If we shoot a bullet with a velocity lower than escape velocity
(primal velocity) from surface of the earth to sky (ignoring air
resistance force), the bullet will back to surround of the earth. In
fact, when we shoot the bullet upside, the bullet will climb to a
certain height, and then its velocity reach zero and then back to
surround of the earth. In peak point, the bullet has just potential
energy. The more primal velocity, the bullet more climbs. By this
discussion, it is possible to define escape velocity:
Escape velocity = the minimum of the necessary velocity not to back
the bullet to surround of the earth.
As the bullet not to back to the surround of the earth, so it will
continue to the extreme and as it is necessary of the minimum
velocity, so it will stop in the extreme. Using the gravity
potential energy and kinetic energy of object, it is possible to
express a formula for escape velocity. If consider gravity potential
energy for a system in the extreme distance as zero, it will easy to
In this equation, U is gravity potential energy, M is mass for
example earth mass, m is bullet's mass, G is gravity global
constant, and r is the distance from the core of the earth to core
of the bullet. Considering to mentioned discussion, it is possible
K is bullet's kinetic energy, vesc
Recent equation is escape velocity for the bullet and as seen, it is
not depend on the bullet mass. Also it is clear that if the distance
between two objects tend zero, the escape velocity
will tend the extreme.
Considering the mass and radius, the escape velocity for some
celestial masses are as below:
The escape velocity from the sun's surround is 617.5 kilometers per
second, the MERCURY is 4.4kps, the VENUS is 10.4kps, the EARTH is
11.2kps, the moon 2.4kps and the MARS is 5kps.
The theorists of the big bang
claim that all the current mass or material and energy of universe
were in a very hot and dense sphere in billions years ago, and after
explosion, its energy and material dispersed and the universe
created. Now want to check if this theory was correct?
For this we shall calculate escape velocity for mass and energy of
the dense sphere (in first of explosion and moments after universe
or space-time creation).
The escape velocity or space-time expansion is equal to limit of
escape velocity general equation, when its mass tend the extreme and
its radius tend zero. Because the universe mass was unbelievable and
the extreme, and also sphere's radius is about zero as its
unbelievable gravity pressure (it means about radius of an atomic
particle). The general amount of this limit is the extreme, so it is
easy to conclude that nothing (material, mass or energy) could not
exit or escape from the sphere. Anyway the final velocity limit is
expressed in relativity theory of light velocity and of course the
light velocity is negligible compared this extra and unbelievable
velocity. So it is possible to conclude that the mentioned sphere
(if really existed) was a closed space that could not exit or escape
from it. So if the sphere with such specifications was formed in
universe because of all masses and energies aggregation, the
material and energy would have to be in inelegant status and no
factors would be possible to re-extract the material and energy from
the sphere and make similar universe as our universe. So the Big
Bang theory which is our universe existence cause and its expansion
is impossible. Simply, as we knew, the light can not exit and escape
from black hole (lower than Schwartz shield radius). Now this
question is asked that how the light created by the Big Bang escaped
from unbelievable gravity field and after chilled, converted to
universe background waves?
The light does not basically chill, but the intensity of dispersed
spectrum of the hot objects move to red spectrum in chilling time.
Final limit for velocity is in relativity theory in light velocity
that is not sufficient for the Big Bang theory. The Big Bang theory
to vindicate universe needs extreme velocity which breach the
Now we have two options:
The accuracy of the relativity theory.
The accuracy of the Big Bang theory.
You are free to decide. But now it seems to select the accuracy of
the relativity theory and reject the Big Bang theory!
Now we consider the issue from the standpoint of Finite but
Here r is the radius of the universe. In this case, the distance
between two mass, that is r, equals πr (the blue
arc), because the circumference of this circle is 2πr and we should
replace r with πr in the above equation. Since π possesses a fixed
amount, then we will reach to the previous result. It should be
explained that the universe is expanding on the surface of
hypothetical sphere in this standpoint (an inflating balloon).