Gravitation
A complete physics guide covering Newton’s Law of Gravitation, universal gravitation, acceleration due to gravity, free fall, satellites, orbital velocity, escape velocity, Kepler’s laws, examples, diagrams, formulas, and solved problems.
1. Introduction to Gravitation
Gravitation is the force of attraction between any two objects having mass. Every object in the universe attracts every other object with a force called gravitational force.
The force that keeps planets revolving around the Sun and keeps us attached to Earth is called gravity.
2. Isaac Newton and Gravitation
Sir Isaac Newton proposed the Universal Law of Gravitation after observing a falling apple. He concluded that the same force that pulls the apple downward also keeps the Moon in its orbit.
3. Universal Law of Gravitation
According to Newton’s Universal Law of Gravitation:
Where:
| Symbol | Meaning |
|---|---|
| F | Gravitational Force |
| G | Universal Gravitational Constant |
| m₁, m₂ | Masses of two bodies |
| r | Distance between centers |
Example
Two bodies of masses 5 kg and 10 kg are placed 2 m apart. Find the gravitational force.
Given:
m₁ = 5 kg
m₂ = 10 kg
r = 2 m
G = 6.67 × 10⁻¹¹ Nm²/kg²
Formula:
Calculation:
F = 6.67 × 10⁻¹¹ × (5×10 / 2²)
F = 6.67 × 10⁻¹¹ × 12.5
F = 8.34 × 10⁻¹⁰ N
4. Acceleration Due to Gravity
The acceleration produced in a body due to Earth’s gravitational pull is called acceleration due to gravity.
Its average value on Earth is:
Factors Affecting g
- Height above Earth surface
- Depth below Earth surface
- Rotation of Earth
- Shape of Earth
5. Free Fall
When a body falls under the influence of gravity alone, its motion is called free fall.
Solved Problem
A stone is dropped from a tower. Find velocity after 3 seconds.
Given:
u = 0
g = 9.8 m/s²
t = 3 s
Formula:
Calculation:
v = 0 + (9.8 × 3)
v = 29.4 m/s
6. Mass and Weight
| Mass | Weight |
|---|---|
| Amount of matter in a body | Force with which Earth attracts a body |
| Constant everywhere | Changes from place to place |
| Measured in kilogram | Measured in Newton |
| Measured using beam balance | Measured using spring balance |
7. Satellites
A satellite is a body that revolves around a planet due to gravitational attraction.
Types of Satellites
- Natural Satellite (Moon)
- Artificial Satellite (INSAT, GSAT)
Orbital Velocity
Escape Velocity
Escape velocity of Earth is approximately 11.2 km/s.
8. Kepler’s Laws of Planetary Motion
First Law
Planets move in elliptical orbits with the Sun at one focus.
Second Law
The line joining planet and Sun sweeps equal areas in equal intervals of time.
Third Law
The square of orbital period is proportional to the cube of distance from the Sun.
9. Practice Exercises
Short Questions
- Define gravitation.
- Write Universal Law of Gravitation.
- What is acceleration due to gravity?
- Define free fall.
- What is escape velocity?
Numerical Problems
- Calculate the gravitational force between two masses of 20 kg and 30 kg separated by 5 m.
- Find the weight of a 60 kg person on Earth.
- A body falls freely for 5 seconds. Find its final velocity.
- Find the height covered by a freely falling body in 4 seconds.
10. Important Formulas Summary
| Topic | Formula |
|---|---|
| Gravitational Force | F = G(m₁m₂ / r²) |
| Acceleration Due to Gravity | g = GM / R² |
| Weight | W = mg |
| Velocity in Free Fall | v = u + gt |
| Distance in Free Fall | s = ut + ½gt² |
| Orbital Velocity | v = √(GM/R) |
| Escape Velocity | Ve = √(2GM/R) |