Why Does an Object Far Away Seem Slow?

In summary, the conversation discusses the concept of perspective and how it affects our perception of distance and velocity. This is demonstrated through examples such as an airplane appearing to move slower when far away and the moon appearing smaller despite its actual size. The group also explores the mathematical explanation behind this phenomenon and how it can lead to misinterpretations, such as UFO sightings. Overall, the conversation highlights the importance of considering perspective when making observations and drawing conclusions.
  • #1
Raza
203
0
Why does an object far away looks like it's going very slow when it's going really fast? And then the object seems really fast when it's near me. I just started driving and I always try to find an answer but really can't.

Thanks :)
 
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  • #2
perspective

Look up "perspective": http://en.wikipedia.org/wiki/Perspective_%28visual%29" [Broken]
 
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  • #3
I think Raza's question is more complicated (and fascinating) than the simple fact that objects that are close to you appear bigger than when they are far away. That's easily explained.

Consider instead watching an airplane just before landing at an airport.

I'm guessing it is probably traveling at 150 mph at least. That's 220 feet per second. So depending on the size of the airplane, it should be traveling more than once its own length per second.

But when you look at it versus the background of sky and clouds, it sometimes appears to be moving much slower than that. Almost "hovering" in the sky sometimes.

Part of this would be explained if the airplane was flying at an angle toward or away from you. But I've even noticed it when the airplane is traveling perpendicular to my line of sight.

Optical illusion? Poor assessment of the facts on my part? Lack of stationary reference points behind the airplane?

Or is it something more fundamental with the spherical geometry of our field of vision, etc. ??

Paul
 
  • #4
smithpa9 said:
Consider instead watching an airplane just before landing at an airport.I'm guessing it is probably traveling at 150 mph at least. That's 220 feet per second. So depending on the size of the airplane, it should be traveling more than once its own length per second.

You're absolutely right. A Jumbo 747 generally lands at between 150 and 200 mph depending on the specific airport and local weather conditions at the time. But it certainly looks a lot slower than that.
 
  • #5
I still don't get it. Can somebody explain it to me more in dept?
 
  • #6
Raza said:
I still don't get it. Can somebody explain it to me more in dept?

I think your first response from Doc Al was as close to the truth as you'll ever get. Perspective.

A distant object IS moving fast. just the angle that movement makes at your eye is smaller the further away the object is, so the angular speed is smaller. That's all you're saying really - the further away the object is from you, the smaller the angular speed is. :wink:
 
  • #7
YellowTaxi said:
the further away the object is from you, the smaller the angular speed is. :wink:

Just like the further away the object is from you, the smaller it appears to be. When you look up at the moon at night, you can cover it up with the tip of your finger, held out at arm's length. But the moon is really one heck of a lot bigger than your finger! :bugeye:
 
  • #8
Thank you, taxi, I got it. :)
 
  • #9
I'm curious as to how this changes apparent observations of the observer verses a stationary one. Not in terms of different physical phenomena, but in terms of how the geometry changes when moving at a constant speed, in short, what changes to the manner in which the moving observer makes his measurements in order to agree with the stationary observer. How is this different in the constant and accelerating frames of reference?
 
  • #10
It is just about perspective. In this view, something far away is smaller because our eyes perceive them smaller due to our brain trying to interpret distance. Thus if distance is smaller, velocity would appear smaller. So it is just about our perception.
 
  • #11
A graph of y=arctan(1/x) will help explain this:

http://jeffareid.net/misc/pa.jpg [Broken]

A 747 aircraft appears to be slow, because our brains don't properly interpret the size of the aircraft, and mis-interpret the aircraft as being closer than it really is. Having a small jet fly side by side with the 747 helps reduce this affect. Experience watching aircraft reduces this effect.
 
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  • #12
Jeff Reid said:
A graph of y=arctan(1/x) will help explain this:

How it explains? What is x and y?
It will be greatly appreciated if you give a proof.
 
  • #13
Ahmed Abdullah said:
How it explains? What is x and y?
It will be greatly appreciated if you give a proof.

