Calculation of the average radius of the Earth by the gravitational parameter of the Earth and
the
fundamental physical constants
The
calculation formula is the following:
where
µ
≈
3.9860·10^{14}
m^{3}/s^{2
}is the
reference value
of
the
Earth's gravitational parameter (the geocentric gravitational constant),
m_{e} is the electron rest mass,
ħ
is the reduced Planck constant,
c is the speed of light in vacuum,
R_{c} is the Rydberg constant (in Hz),
α
≈
1/137.04 is the finestructure constant.
Since this
equation
is
derived
by
using
the
fundamental physical constants, the calculated
Earth's
radius with a large degree of certainty
may
be called the
absolute radius of the
Earth.
It roughly corresponds to the
geocentric radius
of the Earth
at the
geodetic
latitude
about
45°46°:
Accordingly, the absolute gravitational acceleration
g near the Earth's surface, independent of the centripetal acceleration, can be calculated by the
following
formula:
It is curious that we can solve the inverse problem: that is, to obtain
some
fundamental physical constants
by
the radius of the Earth. For example, we can
obtain
the Planck constant by the
following
equation:
where
R_{E}^{
}is the
absolute radius of the Earth.
