If I understand the terminology correct, an body’s escape velocity is the speed an object must obtain in order to be able to continue moving away from the body indefinitely. If it fails to achieve that speed, it will simply go into orbit or fall back to the body.
Since the Earth’s escape velocity is 11.2km/s, I would have to go that fast to avoid going into orbit or falling back to Earth.
So far, so good, correct?
But suppose I had a ladder or staircase that went up from the Earth infinitely. I could start climbing on the ladder and I know that I will never reach 11.2km/s. Yet (barring falling from fatigue), I won’t fall back to Earth either and I can continue moving away from the Earth indefinitely.
So, how is it possible for me to continue moving away from the Earth without hitting the escape velocity?
If you’re in a rocket, the net force on you is non-zero; gravity will be constantly decelerating you. If you start out with your speed equal to the escape velocity then your continually decreasing velocity will never quite reach zero.
If you are climbing a ladder, the ladder is providing a force to overcome gravity, so then net force on you is zero (ignoring the rotation of the Earth.) There will be no acceleration on you, so you don’t have to worry about your speed decreasing. You can come to a halt on the ladder, then start moving again, whatever.
That may be fine and well, but if the escape velocity is going to drop to the point where I can escape by simply walking away, then what is the point of the escape velocity?
Escape velocity is usually sufficient but not required to leave the planet. In case of a ladder you have slow but continuous system of propulsion. Escape velocity is the velocity you can reach and then turn off the engines, and you’ll still leave the planet.
In other words, escape velocity is not only the function of the two masses, but also of the distance ‘r’ between the two objects. In case of the ladder, you are putting in energy until escape velocity gets low enough for you to reach it by just taking a step. As long as your acceleration is greater than the acceleration due to gravity you will put distance between you and the planet, and it will get easier and easier as you get farther.
I don’t know if I made things clearer, made them more complicated, or made any mistakes, but I hope this helps.
Escape velocity is what you need to reach at or near the surface of the earth. Once you’ve reached that velocity, you need add no more energy to keep increasing your distance from the earth indefinitely.
The “infinte ladder” is another method. Here, you add energy over a long time/large distance.
So far, the first method has proven to be more practical.
Yes more or less. Escape velocity is found by integrating potential energy due to gravity from 0 to infinity. So if you shoot something off at escape velocity it will come back an infinite amount of time later.
The rest of your question has been answered already.
As a demonstration of the significance of the escape velocity, the space shuttle does not reach the earth’s escape velocity. As a result, it needs a big ol’ honkin’ fuel module strapped to it to provide the fuel for the continuous thrust you need to break free if you do not reach the escape velocity.
To put it in simpler terms (and hopefully without introducing too many errors in the process), consider the following:
Suppose you have a big cannon capable at launching you at a speed of roughly 12 km/s when you leave the barrel. Since this speed is higher than the escape velocity of the planet, you can make it into outer space. Note that in this case, all the energy used to take you to outer space is supplied at the beginning of the trip (i.e., when the cannon fires). Alternately, you can take the infinite staircase, and reach space all the same. The difference is that you’d be doing work for the entire duration of the trip.
Escape velocity, then, has to do with the case where an object is given some initial velocity (in, say, the upward direction) but no further forces other than the planet’s gravity (and drag forces, but let’s ignore those) then act on it.
More to the point, the escape velocity is what you need to coast away from a body, not what you need to get away from it. There’s no minimum speed for getting away from a body.
There is a “point” to this from our perspective of using rockets. Moving slowly away from the Earth takes too much fuel. If you designed a rocket to climb at one mile per hour, it would only make it a few thousand feet before running out of fuel. But the escape velocity is no magic number in this regard. They just have to make sure the fuel lasts long enough to reach the escape velocity (whatever that is where the fuel runs out).
But the shuttle doesn’t escape - it goes into orbit. It needs all the fuel it brings just to get there - it would need more to get out of orbit. If it just sat in orbit indefinitely, it’s orbit would eventually decay and it would return to Earth. It is still firmly a prisoner of Earth’s gravity at all times.
The reason it needs so much fuel is because it’s enormous - compare the size of the shuttle to your average satellite or moon shot capsule.
In this scenario, the rocket is very much like the ladder. Either way, you’re continually pushing yourself up. Except the rocket doesn’t have to push forever, but you’d have to keep climbing nearly to infinity.
As long as the rocket is firing, it’s pushing it self up, and once it’s got to the local escape velocity (the EV at the atlitude), it can shut off and coast. If you could accelerate up the ladder under your own power until you hit local EV, you could let go and keep flying away from Earth forever.
Remember, though, that when people refer to escape velocity they rarely include the effect of drag. So, you would need to be moving at 11.2 km/s from the Earth’s surface to escape Earth’s gravity well, but only if all the atmosphere had been sucked off the Earth. In reality you would need to go much faster to compensate for all the energy you would be losing to drag.
I agree the shuttle is a huge payload. But wasn’t the total size of the Saturn V rockets that launched the Apollo moon missions larger than the ready-to-launch size of a shuttle mission?
Apollo Command Service Module: 30 tons
Apollo Lunar Module: 15 tons
Saturn V total launch weight: 3200 tons
Fraction of “payload” to total weight: 1.4%
Space Shuttle orbiter dry mass: 80 tons
Space Shuttle payload: 25 tons
Shuttle total launch weight: 2000 tons
Fraction of orbiter+payload to total weight: 5.3%
In order to get into orbit, a spacecraft needs about 7.5 km/s of speed. To escape, it needs 11.2 km/s. Kinetic energy goes as square of speed, so you need roughly 2.2 times more energy to reach escape speed than orbital speed. That’s a bit off from the above numbers because fuel requirements aren’t linear (you are lifting not just the payload, but all the remaining fuel). Also the Shuttle orbiter includes the engines.
Again I say, SDMB rocks!!! I knew about the escape velocity, but never understood it before. Just took it on faith that NASA knew what it was talking about. Thanks for the question, thanks for the answers!!!
