According to this page, “A rocket must accelerate to at least 25,039 mph (40,320 kph) to completely escape Earth’s gravity and fly off into space.” I’ve never understood this. Why must a body be traveling at a certain velocity in order to escape the gravity of another body? Going by my pathetically poor memory of high school physics, I would think you’d need “escape work” instead–that is, a force applied over a certain distance. Why does it matter how fast you travel when leaving the earth? As long as you’re moving away from it at any speed, you’d break free eventually, right?
Consider: supposed I invent a miraculous engine that can generate a broad range of thrust, from miniscule through prodigious, while consuming only a tiny amount of fuel (so that the weight of fuel doesn’t enter into the equation.) Couldn’t I blast off, accelerate to, say, 100 mph, then just keep moving at 100 mph until I leave the solar system? Sure, it would take many lifetimes to leave the solar system at only 100 mph, but, hypothetically speaking, wouldn’t it be possible?
Welcome to the SDMB, Arcite…good, well-worded question.
I found the following derivation of the equation for escape velocity, which explains where the formula comes from. Intuitively, and in non-mathematical terms, I have trouble explaining and understanding why you couldn’t just travel at 100 mph continuosly and get off, whatever the E.V.
IANAP, but it is precisely because rockets do not continually fire that escape velocity is important. Rockets bring a body up to a speed. Below escape velocity, a body which does not have a constant force working on it will eventually be tugged back to earth.
As the space elevator concept shows, any speed will indeed remove you from the earth’s surface as long as force is being continually applied. I see no reason why this could not continue indefinitely.
You are right. The escape speed is how fast you have to throw something so it never comes back down to earth. It doesn’t apply to a spacecraft which can run its engines continuously.
But in reality, most spacecraft use rocket engines which have large thrust and short burn time. You fire the rockets briefly to achieve escape speed, then coast all the way to the destination. That’s how the Apollo spacecraft worked, as well as most interplanetary probes.
so it seems that a space shuttle at 8km/sec (faster than your proposed 100mph) will still not leave the earth’s orbit due to the gravitational attraction, but will instead orbit the earth…
so maybe a rocket doing 290mph would escape the earth ?
Exapno and scr4 have it right. Escape velocity is the speed at which an object will leave the earth forever, with no further application of thrust.
Think of it this way, if you throw something up in the air, you know that the faster its speed (when it leaves your hand, ignore the atmosphere) the higher it will go. If you throw it up at a speed less than escape velocity, it will go slower as it goes higher, but will eventually turn around and fall back down, or be in a closed orbit. If you throw it at a speed greater than escape velocity, it will still go slower as it goes up, but will never ever turn around, or be in a closed orbit.
Generally speaking, escape velocity varies with the distance from the center of the earth. If you’re already up in a closed orbit (like on the space shuttle) the escape velocity from there is less than at the surface of the earth.
think of it this way. Say you have a 1 lb ball on a string that will break at 20 lbs. now you swing the ball over your head until you have it going at 20g’s at this point the string breaks and the ball flys away. The string represents gravity. Now if you take that same ball and shoot it out of a gun at that same speed the string will break and the ball will continue forward until something else stops it. 20g’s could be considered the “escape velocity” of the ball/string system. If you don’t reach that speed the “string” will keep the ball in the system.
(Ignore atmospheric friction etc) You throw a ball up and it comes down again. The more speed you give it up, the higher it goes and the longer it takes to come down. There is a certain speed at which it will not return and this is called escape velocity.
Escape velocity diminishes as you go farther away from the surface. In fact, if you shoot a ball up with escape velocity, as it goes up and slows down it will have escape velocity for each altitude.
Escape velocity is that which gives sufficient kinetic energy to escape.
Orbits are a different thing alltogether. If you throw something up with less than escape velocity it will fall back down, it will not go into orbit. Escape velocity refers to the vertical component while to put something in orbit you need a tangential component.
you never do, the force just becomes negligible. Newton states that "every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses, and inversely proportional to the square of their distances apart”
Chronos (as quoted by Shagnasty) is correct, and sailor’s post is a bit misleading. Direction doesn’t matter. If you throw something horizontally at escape speed, it will never come back to the earth - just like if you threw it upwards at the same speed.
