Can someone explain why there is a minimum speed (an escape velocity) for objects to escape earth’s gravity before they can be propelled to other solar bodies. I believe that a rocket must push a ship or satellite to something like 25,000 mph before it can escape an earth orbit. This seems a little strange. For arguments sake, let’s say I build a super-efficient but very SLOW rocket pack that can send me to the moon at an upward sustained speed of say 100 mph. Why couldn’t I just jump in a space suit, throw on the pack, fire it, and be out of earth orbit heading towards the moon within a few hours? This is all theoretical so please take it easy on the practical details.
Say I throw a baseball straight up in the air at 50 mph. It will get to a height of (I’m feeling a little lazy this morning) x feet and then fall back to Earth. Say I throw a baseball straight up in the air at 100 mph. (I should try out for the Cubs) It will go higher than x feet.
Physics guys can figure out how high an object will go based on it’s initial velocity. When you reverse the equation you can figure out how fast you need to be going to get to a certain height. When you solve that equation for a height of infinity, you get the escape velocity.
Therefore, escape velocity is the velocity you need to travel at to get an infinite distance from something. Bear in mind that escape velocity assumes no method of propulsion after the get go. Like something being fired out of a cannon. If your rockets are burning, you’d have to constantly refigure your escape velocity. This is the reason why you think you could use your 100 mph rocket to get to the moon. And you could do it, if you had sufficient fuel.
When an object reaches escape velocity, it has enough momentum to coast out of the gravitational field it’s in. Sure, you could build a 100mph rocket if you wanted, but there would be two problems: The amount of fuel required would be (pardon me) astronomical, and it’d take a really, really long time to get anywhere useful.
The formula is v=(2gr)^1/2 where g is the acceleration due to gravity at the earth’s surface and r is the radius of the earth. This is also the speed a body would have just before hitting the earth (neglecting air resistance), if dropped from a very great height (approaching infinite height), provided there were no other massive bodies around (sun, moon).
Jo3sh posted:
Just a quick clarification: a gravitational field is infinite, ergo, an object cannot coast out of the field.
If anyone is interested, and if I recall correctly, the escape velocity for earth is 11.2 m/s.
It could if it had an infinite amount of time. 
And I think Nen’s figure is pretty close, only it’s off by a factor of 1000. That’s right. The escape velocity of Earth is 11.2 km/s, which is indeed around 25,000 MPH. That always seemed pretty high to me, but I’ve done the math a dozen times. I guess I won’t be launching anything into space anytime soon…
Escape velocity is the term used for unpowered projectiles and doesn’t really apply to rockets/the shuttle and such like.
if you shoot a projectile from the surface at that speed it will coast into space and it is the most efficient form energy-wise (that ignores the atmosphere and other practical problems). The slower the rocket, the more energy it will take to get out. So you have to compromise with an acceleration slow enough to allow your astronauts to survive.
Sorry about this, but it’s a pet peeve of mine… Escape velocity is a misnomer. The correct term is escape speed. The difference? Velocity is a vector, and has magnitude and direction. Speed is a scalar, and does not have any particular direction. If I had a cannon with a muzzle speed of 11.2 km/s, and I shot it straight up, the cannonball would never fall back to Earth (we’re neglecting air resistance here). Now, if I took that same cannon, and aimed it exactly horizontally, the ball would still never fall back to Earth. If I shot it down, provided that there were a tunnel through the Earth for the ball to travel through, the result would be the same, likewise for any angles in between.
The only reason that people call it escape velocity is because it sounds more “scientific”.