Table of contents
- Universal Law of Gravity or Newton's Law of gravitation
- Kepler's law of planetary motion
- Free fall
- Acceleration due to gravity(g)
- Equation of motion for freely falling bodies
- Mass and Weight
Gravity pulls objects toward a planet's centre and keeps planets in orbit around the sun. 🌍✨
Gravity on Earth: -
Gravity is crucial for life on Earth. It keeps Earth in orbit around the sun, at a comfortable distance for light and warmth, and holds down our atmosphere and the air we need to breathe.
[1] Universal Law of Gravity or Newton's Law of gravitation: -
The attraction force between two particles is directly proportional to their masses and inversely proportional to their square distance.
Note: - F12 and F21 are directed towards the centre of the two particles, so gravitational force is a central force
Gravitational Constant
we know
F=G∗M1∗M2r2
If we take m1=m2=1,r=1
then F=G
G=6.67×10−11Nm2kg2
F=6.67×10−11 N
G is the universal constant
- Only attraction no repulsion
- Not affected by medium
- Long range
- Conservative
- This force is along the line of joining to the line, we can write in vector form
Note: -
- When both objects have large masses, the gravitational force between them is extremely strong.
- The gravitational force between the Sun and the Earth keeps the Earth in a uniform circular motion around the Sun.
- The tides in the sea are due to the gravitational forces of the moon and the sun.
[2] Kepler's law of planetary motion
Johannes Kepler, a 16th-century astronomer, established three laws governing planetary motion around the sun, known as Kepler's laws.
1: -Kepler's first law
Kepler's first law states that planets move in elliptical orbits around the sun.
2: -Kepler's second law
- Kepler's second law states that each planet orbits the sun so that the line joining the planet to the sun sweeps over equal areas in equal intervals of time.
- Planets move faster when they are closer to the sun and move slowly when they are farther from the Sun.
- The planet does not move at a constant speed around the sun, moving faster when closer to the sun and slower when farther away.
t1=t2
A1=A2
soAt=constant
3: -Kepler's third law (Law of period)
The cube of a planet's mean distance from the sun is directly proportional to the square of its orbital period.
r3∝T2
r3T2≐constant
Where
r=mean distance of the planet from the sun
T=Time period of the planet (around the sun)
The cause of the motion of a planet is the gravitational force that the sun exerts on it.
[3] Free Fall
Free falling occurs when a body falls towards the Earth under the influence of gravity without any other forces acting on it. Such bodies are referred to as free-falling bodies.
The acceleration of an object falling freely towards a does not depend on the mass of the object.
Note: - From this equation, we can observe that acceleration does not depend on the mass of the stone.
[4] Acceleration due to gravity(g)
The acceleration experienced by a falling body due to Earth's gravity is denoted by the symbol g.
When a body is dropped freely, it falls with an acceleration of 9.8 m/s². When a body is thrown vertically upward, it undergoes a retardation of 9.8 m/s².
[5] Equation of motion for freely falling bodies
[6] Mass and Weight
Mass
- The mass of a body is the quantity of matter contained in it.
- It is a scalar quantity.
- The mass of a body cannot be zero
- The mass of a body is constant and does not change from place to place.
- "Mass is a physical quantity that measures inertia."
Weight
- The weight of a body is the force with which it is attracted toward the centre of the earth
- It is a vector quantity
- It varies from place to place
- The weight of the body cannot be zero
- On the moon, objects weigh about 1/6th of what they do on Earth
- WmoonWearth=16