Physics Formulas
GRAVITATION
Kepler's Laws
Towards the end of the sixteenth century, Tycho Brahe collected a huge amount of data giving precise measurements of the position of planets. Johannes Kepler, after a detailed analysis of the measurements announced three laws in 1619.
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
About fifty years after Kepler announced 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 rthe 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.
PROPERTIES OF MATTER
Density
The mass of a substance contained in unit volume is its density
Kepler's Laws
Towards the end of the sixteenth century, Tycho Brahe collected a huge amount of data giving precise measurements of the position of planets. Johannes Kepler, after a detailed analysis of the measurements announced three laws in 1619.
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
About fifty years after Kepler announced 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 rthe 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.
PROPERTIES OF MATTER
Density
The mass of a substance contained in unit volume is its density