The Story of the HeavensBall, Robert S. (Robert Stawell)
History
The Story of the Heavens
Ball, Robert S. (Robert Stawell)
Astronomy
A stone thrown into the air soon regains the earth. A rifle bullet
fired vertically upwards will ascend higher and higher, until at length
its motion ceases, it begins to return, and falls to the ground. Let us
for the moment suppose that we had a rifle of infinite strength and
gunpowder of unlimited power. As we increase the charge we find that the
bullet will ascend higher and higher, and each time it will take a
longer period before it returns to the ground. The descent of the bullet
is due to the attraction of the earth. Gravitation must necessarily act
on the projectile throughout its career, and it gradually lessens the
velocity, overcomes the upward motion, and brings the bullet back. It
must be remembered that the efficiency of the attraction decreases when
the height is increased. Consequently when the body has a prodigiously
great initial velocity, in consequence of which it ascends to an
enormous height, its return is retarded by a twofold cause. In the first
place, the distance through which it has to be recalled is greatly
increased, and in the second place the efficiency of gravitation in
effecting its recall has decreased. The greater the velocity, the
feebler must be the capacity of gravitation for bringing back the body.
We can conceive the speed to be increased to that point at which the
gravitation, constantly declining as the body ascends, is never quite
able to neutralise the velocity, and hence we have the remarkable case
of a body projected away never to return.
It is possible to exhibit this reasoning in a numerical form, and to
show that a velocity of six or seven miles a second directed upwards
would suffice to convey a body entirely away from the gravitation of the
earth. This speed is far beyond the utmost limits of our artillery. It
is, indeed, at least a dozen times as swift as a cannon shot; and even
if we could produce it, the resistance of the air would present an
insuperable difficulty. Such reflections, however, do not affect the
conclusion that there is for each planet a certain specific velocity
appropriate to that body, and depending solely upon its size and mass,
with which we should have to discharge a projectile, in order to prevent
the attraction of that body from pulling the projectile back again.
It is a simple matter of calculation to determine this "critical
velocity" for any celestial body. The greater the body the greater in
general must be the initial speed which will enable the projectile to
forsake for ever the globe from which it has been discharged. As we
have already indicated, this speed is about seven miles per second on
the earth. It would be three on the planet Mercury, three and a half on
Mars, twenty-two on Saturn, and thirty-seven on Jupiter; while for a
missile to depart from the sun without prospect of return, it must leave
the brilliant surface at a speed not less than 391 miles per second.
Public-domain text, read in full here on John Shaqi.
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