Gravity laws
Kepler's Laws
Towards the end of the XVI century, Tycho Brahe collected a huge amount of information giving precise measurements of the position of planets and their gravitation. Johannes Kepler, after a detailed analysis of the measurements announced 3 laws in 1619:
1. The orbit of every planet is an ellipse which has the Sun at 1 of its foci.
2. Every planet moves in such a way that the (imaginary) line joining it to the Sun sweeps out equal areas in equal times.
3. The squares of the periods of revolution of every planets about the Sun are proportional to the cubes of their mean distances from it.
Newton's law of universal gravitation
About 50 years after Kepler said the laws now named after him, Isaac Newton showed that every particle in the Universe attracts every other with a force which is proportional to the products of their masses and inversely proportional to the square of their separation.
Hence:
If F is the force due to gravity, g the acceleration due to gravity, G the Universal Gravitational Constant (6.67x10-11 N.m2/kg2), m the mass and r the distance between 2 objects. Then
F = G m1 m2 / r2
Acceleration due to gravity outside the Earth
It could be shown that the acceleration due to gravity outside of a spherical shell of uniform density is the same as it would be if the entire mass of the shell were to be concentrated at its center.
Using this we could express the acceleration due to gravity (g') at a radius (r) outside the earth in terms of the Earth's radius (re) and the acceleration due to gravity at the Earth's surface (g)
g' = (re2 / r2) g
Acceleration due to gravity inside the Earth
Here let r represent the radius of the point inside the earth. The formula for finding out the acceleration due to gravity at this point becomes:
g' = ( r / re )g
In both the above formulas, as expected, g' becomes equal to g when r = re.
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