Can we do this with simple mechanics, or does that get us into trouble?
Let’s see. The force acting on you due to gravity is given by f = gm1m2/r-squared.
(where g = gravitational constant, m1, m2 are the masses of the two bodies involved, and r is the distance between 'em)
If you have constant velocity (5 mph in this example), then your engines/cavorite/whatever must be generating an exactly equivalent but opposite force (otherwise your velocity would change).
Now a force f = m * a
(where m is your mass and a is an acceleration).
if you are moving upward at constant velocity, then the two forces must balance, which means that
f = ma = gmm2/r-squared
which looks like you would need to be accelerating at 1 gravity for as long as it took to get out of the atmosphere. At 5 miles per hour vertical velocity, and assuming that you would be clear of atmosphere somewhere around 150,000 feet (Wild-assed assumption), then it would take you 150,000/(5*5280) hours to get out into space which is about 5.7 hours.
Of course, as soon as you turned off the engine, you would start falling back to earth!
Right, but the escape speed goes as the inverse square root of your distance up, so it drops off a bit slower than gravitational force. My point, though, is that if they get up to speed before 100 miles up, they’ll still have to achieve 24,700 MPH. Honestly, though, I don’t know the altitude at which they typically stop accelerating.
At the top of a 10000 miles ladder, the escape speed is still 13323 MPH, or 53% what it is at ground level.
You don’t actually need to travel that fast, the velocity only represents the velocity for something that doesn’t have it’s own source of ‘fuel’ i.e. after the initial force is exerted on it, no more force is exerted on it, like for example throwing a baseball.
So what you’re saying is, in a rocket ship with my own source of fuel, I can go any speed I want, but if I am Superman here on Earth, I would have to throw a baseball about 25,000 mph for it to escape the pull of Earth’s gravity?
MC Master of Cermonies: “I imagine if you climbed the ladder at roughly two miles an hour you’d have a long way to climb.”
Ha ha, fair enough. I was mostly responding to bbeaty who said you wouldn’t have to jump nearly as fast. That’s right, instead of 4000 times faster than is humanly possible, you’d only have to jump 2000 times faster.
Though even if you are a rocket ship, it’s more efficient to go faster. When you go up in a rocket, the engine is really doing two things: hovering and climbing. It takes a certain amount of energy per second just to stay in the air (or vacuum), so the faster you get it over with the better.
Are you sure scr4? What if I (Superman) throw a huge ball weighing a thousand lbs. in the air? It would seem to me I would have to throw it much faster than the baseball to get high enough to escape the pull of Earth’s gravity.
If you fire a rocket straight up at 25,000 mph and ignore atmospheric drag, you WILL NOT escape the earth’s gravity well. You WILL eventually fall back in. Same goes with 250,000 mph. The key understanding that so many seem to be missing is that the 25,000 mph is tangential to the Earth’s surface. Only with a corresponding horizontal velocity (an orbit) will you escape the gravity well.
That’s not true. You can launch at 25,000 mph at any direction except down. Escape speed is simply the speed at which the kinetic energy equals the energy needed to escape to infinity.
If you want to go into a low earth orbit then that’s a different story. You need a hirozontal speed of 1600 mph. Otherwise the orbit will not be circular and will intersect with the earth.
No sigSEGV if you launch a rocket straight up (ignoring factors such as drag) at the escape velocity it will not fall back, it will keep on going in the direction you fired it in (providing it doesn’t hit anything along the way) and thus ‘escape to infinity’. An object that is orbiting the earth has not ‘escaped to infinty’ as it is still being acted upon by the earth’s gravitational forces.
Don’t be confuse “velocity” with the “force” required to get an object to some specified velocity. You would have to use a lot more force to get a heavy object to escape velocity than you would a light one. But if you had the force available and did get the object to the velocity it would go on indefinitely without falling back.
You also have to understand that this assumes that the earth and the object are the only two things in the hypothetical universe. Other planets, the sun etc. need to be considered in the actual case.
My point was if I throw say, a marble and a cannon ball up in the air, both leaving my hands at 30mph, I’m sure the cannonball will start coming down before the marble. So where is this 25,000mph speed coming from? doesn’t it depend on the weight of the object?
Escape velocity refers to the speed at which an object needs to be traveling to escape Earth’s gravitational field. The friction of the atmosphere IS a factor, but a minor one – when you walk, you need to push air out of the way in front of you, but I don’t see anyone straining.
Escape velocity is about seven miles per second, as I recall. Don’t remember what it works out to in MPH, but I remember that bit of data from grade school.
Would gravity pull the bullet downward? Sure it would. But if I aim the Super Gun straight up, the bullet will escape Earth’s gravity before it runs out of velocity. If I aim it parallel to the ground, and the bullet doesn’t hit anything, the bullet WILL travel downwards towards the earth… but due to the earth’s curvature, the ground will drop away from the bullet as it travels, while simultaneously pulling down on the bullet, while simultaneously falling away from the bullet some more, because of that curvature. If your speed is just right, it is possible to fall forever towards the ground without ever actually hitting it!
This is called “being in orbit”. Admittedly, an orbit six feet off the ground would be a hell of a trick, and would definitely require some planning to avoid buildings, people, and natural obstacles, especially at those speeds, but it’s theoretically possible.
One does not need to travel at escape velocity in order to leave the planet. Aircraft manage it all the time. Theoretically, a sealed aircraft with rockets or jets of some sort could simply keep ascending until it left Earth’s gravitational field, speed being pretty much irrelevant, except as necessary to keep the thing in the air (and eventually, out of it). I could be wrong, but I’m told that the SR-71 spy plane could theoretically actually manage this, if you weren’t real picky about getting the plane or its pilots back anytime soon.
Admittedly, this would require a hell of a lot of fuel (although not an infinite amount). We use big giant solid-fuel boosters that shoot you straight up at seven miles a second, because that’s the most cost-effective way to do it, that’s all.