On the graph, Y is the perceived angle in radians. X is the distance of the object in multiples of height.

The perceived angle of the object is the angle determined by the ratio of height to distance. For my example, I set the viewer's eye level on the ground, and the perceived angle is relative to the horizon. This is arctan(height / distance). The graph shows the angle as radians, so the maximum angle perceived is pi/2 (vertically looking up at the top of the object as it passes directly by). For 0 distance, I used the limit as X approaches zero to get an angle of pi/2 (actually I used a 2 paramter arctan function, that takes x and y as separate components, to eliminate division by zero for distance zero).
 
  • #14
Dbjergaard said:
I'm curious as to how this changes apparent observations of the observer verses a stationary one. Not in terms of different physical phenomena, but in terms of how the geometry changes when moving at a constant speed, in short, what changes to the manner in which the moving observer makes his measurements in order to agree with the stationary observer. How is this different in the constant and accelerating frames of reference?
This is the cause of a large fraction of "credible" UFO sightings, including a famous one by the Mexican Air Force a while back that got months of discussion here before someone (not from here) figured it out.

The fact that all motion is relative makes it utterly impossible to distinguish one motion from another without contextual clues about your velocity vs the velocity of what you are looking at. In this case, a couple of pilots "saw" some UFOs with an infrared camera. With no reference to size or distance, they concluded the "objects" were flying and maneuvering in close formation with them. It turned out that the "objects" were methane gas flames atop oil rigs some 40 miles away. Without knowing either distance or size, it is impossible to compute how the object is actually moving. The geometry is straightforward for relative motion: you just need to know 3 of the six pieces of information about a triangle (1 or 2 legs and 1 or 2 angles) to solve for the rest. At short angles/long distances, you can aproximate it pretty accurately with one angle and one leg.

Perhaps the easiest (maybe the only) way to deal with this problem is to view all events from a top-down, stationary 3rd party perspective. You should at least know your own speed and using vectors, you can compute the "absolute" motion of another object with some relative motion information. The catch here is that if you don't know distance, you get a range of possible "absolute" distances vs speeds for a certain observed relative motion. For this particular case, a little bit of logic might have led someone to consider the possibility of the objects being stationary, or being on the surface, and using that information the problem could have been solved with ease.

This is a common navigation problem, solved with a "maneuvering board": http://navsci.berkeley.edu/ns12b/lectures.htm [Broken]

Solving the problem during acceleration (such as in a turn) is only really possible (without some heavy math) during times of constant acceleration.
 
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1. Why does an object far away seem slow?

Objects appear to move slower when they are further away because of the phenomenon known as "perspective." Perspective is the way our eyes interpret the size and distance of objects based on their appearance. When an object is far away, it appears smaller and therefore seems to be moving slower compared to objects that are closer to us.

2. Does the speed of light affect how an object appears to move?

The speed of light does not directly affect how an object appears to move. However, the speed of light does play a role in how we perceive objects that are extremely far away. Since light takes time to travel to our eyes, the further an object is, the longer it takes for the light to reach us. This can affect our perception of the object's speed.

3. Can atmospheric conditions affect how an object appears to move?

Yes, atmospheric conditions can affect how an object appears to move. In particular, air density can play a role in how fast an object seems to be moving. In denser air, objects may appear to move slower, while in less dense air, they may seem to move faster. This is because denser air creates more resistance, making it more difficult for objects to move through it quickly.

4. Is there a limit to how slow an object can appear to move?

There is no specific limit to how slow an object can appear to move. The perceived speed of an object depends on various factors, such as distance, size, and perspective. However, our brains are capable of perceiving very slow movements, so an object can technically appear to move very slowly, as long as there is some movement present.

5. How does the brain process visual information to perceive an object's speed?

The brain processes visual information by combining visual cues, such as size and distance, to determine an object's speed. It also takes into account our previous experiences and knowledge of how objects typically move. The brain then uses this information to create a perception of an object's speed, which may not always be completely accurate.

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