How fast would an object have to move before it was imperceptible to the human eye?
For example, let's say you were watching a video on a video player that played at 10,000 fps. The video you were watching was that of a small red dot moving across the screen very quickly, over and over. The video starts with the dot only appearing for a single frame. However, each time the dot moves across the screen again, it takes one frame longer to make its trip than it did the previous time. At what point would the average human notice the movement of the dot, if only as a blur? To clarify, I'm not asking how long it would take an average human to react to the movement, but how long it would take to perceive.
If an object continuously appears and disappears for fractions of time that make both its appearance and disappearance imperceptible to the human eye, would a person see these object all the time or would the person not see it at all?
A few of the answers so far have referenced movies. I've been a motion picture projectionist for 20 years, and I have a degree in cinema from USC. So, let me add: It gets even more interesting. A movie screen is blank more than half the time!Yes, films are (typically) projected at 24 frames per second, but each frame gets less than its 1/24th second. This is because the gate has to be obscured as the frame is being pulled down into the "dwell" position. Each frame has to be held still before the gate opens, or you'd see streaks caused by the movement. Additionally, each frame needs to be projected (at least) twice, so the gate goes dark one more time, even though the frame is still there. These "dark times" are accomplished by a rotating blade. A basic "two wing shutter" is essentially a circular piece of metal with notches cut out on opposite sides -- to allow the projector's lamp to illuminate the frame. All of the shutters I have seen have more metal than notch. Hence, "dark time" is greater than "on" time. Now, you may be wondering why it's necessary to flash each frame more than once. This is where the concept of flicker fusion comes in. A strobe appears to become a constant stream of light as it approaches or exceeds 50 flashes per second. So, the flicker of a movie projector would be apparent (and distracting) if it were happening at a rate of 24 per second. Flashing each frame twice conveniently doubles the flicker rate, from 24 to 48 -- much closer to the critical threshold of 50 flashes for flicker fusion to occur. (A fancy 3-wing blade would increase the flicker rate beyond that threshold -- all the way to 72 flashes per second, but at the expense of luminance.)Okay, so why not simply shoot at 48 or 50 or 72 frames per second (or more) and project each frame once? Because persistence of vision doesn't demand that. Shooting at 24fps uses less film (or data) and is more than adequate to create the illusion of movement. In fact, persistence of vision works at fps rates as low as 8-12 fps. Indeed, silent films were typically shot at speeds in the 16-22fps range. The transition to sound demanded a higher inch-per-second (ips) speed to accurately capture/reproduce the entire sound frequency spectrum and increase the signal to noise ratio --and that's how we ended up with a standard of 24fps for motion pictures.
If a star located 1 million light years away were to move at the speed of light, would we detect it moving across the sky?
Well, as you know, nothing with mass can ever move at the speed of light, but I’ll assume you mean almost the speed of light.If the star was moving at nearly the speed of light perpendicular to our current “line of sight” a million years ago, the light arriving now would appear to be coming from a moving source, yes.However, it would take 1,000,000/360 = 2778 years for it to move one degree across the sky, 46 years to move by one arc-minute and just over 9 months to move by one arc-second. So while astronomers would certainly notice the changes in their starfield photographs, you wouldn’t be able to see it move with your naked eye.
Why can’t the Doppler effect be perceived by our eyes (colors) but only by our ear (sound)?
To perceive the doppler effect in a wave, the velocity of the object (relative to you) must be a significant percentage of the velocity of the wave. The speed of sound is about 350 meters per second. So the speed difference of say a train passing you at 20 meters per second is significant in comparison to that, and you can hear the change in pitch of the sound.In contrast to that, the speed of light is 300,000,000 meters per second. For a similar doppler shift, the speed of the moving object would have to be about 15,000,000 meters per second. That’s faster than any object in the solar system, other than individual atomic or subatomic particles. So nothing is moving fast enough for you to be able to see this effect. Only far-off astronomical objects are moving fast enough for the color changes to be visible, and this only with the aid of a telescope since they are so dim in the sky.
Is it possible to see the curvature of the Earth with the naked eye?
If the solar system travels millions of miles per hour in the Milky Way, why do we still see the same constellations?
The whole universe is moving and the stars, that forms the constellations, travel in their own separate orbits through the Milky Way galaxy. The stars move along with great speeds, but they are so far away that it takes a long time for their motion to be visible to us. You can understand this by moving your finger in front of your eyes. Even when you move it very slowly, it may appear to move faster than a speeding jet that is many miles away.Even if you consider the stars that are moving fastest as compared to Earth would take a long time to travel a noticeable distance. A faint star named Barnard's Star moves the fastest through our skies, relative to Earth. Still, for it to change its position only by an amount equal to the diameter of the moon it would take about 180 years. The constellations surely change shape, but seeing the changes would require more than just human eyes. The first person to notice these changes was none other than Edmond Halley. He noticed that a few stars in charts made by Greek sky watchers were not in quite the same location anymore. Those charts were more than 1600 years old then, and even over that time, the bright stars Sirius, Arcturus, and Aldebaran had shifted position only slightly.If you wait long enough, the patterns of stars you would see in the sky would change completely. The Big Dipper is the easily recognizable part of a constellation called Ursa Major, or the Great Bear. The star at the end of the handle and the one at the far tip of the bowl happen to be moving in the opposite direction from the other stars in the Big Dipper. In the future, the handle will appear to be more bent, and the bowl will spread out. So, it wouldn’t be wrong to say that it would change its shape in 50,000 years from now.
If I'm staring at something and it's moving, how slow can it move and still be perceived as continuous movement?
Weirdly this depends on how much practice you get. Anyone who is learning to drive will know how difficult it is to figure out whether you're getting closer or farther away to the car in front of you, often resulting in learner drivers alternatingly being too close, and then too far from the car in front as they struggle to percieve how the distance between them and the car in front is changing. You're far enough away that you don't have any distance queues from parallax (depth perception), so you have to rely on the apparent size of the distant object in front of you, and in the beginning, you're not very good at percieving how this size changes.As you get better at driving, you'll find yourself being able to work out whether your speed is matched by the tiny, almost consciously imperceptible change in apparent size of the car in front.
Why doesn't Polaris (the Pole Star) move if Earth is revolving around the sun and the sun is also revolving around the center of the galaxy?
Polaris is just so far away that its motion is impossible to see with our eyes. The distance to Polaris is 434 light years. That's 27.4 million AU, where an AU is the distance from the sun to the earth. So the motion of the earth around the sun over a year causes an incredibly small shift in the apparent location of Polaris. That angle is 2/27,400,000 radians = 0.0000042 degrees. Next, you mentioned the motion of the sun. The sun moves more in a year than the distance between the earth and the sun. The sun is travelling at about 108,000 km/hour, so in a year, it moves about 6.3 AU. The apparent movement of Polaris due to our being carried along by the sun (orbiting the center of the galaxy) is 6.3/27,400,000 radians = 0.000013 degrees. But Polaris is also moving around the center of the galaxy and moving very approximately at the same speed and direction as the sun, so the actual angle change on the sky will be even less than the above number. The rotation axis of the earth essentially does not change as the earth goes around the sun each year. It points to the same spot on the sky, which is very close to Polaris. The earth's spin axis does move over thousands of years, but the movement from year to year is too small for us to notice without telescopes.