essentialsaltes
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Yup. You've got it right.
Yes like I said if the centre of the two spheres coincide then the gravity at the centre is zero. I missed the part where the centre of the two spheres do not coincide.Umm, no. Too early for answers yet. essentialsaltes had the right answer for concentric spheres. If they share the same center the gravity in the hollow is zero.
In this case the center of the two spheres is not concentric.
What is the least detectable difference in angles for modern telescopes?
I assume one exists because of the non-continuous, or seemingly so, micro-universe.
For example:
You send out three photons from the same source in the same direction (slightly different angles, but the same time).
When (/at what angle and distance between them) will we be unable to say that they're possibly from the same light source because of our unability to discern them as unparallel?
Thanks for the replyIt is more a question of pattern recognition. Let's use convex mirrors as an example. Light paths bouncing off of a convex mirror to our eyes are not parallel. Those paths are actually diverging and are not parallel. This produces distortions like those in this pciture:
What allows us to piece an image together is that the image is uniformly distorted. This differs light that has been scattered, such as light from behind cloud cover or an image that is passing through sand blasted glass. In this case, the paths are not uniformly distorted so we have to model the actual distortion in order to piece the picture back together.
I'm assuming that we're able to measure the angle of a single photons direction though.
Further clarification:
If we have one point that sends out ten photons in a plane, evenly spaced, we can come to the conclusion that there's a 36 degree angle between them, all the time. Increasing the distance between the observer and the point emitting the light will decrease the number of photons observed (due to lens width).
Given a sufficiently large amount of photons, along with a distance that will allow the observer to observe only three photons through that lens, at what angle between the photons will the angle be observed as zero? (Thus promoting the conclusion of separate light sources)
I've been thinking about this for a while and I have a suspicion that a lens/mirror (i.e. the observer) made out of atoms (i.e. something discrete) have a hard limit to what the minimum observable angle is (since the possible angles are, at least it seems like so to me, continuous).
If I've expressed myself vaguely don't hesitate to point it outcheers!
OkIn order to do that we need to know the source, where it is detected, and the conditions in between. Given complete knowledge and proper computing power we could reconstruct the most scattered and blurred images imaginable. However, we usually don't have anywhere near the info or silicon to do this.
If memory serves, doubling the distance between the observer and a candle cuts the intensity of the light by 25%. This principle is used in astronomy for "standard candles" such as type Ia supernovae.
This is know as resolving power:
Angular resolution - Wikipedia, the free encyclopedia
It is interesting that you can increase the resolving power by using separate telescopes that are separated by a certain distance. You can combine the image from the two telescopes and get a small image with the resolving power equal to the distance between the two telescopes. They use this technique on the big telescopes in Hawaii (forget the name of it at the moment).
If I understand optics correctly, resolution is dictated by the size the telescope, and the sensitivity is determined by the transparency or reflectivity of the telescope.
I didn't know that. Darn you, now I've exceeded my "learn-one-thing-per-day" quota.A side note to Loudmouth's answer to Elendur, the limits of resolving power are why we don't use the Hubble telescope, or any other Earth based telescope, to look at the Moon for evidence of the various Apollo Lunar Missions. The Hubble, for example, has a minimum resolution of 100 meters at the Earth/Moon distance. Anything smaller than that is not detectable. The stories of spy satellites that can read license plates, as you see in certain spy movies, are also a myth due to this "law".
Spy satellites are in low earth orbit and depending on the light wavelength they use to "see" then the resolving power can easily be achieved to see licence plate numbers from a few hundred kilometres. As for the moon I agree since the distance is too great for any telescope on earth or in orbit around earth to resolve objects left behind on the moon by man.A side note to Loudmouth's answer to Elendur, the limits of resolving power are why we don't use the Hubble telescope, or any other Earth based telescope, to look at the Moon for evidence of the various Apollo Lunar Missions. The Hubble, for example, has a minimum resolution of 100 meters at the Earth/Moon distance. Anything smaller than that is not detectable. The stories of spy satellites that can read license plates, as you see in certain spy movies, are also a myth due to this "law".
