Another way to look at this (which is somewhat more abstract but doesn’t involve messing about with any conic sections) is that in order to escape the gravity field of a planet, you need a certain level of kinetic energy relative to the planet. Once you achieve that level, you will be in an escape trajectory, regardless of what direction you are pointing (assuming, of course, that your trajectory doesn’t take you back through the planet). Such energy methods are quite useful for determining required velocities and momentum to achieve a particular orbit or transfer from one to another, but if you want specifics on where and what direction, you have to consider actual geometry.
Properly speaking, there is no such point - the force of gravity is greater than zero at any finite distance.
But it’s also true that a projectile that starts at or above the appropriate escape speed never slows to zero. So it never falls back to earth.
Note that escape speed is basically equal to the speed that an object would have at the earth’s surface if it started falling from zero velocity and an enormous distance.
Well, it matters to the occupants how fast it goes; 20Gs of acceleration (particularly in the inverted position in which the Shuttle ascends to orbit) would definitely be detrimental to the health and well-being of the crew.
Pedantic addition, but after MECO (Main Engine Cut-Off), the OMS (Orbital Maneuvering System, the small pods on the aft of the Shuttle straddling the SME housing) perform an orbital insertion burn to circularize the orbit, otherwise the Shuttle reenters the atmosphere somewhere around the Indian Ocean or Pacific Ocean, depending on trajectory plan.
I missed this one yesterday. Yes, technically speaking, the gravitational attraction for a specific body approaches zero asymptotically (but never quite reaching it); in practice, as least insofar as plotting orbital or celestrial trajectories, once an object is past the sphere of influence (SOI), a small body (one for which it’s gravitational field is essentially negligible) it outside the effect of the planet and will never return or remain in orbit in absence of any other influences. The SOI for the Earth is ~145 radii or 925,000km. Anything that reaches that distance (regardless of what instantaneous speed it attains in the interim) has effectively escaped the Earth’s gravitational influence. Of course, at that point, escape speed is essentially zero, so as long as you keep going, at some point you’ll attain escape speed regardless of how slow you are moving.
