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From Karnataka Open Educational Resources
→Inertial and gravitational property of mass
F = G m~~1m~~2 / r^^2
F = G m1m2 / r2
* F is the force between the masses,
* F is the force between the masses,
In SI units, Force, F is measured in newtons (N), masses m1 and m2 are measured in kilograms (kg), and the distance between the masses is measured in metres.
In SI units, Force, F is measured in newtons (N), masses m1 and m2 are measured in kilograms (kg), and the distance between the masses is measured in metres.
Universal Gravitational Constant
<br><br> '''Universal Gravitational Constant'''
The magnitude of G is identical to the magnitude of the force between a pair of 1-kg masses that are 1 metre apart and has been experimentally determined to be equal to 6.674×10−11N m2 kg−2. The value of the constant G was first accurately determined from the results of an experiment conducted by the British scientist Henry Cavendish in 1798. He accomplished by measuring the tiny force between lead masses with an extremely sensitive torsion balance.
The magnitude of G is identical to the magnitude of the force between a pair of 1-kg masses that are 1 metre apart and has been experimentally determined to be equal to 6.674×10−11N m2 kg−2. The value of the constant G was first accurately determined from the results of an experiment conducted by the British scientist Henry Cavendish in 1798. He accomplished by measuring the tiny force between lead masses with an extremely sensitive torsion balance.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inverse-square laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb's Law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant. One important point of comparison is that the the value of the constant in Coulomb's law (for force between two charges of 1C separated by a distance of 1 m) is of the order of magnitude 109, which is 1000 billion billion times more than the gravitational constant. This means that the electrostatic force is a much stronger force than the gravitational force.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies. Both are inverse-square laws, in which force is inversely proportional to the square of the distance between the bodies. Coulomb's Law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant. One important point of comparison is that the the value of the constant in Coulomb's law (for force between two charges of 1C separated by a distance of 1 m) is of the order of magnitude 109, which is 1000 billion billion times more than the gravitational constant. This means that the electrostatic force is a much stronger force than the gravitational force.
Why should this be so?
'''Why should this be so?'''
When we consider the gravitational field of a mass, we consider it to be a point mass. For any object, this can be approximated and we can find that this holds true. Some standard physics textbooks will give us this mathematical derivation as well. If there is a point mass and there is a field originating from it, the field must originate uniformly in all directions. If we imagine enclosing this point mass in a sphere and if we represent the field by field lines (called flux), we can visualize that these field lines must pass through uniformly throughout the surface area of the sphere. Now we can use simple geometry to explain why the field varies with inverse square of the distance. For the same area, the number of flux lines that will cut through a given area will reduce the farther the area is from the source. If we consider the area as a square on the surface of a sphere, the density of flux lines that will cut through the surface of a sphere is inversely proportional to the square of the distance from the source as the surface area of a sphere increases with the square of the radius. Hence the field strength will vary inversely with the square of the distance.
When we consider the gravitational field of a mass, we consider it to be a point mass. For any object, this can be approximated and we can find that this holds true. Some standard physics textbooks will give us this mathematical derivation as well. If there is a point mass and there is a field originating from it, the field must originate uniformly in all directions. If we imagine enclosing this point mass in a sphere and if we represent the field by field lines (called flux), we can visualize that these field lines must pass through uniformly throughout the surface area of the sphere. Now we can use simple geometry to explain why the field varies with inverse square of the distance. For the same area, the number of flux lines that will cut through a given area will reduce the farther the area is from the source. If we consider the area as a square on the surface of a sphere, the density of flux lines that will cut through the surface of a sphere is inversely proportional to the square of the distance from the source as the surface area of a sphere increases with the square of the radius. Hence the field strength will vary inversely with the square of the distance.
Law of gravitation and relativity
<br><br>'''Law of gravitation and relativity'''
Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as it is, as an excellent approximation of the effects of gravity. Gravitational force acts at a distance. The properties of the space surrounding any massive body can be considered to be altered in such a way that another massive body in this region experiences a force. This alteration of space is a gravitational field. Einstein perceived a gravitational field as a geometrical warping of four dimensional space and time; masses “bend” the space around them. Gravity is the property of matter that possesses mass that causes a force of attraction to exist between any two particles in space.
Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as it is, as an excellent approximation of the effects of gravity. Gravitational force acts at a distance. The properties of the space surrounding any massive body can be considered to be altered in such a way that another massive body in this region experiences a force. This alteration of space is a gravitational field. Einstein perceived a gravitational field as a geometrical warping of four dimensional space and time; masses “bend” the space around them. Gravity is the property of matter that possesses mass that causes a force of attraction to exist between any two particles in space.
Acceleration due to gravity
<b><br>
Concept flow
= Acceleration due to gravity = <br>
== Concept flow ==
Some of the key ideas we will cover in this section are:
Some of the key ideas we will cover in this section are:
* Gravitational force due to the Earth produces an acceleration in the objects. This is the force acting on a freely falling object.
* The value of acceleration is not dependent on the mass.
* All freely falling bodies gain same acceleration.
Free fall and acceleration due to gravity
=== Free fall and acceleration due to gravity ===
A freely falling body undergoes acceleration. This acceleration is caused by the gravitational force exerted by the larger mass of the Earth. This is referred to as acceleration due to gravity. The Earth also undergoes an acceleration due to the gravitational force exerted by the object. We do not notice it because of the mass of the Earth.
A freely falling body undergoes acceleration. This acceleration is caused by the gravitational force exerted by the larger mass of the Earth. This is referred to as acceleration due to gravity. The Earth also undergoes an acceleration due to the gravitational force exerted by the object. We do not notice it because of the mass of the Earth.