Spy satellites are in low earth orbit and depending on the light wavelength they use to "see" then the resolving power can easily be achieved to see licence plate numbers from a few hundred kilometres. As for the moon I agree since the distance is too great for any telescope on earth or in orbit around earth to resolve objects left behind on the moon by man.
Just google earth and you can see things the size of toys. Spy satellite technology is restricted information thus we are unable to know what their resolving power is.
They are normally placed on a LEO of approximately 200 kilometres.I seriously have my doubts about that.
I will have to plug some numbers into the equations. I will be very generous and use a low altitude of 100 kilometers, officially the edge of space, though any satellite that dipped that low would probably hit too much atmosphere to recover.
They are normally placed on a LEO of approximately 200 kilometres.
Regarding the ability to read licence plates at 200 km is just an indication of resolving power.The thing that is important is having the ability to resolve objects as small as a few centimetres at LEO. It is about the technology that I am referring to and not its use. I agree with you on the limitations of reading a number that is placed perpendicular to the line of vision.That would be even worse than the number that I used. Remember you cannot shoot straight down. License plates that you would want to read are mounted vertically. So call it a distance of at least 300 kilometers and see how you do.
I came up with the same figures, so you are correct!I am up way too late and should go to bed. I was wondering with what sort of figures you came up with. I used the very simple, but good enough for this work formula of:
R = lambda/D Where R is the minimal resolution angle in radians (what the heck, my Firefox spell checker does not like the word "radians"). Now at 300 km, remember we will not be looking at the license plate straight down, an I is roughly 4 cm by .5 cm. So let's say to read letters like B and numbers like 8 we will need at least 1 cm of resolution. At very low angles sin(theta) is equal to theta. Therefore we need .01 m/300,000 m= 3.33 E -8 radians. of resolution to read the license plate of a car. Let's get into the purple, even though the light intensity starts to drop off rapidly at higher frequencies and use a wavelength of 400 nm or 4.00E-7 m. Even if we have a 1 meter lens, and that is a big lens, we could only resolve images down to 4.00 E-7 radians. Approximately 1 tenth of the resolution needed.
In other words to comfortably read a license plate from LOE we would need a telescope with a lens of about 10 meters across. Your typical movie spy camera is 10 centimeters if you are lucky.
That was my thoughtI came up with the same figures, so you are correct!
Apparently commercial satellites now offer resolutions at a lower price than their military counterparts and yes you are right; We have reached the limit of resolution.
Drones can do a better job and they are stealthy enough to go undetected in most cases.
However it is theoretically possible to use multiple satellites as one "telescope" and with image processing software to actually be able to resolve objects much smaller.
Too tired to delve further into this today. Have you seen the images from the Mars orbiter? Neat eh!Good night
I came up with the same figures, so you are correct!
Apparently commercial satellites now offer resolutions at a lower price than their military counterparts and yes you are right; We have reached the limit of resolution.
Drones can do a better job and they are stealthy enough to go undetected in most cases.
However it is theoretically possible to use multiple satellites as one "telescope" and with image processing software to actually be able to resolve objects much smaller.
Too tired to delve further into this today. Have you seen the images from the Mars orbiter? Neat eh!Good night
Ah yes; I once argued that something cannot use the wind to travel faster than the wind acting on it but boy was I wrong!!!! Aerodynamics my dear fellow; Elementary EH!Yes, multiple satellites give better resolution. But I don't think we are getting one centimeter of resolution that way. Hmm, I will have to check into it, I used to debate against a particular topic until <gasp!> I found out I was wrong and then I became a huge fan of it (Google search DDWFTTW) the guy who built a successful machine works quite a bit with GPS sometimes. PS, if you are an American sports fan you have seen his work.
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