be to see it depends on how far away it is and how much light is coming from it.

 

There's no single value for either of those things because they each depend upon the other, plus illumination.

 

There is some kind of answer... because if I scaled it down to my airplane example, you could say that an object the size of an airplane can be seen for about a half minute going the speed of sound if you are standing 5-10 miles away.

 

To see an airplane going the speed of light, you would have to be sooo far away, but the airplane isn't big enough to see from that far away, so it'd have to be bigger. How big, how far away?

 

 

EDIT: Or close to the speed of light (since mass can't go that fast).

Edited August 25, 2016 by Banshii

[John Cuthber]

The only thing that can travel at the speed of light is light.

If ilight travels across in front of you like a plane, you won't see it.

[Banshii]

The only thing that can travel at the speed of light is light.

If ilight travels across in front of you like a plane, you won't see it.

 

Yes I edited my last post as you said that... then close to the speed of light.... 95% the speed of light? I'm looking for ballpark...

[John Cuthber]

Well, if a fly crosses my room (about 12 feet across and about 12 feet from me) in 12 seconds I can see it easily.

If the fly was doing near the speed of light (almost exactly a billion feet per second) it would cross the room in 12 nanoseconds or so- that's too quick for me.

But if my room was a 12 billion foot cube then I'd see the fly (as long as it was brightly enough lit).

That's about 3.6 billion metres.

The sun is about 149 billion metres away.

So an object roughly a 50th as far away as the sun but travelling near the speed of light would be visible (assuming I got the maths right).

How big it is doesn't really matter- what would make a difference is how bright it is.

Since it's 50 times nearer than the sun it could be about 2500 times less bright- and still "look" as bright as the sun.

At night it could be much less bright, but still be visible.

The moon is something like a million times less bright than the sun.

So something about 3.6 billion metres away and emitting about a bilion times less light than the sun would be visible if it passed us at "near" the speed of light.

It would almost certainly kill us.

[Banshii]

Well, if a fly crosses my room (about 12 feet across and about 12 feet from me) in 12 seconds I can see it easily.

If the fly was doing near the speed of light (almost exactly a billion feet per second) it would cross the room in 12 nanoseconds or so- that's too quick for me.

But if my room was a 12 billion foot cube then I'd see the fly (as long as it was brightly enough lit).

That's about 3.6 billion metres.

The sun is about 149 billion metres away.

So an object roughly a 50th as far away as the sun but travelling near the speed of light would be visible (assuming I got the maths right).

How big it is doesn't really matter- what would make a difference is how bright it is.

Since it's 50 times nearer than the sun it could be about 2500 times less bright- and still "look" as bright as the sun.

At night it could be much less bright, but still be visible.

The moon is something like a million times less bright than the sun.

So something about 3.6 billion metres away and emitting about a bilion times less light than the sun would be visible if it passed us at "near" the speed of light.

It would almost certainly kill us.

 

Say your back is to the sun, in space. There's something the size of the moon in front of you, lets say 3 times the distance the moon is from the earth. Due to the suns light reflecting off of the moon-sized object, you'd be able to see it, just as you can see the moon at night from earth.

 

So, that object is now moving across your field of view close to the speed of light. It's big enough you can see it from that far away (I think, didn't do math but seems like it would be)... but are you far enough away to be able to see it go across your "horizon field of view" at the speed of light? Or are you too close, meaning you'd see it for a nanosecond?

 

Say your back is to the sun, in space. There's something the size of the moon in front of you, lets say 3 times the distance the moon is from the earth. Due to the suns light reflecting off of the moon-sized object, you'd be able to see it, just as you can see the moon at night from earth.

 

So, that object is now moving across your field of view close to the speed of light. It's big enough you can see it from that far away (I think, didn't do math but seems like it would be)... but are you far enough away to be able to see it go across your "horizon field of view" at the speed of light? Or are you too close, meaning you'd see it for a nanosecond?

 

So, do you see where the problem lies? If you have to go even further away from the moon-sized object in order to see it for a good half minute traveling near the speed of light across your plane of view, then the moon-sized object will be too small to easily see. That means it would have to be bigger than moon-sized. It's all related.

[studiot]

Here is the back of my envelope for the unaided human eye.

 

The receiving angle or angular field of view is 114^o or 2 radians.

 

Light travels at about 3 x 10⁸ metres per second or 3 x 30 x10⁸ metres in 30 seconds approx 10¹⁰ m

 

So the arc of your max field of view is 10¹⁰ m.

 

This is equal to [math]r\theta [/math] or the radius times the angle.

 

The radius is of course the distance away of the travelling object.

 

2r = 10¹⁰ m

 

r = 5 x 10⁹ m or 5 million kilometers.

 

 

Now if you will supply details of the illumination of the object, or if the object emits light in concentrated beams eg then the minimum size of object to supply the minimum eye sensitivity over this distance can be estimated.

 

 

[Mordred]

nice back of the envelope. +1

[Delta1212]

Is that field of view without moving your head or eye, though? I had assumed based on the airplane example that this was a case where the object was traveling laterally along your field of vision at some fixed distance until it became too small to see, rather than entering your field of vision on one side and exiting the other as you remained still.

 

That would require determining how far away, based on size and illumination, an object needs to be before it becomes invisible to the naked eye, and then figuring the straight line path it would need to travel within a circle with a radius of that size in order for the time between crossing into the circle of visibility to crossing out of it is at least 20 seconds.

 

20 light seconds is a bit over 3.7 million miles, so assuming that the object is traveling at almost light speed and takes a path that cuts straight through the middle of the circle and blows right past you, you'd need a circle with a radius of at least 1.9 million miles -ish.

 

Then you just need to work out what size/illumination is visible out to 1.9 million miles.

 

If you want to be able to watch it travel the full distance without having to turn around, or want it to remain a set distance away from you, that can be worked out based on what you want.

 

Converting over to the same units as studios, it looks like you'd need an object whose size/illumination allows it to be visible at least out to 3-5 million kilometers depending on how much you want to have to turn in order to watch the object from the time it enters visibility to the time it leaves your visibility, with 3 million kilometers allowing you to watch for 20 seconds if you turn completely around and 5 million kilometers allowing you to watch it for 30, seconds without moving.

 

Although, actually, studiot, is your calculation assuming a curved path traced around the edge of a circle of visibility 5 million kilometers in radius? Because if the plane is traveling in a straight line, then the outer edge of the circle would need to be farther away than that, since a secant line cutting through the circle perpendicular to your field of view would need to have the distance you used for the arc length.

 

I suppose a lot of this depends on the parameters of the problem needing to be better defined.

 

How much can you turn to watch the object travel, if at all?

 

Can the object follow a curved path or must it travel in a straight line?

 

How much light is being given off/reflected by the object.

 

Given those three variables, I think you should be able to pin down a specific size and distance.

[John Cuthber]

nice back of the envelope. +1

Thanks