Table of content

**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