Scott Lowrey writes:

To get into orbit, your ship has to move at a speed high enough so that
the Earth's gravity can't "catch it" and bring it back down.

To get into orbit, you must place your craft in a free-fall trajectory
that does not intersect with the Earth's surface or atmosphere. This
requires that you first get many miles above the planet's surface (in
order to avoid the atmosphere) and then move in a direction tangent to
the surface until the path of your free-fall trajectory misses the
Earth.

In practice, this means that you must reach an altitude of at least 185
km. The speed required tangent to the surface in order to enter a
stable orbit depends on your altitude, but at 200 km the speed is about
15,300 kt (yes, really!), or nearly 8 kilometres per second. Getting
that high and going that fast requires tremendous acceleration in order
to be achievable, and air-breathing craft cannot manage it.

Gravity gets weaker as you get further away from a massive
object like Earth, so the speed required to break away is
called "escape velocity". It works out to about 7 miles
per second (around 25,000 MPH) for a human-scale ship.

Escape velocity won't put you in orbit; escape velocity is the minimum
velocity required to leave the Earth's gravitational field faster than
it can decelerate you. If you can manage to reach a speed of 22,000 kt
at the surface of the planet, you'll zip right out of the Earth's
gravity and on into space. However, if you try this without leaving the
atmosphere first, only the burnt-out cinder of your craft will remain by
the time it gets out of the atmosphere, thanks to friction. Best to try
it only after getting above the atmosphere at lower speed.

If you can't get to escape velocity, you can't truly escape Earth's
gravity no matter how high you fly - even if you've got engines that
don't use air (rockets).

If you have unlimited propulsive power, you can escape gravity at any
speed, even at walking speed. The problem is that any propulsion system
with this kind of power and endurance would be too heavy to lift itself,
so in practice it can't be done (with current technology). The only
other option, then, is to accelerate so much that you can coast out of
the Earth's gravity without any additional propulsion. The faster and
harder you can accelerate, the more efficiently you can accomplish your
escape.

To be "in orbit" essentially means that you are constantly falling but
always "missing" the Earth!

Exactly. If the Earth were a dimensionless point with the same mass, it
would be virtually impossible to _prevent_ anything from going
immediately into orbit.

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