8 ms·
Escape velocity is actually only necessary for launching ballistic objects such that they will never return to the surface of the planet over an infinite amount
by nilkn 9y ago
Escape velocity is actually only necessary for launching ballistic objects such that they will never return to the surface of the planet over an infinite amount of time (assuming no other interactions occur). It's not necessary when you have a method of providing continual propulsion and acceleration. Speed is mostly irrelevant if you can provide propulsion indefinitely. Escape velocity is an important concept because, realistically, you can't actually do that or it's extremely cost inefficient to attempt to do so.
- larkeith 9y agoEscape velocity is the total amount of acceleration necessary to escape a gravity well, aka the minimum amount of energy.
- nilkn 9y agoNo, it's explicitly defined as a speed or velocity, not as acceleration and not as energy.
- larkeith 9y agoA velocity is the total of acceleration over time (as was referred to). A mass (the spacecraft) moving at a velocity has a given amount of energy, and in this context may be used interchangeably.
- mannykannot 9y agoThis is just pointlessly pedantic. You are going to get into all sorts of problems if you arbitrarily substitute any of velocity, acceleration or energy for any of the others. Having unstated dependencies is only going to lead to avoidable confusion. The key insight revealed in the term 'escape velocity' is that it is independent of the mass of the body. It is also independent of how quickly it acquires that velocity.
- aphextron 9y ago>Speed is mostly irrelevant if you can provide propulsion indefinitely Except you can't, so speed is very definitely not irrelevant.
- nilkn 9y agoIt would probably be enlightening to read the sentence that immediately followed.
- garmaine 9y agoThis is very confused. To leave the Earth’s gravitational grip you need to impart a certain minimum change in velocity. You can do this all at once or or we time but it doesn’t matter. The delta-V is the same.
- nilkn 9y agoThis is simply false. The needed escape velocity decreases with distance from the planet, so applying a change over a long period of time actually can very materially change the requirements. To give an example, if you provided propulsion to move an object at 1 mile per hour, you could turn off all propulsion and the object would have escaped Earth's gravity once it was 4 * 10^12 km away. This is, of course, an extraordinary waste and probably practically impossible.
- larkeith 9y agoYour "example" seems to predicate on a world without gravity. The reason escape velocity is reduced based on the distance from the surface is that you have already provided enough energy to overcome the vertical difference - you can see this reflected in the difference in gravitational potential energy.
- nilkn 9y agoEscape velocity is reduced based on distance because gravity itself is reduced based on distance. This is obvious from the the expression sqrt(2GM/r), which is the escape velocity at a distance r from the center of a spherically symmetric body of mass M. From this expression one can easily calculate the distance I provided. This computation is completely based on Newtonian gravity and would make no sense in a world without gravity.
- garmaine 9y agoThat’s not how physics works. I suggest reading up on conservation of energy and gravitational potential energy.
- isostatic 9y agoThe further you get from the planet, the lower escape velocity becomes. At some point you will be going faster than escape velocity.
- nilkn 9y agoIndeed -- this is illustrated in my example below where one moves an object at 1mph (fixed speed) for about 283 million years until it's 4 * 10^12 km away from the Earth, where the escape velocity is right around 1mph.