why does it take mach 25 to leave earth gravity?

If you throw an object straight up, it will rise until the the
negative acceleration of gravity stops it, then returns it to Earth.
Gravity's force diminishes as distance from the center of the Earth
increases, however. So if you can throw the object with enough initial
upward velocity so that gravity's decreasing force can never quite
slow it to a complete stop, its decreasing velocity can always be just
high enough to overcome gravity's pull. The initial velocity needed to
achieve that condition is called escape velocity.

From the surface of the Earth, escape velocity (ignoring air friction)
is about 7 miles per second, or 25,000 miles per hour. Given that
initial speed, an object needs no additional force applied to
completely escape Earth's gravity.

So escape velocity is defined to be the minimum velocity an object
must have in order to escape the gravitational field of the earth,
that is, escape the earth without ever falling back.

The object must have greater energy than its gravitational binding
energy to escape the earth's gravitational field. So:

1/2 mv2 = GMm/R 

Where m is the mass of the object, M mass of the earth, G is the
gravitational constant, R is the radius of the earth, and v is the
escape velocity. It simplifies to:

v = sqrt(2GM/R) 

or 

v = sqrt(2gR) 

Where g is acceleration of gravity on the earth's surface. 

The value evaluates to be approximately: 

11100 m/s
40200 km/h
25000 mi/h

Now to define gravity 

The law of universal gravitation is the following:

Every object in the Universe attracts every other object with a force
directed along the line of centers for the two objects that is
proportional to the product of their masses and inversely proportional
to the square of the separation between the two objects.
Considering only the magnitude of the force, and momentarily putting
aside its direction, the law can be stated symbolically as follows.

F = G(m1m2/r2)

where

F is the magnitude of the gravitational force between two objects 
m1 is the mass of first object 
m2 is the mass of second object 
r is the distance between the objects 
G is the gravitational constant 

Strictly speaking, this law applies only to point-like objects. If the
objects have spatial extent, the force has to be calculated by
integrating the force over the extents of the two bodies. It can be
shown that for an object with a spherically-symmetric distribution of
mass, the integral gives the same gravitational attraction as if the
object were a point mass.

The law of universal gravitation was originally formulated by Isaac
Newton in his work, the Principia Mathematica (1687). The history of
the gravitation as a physical concept is considered in more detail
below.

The law of universal gravitation can be written as a vector equation
to account for the direction of the gravitational force as well as its
magnitude. In this formulation, quantities in bold represent vectors.

      Gm1m2     r2-r1
F12= --------- ------
     |r2-r1|^2 |r2-r1|
 
As before, m1 and m2 are the masses of the objects, and G is the
gravitational constant.

F1 2 is the force on object 1 by object 2 
r1 and r2 are the position vectors of object 1 and object 2, respectively 
Since r1 ? r2 = -(r2 ? r1), the force F2 1 on object 2 by object 1 is just ? F1 2.

From here on it becomes more and more a psychics essasy so I will stop here 

oh one more thing

the escape velocity is not mach 25 (that is equivalent to 18800 miles
per hour) it is closer to mach 34

Mach rating of course depends on altitude as well as speed - it is not
really a good measure of speeds at such high rate.

However, I think the question may have been thinking of orbital
velocity, NOT escape velocity. Escape velocity is the speed needed at
the surface of the Earth, in order to escape from Earth completely. In
order to go into a stable orbit around the Earth, you only need half
the energy, or 1 on root(2) of the velocity - that is 7.8 km/s. This
is pretty close to the mach 25 quoted - so the 88 minute orbit of very
low level satellites is about mach 25. And anyone in such an orbit
would feel weightless (like in a space station) even if technically
they have not 'escaped' from the Earth's gravity.

It takes a high mach number because that is the most efficient way to
do it in terms of available energy (ie chemical). If a helicopter
could fly in space, it still couldn?t carry sufficient fuel to escape.
Build a big enough ladder and you could climb it at any speed you
want, just so long as you are going fast enough at the point you let
go so you aren?t ?sucked back?. The further you have gone, the less
speed you will need. We need fusion power.