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Posted by / 12-Sep-2019 05:31

“Light gathering power” is just how much light can be collected by the telescope.

“Resolving power” is a measure of the smallest angle that the telescope can reliably detect.

Telephoto lenses need to be large because the amount of light that bounces off of a distant object and that then goes through the lens is fairly small. They need to be long for other, more subtle, reasons.

Because light is a wave it has a way of spreading out (technically: diffracting).

The smaller the telescope the more the waveness becomes a problem.

It turns out that if that star gets smaller and keeps the same mass, that the shape of the space you’re in stays about the same (as long as you stay the same distance away, the density of an object isn’t relevant to its gravity).

It’s worth stepping back and considering where our understanding of black holes, and where all of our predictions about their behavior, comes from.

Ultimately our understanding of black holes, as well as all of our predictions for their bizarre behavior, stems from the math we use to describe them. It also turns out that no experiment can tell the difference between floating motionless in deep space and accelerating under the pull of gravity (when you fall you’re weightless). Sarcasm aside, what was genuinely impressive was the effort it took to turn those singsong statements into useful math.

The extremely short answer to this question is: the math says nothing can escape, and that the gravity doesn’t “escape” so much as it “persists”. Einstein’s whole thing was considering the results of experiments at face value. Einstein’s stunning insight (paraphrased) was “dudes! What if there’s no difference between falling and floating? After a decade of work, and buckets of differential geometry (needed to deal with messed up coordinate systems like the surface of Earth, or worse, curved spacetime) the “Einstein Field Equations” were eventually derived, and presumably named after Einstein’s inspiration: the infamous Professor Field.

When test after test always showed the speed of light was exactly the same, regardless of how the experiment was moving, Einstein said “hey, what if the speed of light is always the same regardless of how you’re moving? The left side of this horrible mess describes the shape of spacetime and relates it to the right side, which describes the amount of matter and energy (doesn’t particularly matter which) present.

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Even if that object collapses into a black hole, the gravity field around it stays about the same; the shape of the spacetime is stable and perfectly happy to stay the way it is, even when the matter that originally gave rise to it is doing goofy stuff like being a black hole.

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