In 1611, a version of the Bible was translated in English which rendered :
" He stretcheth out the north over the
empty place, and
hangeth the earth upon nothing "
- Job 26:7
In what is the earth hanged upon nothing ?
" It is he that sitteth upon the circle of the earth, ... " - Isaiah 40:22 (KJV)
The Earth has " circle " , which Newton called " orb ".
What causes the earth to remain in that orbit while it is hanged there ? What holds it so that it is hanged upon nothing ?
" Behold, the Lord GOD comes with might, and his arm rules for him; ... Who has measured the water in the hollow of his hand and marked off the heavens with a span, enclosed the dust of the earth in a measure and weighed the mountains in scales and the hills in a balance ?"
- Isaiah 40:10, 12 (RSV)
The biblical teaching is that the earth in its circle is weighing-ly hanged upon nothing.
What is weight ?
Weight is the force with which gravity acts on a mass. It is the gravitational force from an attracting mass to the weighed object: It is considered to be the weight of the falling object. And since gravity means heaviness during those days, this weighing heaviness was since then called gravity.
Force = mass x acceleration
Newton suggested that the rate of fall (i.e. acceleration) was proportional to the strength of the gravitational force.
Force = mass x acceleration
Weight = mass x acceleration due to gravity
Using the modern terminology, the biblical teaching is that the earth is 'gravitationally' hanged upon nothing in its 'orbit'.
" I deduced, " Isaac Newton wrote in 1664, "that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve. "
The Latin-derived word orb is khuwg in the Hebrew Bible which means circle, course or circuit.
Moon orbits on earth, and Newton thought if whether the force which pulled an apple downward to the earth and the force that attracts the Moon to remain in orbit were one & the same or not. The 'acceleration' because of the gravitation is considered to be the gravitational force field strength of an attracting mass (heavier one). By deduction he arrived to a suggestion that the force which keeps a planet in its orbit is reciprocally as the square of its distance from the center of the Sun and center of the earth.
Force = I / d²
Force ╫ (mass) x (Mass) / (distance)²
mass x acceleration ╫ (mass of earth) x (Mass of Sun) / (center to center)²
His gravitational 'inverse square' law needs a proportionality constant. This constant, signified by letter G, must balance the equation. (What balances the equation? It should cancel the d², m, and M , and it should equate to ' mass x acceleration'.)
mass x acceleration = [ (mass x acceleration) d² m - 1 M - 1 ] (m) (M) / d²
m x a = [ ( m x a ) d² m - 1 M - 1 ] (m) (M) / d²
m a = [ G ] (m) (M) / d²
Force = [ G ] m M / d²
F = G m M / d²
F = G m M / d²
With this formula we can now know the gravitational force between two mutually attracting objects. The biblical term for this force is ' weight '.
G or gravitational constant balances the equation and is equal to (mass x acceleration) x square distance x per kilogram of lighter mass per kilogram of heavier Mass (or ma d² m - 1 M - 1 ) .
In ancient time, the easiest way to measure an object's weight is by the balance (scale).
Objects on the both sides of the balance exert pulling force. thinking the planet Earth and the star Sun as such those objects we can have an idea that they are both exerting pulling force.
Such a pulling force is the reason why apples from a tree fall on the ground: the earth's gravitational force pulls the apple, since Earth is heavier than apple.
At the present distance, the gravitational force of the sun is not completely pulling or losing the earth.
John Michell (1724-1793) of Nottinghamshire, England, invented a torsion balance to determine the G, gravitational constant, in Newton's formula, but unluckily he died before he found it.
G = F d² / m M
G m M = F d²
( G m M / d² ) = F
His contemporary Henry Cavendish in 1798 tried it by measuring the force caused by large balls (M) to, and which were drown near to, two light lead balls (m) at each end of a rod, which was hanged by a twistable wire. Having known the attracting force, distance between centers of the heavy & light balls and their masses, he could now solve the strength of the constant G. (the modern value for this G is 6.674 28 x 10 - 11 N m 2 kg - 2 .
With this gravitational constant, it is now possible to calculate the mass ( M ) of the planet Earth by the mass ( m ) of a falling object & its rate of fall and their distance ( d ) center to center through the equation
M = F d² / G m
where F is the weight or gravitational force.
Since object here on Earth is too near, we will use instead the Earth's radius ( r ), the downward acceleration (g) of & the mass (1m) of the falling object with the equation
M = g r² 1m / G 1m
M = g r ² / G
so that it is now easier to calculate the mass ( M ) of a planet or any heavier object, simply by its radius ( r ), and acceleration due to gravity.
To know the value of g (acceleration due to gravity) of a planet , the formula is
g = 4 π ² l / T ²
where l is the length of a pendulum, and T is the period (in second) of swing of the pendulum.
Discovery of Gravity : by Allan Poe Bona Redoña
