Timeline for How can escape velocity be independent of the direction of projection of a body?
Current License: CC BY-SA 4.0
9 events
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| Aug 10, 2021 at 19:45 | comment | added | Guillermo BCN | Thank you. I think his qualitative explanation is basic. He speaks of ‘a velocity’ at which escape happens. He does not say anything about its magnitude being independent of the angle though. In any case, Thank you for your efforts. | |
| Aug 10, 2021 at 18:04 | comment | added | Serge Hulne | Here is another explanation by Neil de Grasse Tyson : youtu.be/7vXoaiu4zFI (the mountain thought experiment by Newton) | |
| Aug 8, 2021 at 12:25 | comment | added | Serge Hulne | If you think about Gauss’s theorem, it appears that the gravitational potential of the Earth is the same as the one you would get from a body with the same mass as the Earth, located at the center of the Earth (basically a small black hole). The potential is exactly the same in the both cases. In the case of a black hole, there would be basically no forbidden trajectories (except a for a head-on collision with its center or rather its event horizon). | |
| Aug 8, 2021 at 11:14 | comment | added | Guillermo BCN | Ok, I get that. And I am sure the analogy is there. However, I think the source of his confusion (as is mine) is the fact that some escape trajectories actually intersect the planet, which seems to contradict the idea of ‘escape’. | |
| Aug 8, 2021 at 11:05 | comment | added | Serge Hulne | It is just a metaphor of a case where a single parameter matters (height) and another don’t (angle). I was trying to give a graphical metaphor for a potential barrier. | |
| Aug 8, 2021 at 11:00 | comment | added | Guillermo BCN | With a fence, it depends on the vertical component of the velocity. It won’t be of any use running very fast toward the fence if your jump speed is low; you will just hit the fence very fast. So it does not seem to be the modulus of the velocity that is crucial. | |
| Aug 8, 2021 at 10:26 | comment | added | Serge Hulne | Think of it as jumping a fence. In order to jump a fence, one merely has to jump in the air high enough (the threshold being the height of the fence). The result does not depend on the angle at which one runs towards the fence. | |
| Aug 8, 2021 at 5:11 | comment | added | Guillermo BCN | I am not sure your answer fully clarifies the issue. Why is the condition that the kinetic energy be larger than the potential energy enough to ensure that the projectile ‘escapes’? If this had been clear to the OP, he may not have posed the question in the first place. | |
| Jun 22, 2021 at 23:10 | history | answered | Serge Hulne | CC BY-SA 4.0 |