GRAVITATION (AQA / GCSE notes)
1. Introduction to Gravitation
ravitation is the force of attraction between any two
G
objects in the universe. Whether it's an apple falling
from a tree or the moon revolving around the Earth, the
universal force responsible is gravity.
Centripetal Force
efore diving into gravity, it's important to understand
B
why objects move in circles (like planets around the
sun).
● Definition: The center-seeking force that causes an
object to move along a circular path is called the
centripetal force.
● If this force is removed, the object will fly off in a
straight line tangent to the circular path.
2. Universal Law of Gravitation
roposed by Sir Isaac Newton, this law states that
P
every object in the universe attracts every other object
with a force.
Statement
The gravitational force between two objects is:
1.Directly proportional to the product of their
masses.
, 2.Inversely proportional to the square of the distance
between their centers.
Mathematical Derivation
et two objects A and B have masses M and m,
L
separated by a distance d.
According to the law:
Force(F) is directly proportional to M×m……………eq (1)
Force(F) is inveresly proportional to d^2……………eq (2)
Combining both equations:
Force(F) is directly proportional to M×m/d^2
To remove the proportionality sign, we introduce a constant G:
Force(F) = G M×m/d^2
Where:
● = Gravitational force between the two bodies
F
● M, m = Masses of the two bodies
● d = Distance between the centers of the masses
● G = Universal Gravitational Constant
3. VALUE AND SI UNIT OF “G”
By rearranging the formula, we get:
G = F×d^2/M×m
● S I Unit of G: Nm^2/kg^2(Newton meter squared per kilogram squared)
● Value of G: 6.673 ×10^-11 Nm^2/kg^2(discovered by Henry Cavendish)
1. Introduction to Gravitation
ravitation is the force of attraction between any two
G
objects in the universe. Whether it's an apple falling
from a tree or the moon revolving around the Earth, the
universal force responsible is gravity.
Centripetal Force
efore diving into gravity, it's important to understand
B
why objects move in circles (like planets around the
sun).
● Definition: The center-seeking force that causes an
object to move along a circular path is called the
centripetal force.
● If this force is removed, the object will fly off in a
straight line tangent to the circular path.
2. Universal Law of Gravitation
roposed by Sir Isaac Newton, this law states that
P
every object in the universe attracts every other object
with a force.
Statement
The gravitational force between two objects is:
1.Directly proportional to the product of their
masses.
, 2.Inversely proportional to the square of the distance
between their centers.
Mathematical Derivation
et two objects A and B have masses M and m,
L
separated by a distance d.
According to the law:
Force(F) is directly proportional to M×m……………eq (1)
Force(F) is inveresly proportional to d^2……………eq (2)
Combining both equations:
Force(F) is directly proportional to M×m/d^2
To remove the proportionality sign, we introduce a constant G:
Force(F) = G M×m/d^2
Where:
● = Gravitational force between the two bodies
F
● M, m = Masses of the two bodies
● d = Distance between the centers of the masses
● G = Universal Gravitational Constant
3. VALUE AND SI UNIT OF “G”
By rearranging the formula, we get:
G = F×d^2/M×m
● S I Unit of G: Nm^2/kg^2(Newton meter squared per kilogram squared)
● Value of G: 6.673 ×10^-11 Nm^2/kg^2(discovered by Henry Cavendish)
