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FORMULAS
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Kepler's Laws 1. The orbit of each planet is an ellipse which has the Sun at one of its foci. 2. Each 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 the planets about the Sun are proportional to the cubes of their mean distances from it. Newton's
law of universal gravitation 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 two objects. Then F = G m1 m2 / r2 |
Acceleration due to
gravity outside the Earth
It can 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 can 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.
