Chapter 7 - Gravitation

Why does an object fall towards Earth? Why does the Moon not fall directly onto Earth? How do satellites remain in orbit?

Gravitation Class 11 explains these questions using the universal force of attraction between masses. The same physical law applies to falling objects, planets, moons and artificial satellites.

Kepler’s laws of planetary motion

Kepler described planetary motion using three laws.

Students learn that:

• Planets move in elliptical orbits with the Sun at one focus

• The line joining a planet and the Sun sweeps equal areas in equal times

• The square of a planet’s orbital period is proportional to the cube of the semi-major axis

These laws were based on observations. Newton later explained them using the universal law of gravitation.

Universal law of gravitation

Every pair of masses attracts each other.

The gravitational force is:

• Directly proportional to the product of the masses

• Inversely proportional to the square of their separation

• Directed along the line joining their centres

Students distinguish between the universal gravitational constant (G) and acceleration due to gravity (g).

Acceleration due to gravity

Near Earth’s surface, objects accelerate downward due to Earth’s gravitational pull.

Students derive the relationship between (g), Earth’s mass and Earth’s radius. They also study how (g) changes:

• Above Earth’s surface

• Below Earth’s surface

• At the centre of Earth

The value of (g) decreases with sufficient altitude and depth.

Gravitational potential and potential energy

Gravitational potential is the work done per unit mass in bringing a test mass from infinity to a point.

Gravitational potential energy describes the energy of a system of masses due to their positions.

When potential is taken as zero at infinity, gravitational potential and potential energy are negative for a bound system.

The negative sign does not mean that energy itself is impossible. It means external energy must be supplied to separate the masses completely.

Escape speed

Escape speed is the minimum initial speed required for an object to move away from a celestial body without further propulsion and reach an infinite distance with zero remaining speed.

It depends on the mass and radius of the planet but not on the mass of the escaping object.

Satellites and orbital velocity

A satellite remains in orbit because gravity supplies the required centripetal force.

Students learn about:

• Orbital velocity

• Time period

• Energy of an orbiting satellite

• Kinetic and potential energy in orbit

• Relation between escape speed and orbital speed

Astronauts in orbit appear weightless because they and their spacecraft are falling together. Gravity is still acting.

Common difficulties

Students often:

• Confuse (G) with (g)

• Use height above Earth where distance from Earth’s centre is required

• Assume gravitational potential energy is always (mgh)

• Ignore the negative sign of gravitational potential energy

• Confuse orbital speed with escape speed

• Say that gravity is absent inside an orbiting spacecraft

Teachoo explains when the near-Earth approximation (mgh) can be used and when the general gravitational expression is required.

How should you study Gravitation?

Understand the universal law before memorising satellite formulas. Many results can be derived using Newton’s law, circular motion and conservation of energy.

For satellite questions, draw Earth and mark the orbital radius from Earth’s centre, not from its surface.

Frequently Asked Questions

What is the difference between (G) and (g)?

(G) is the universal gravitational constant. (g) is the acceleration produced by a particular celestial body at a specified location.

Why is gravitational potential energy negative?

The zero is chosen at infinity. A bound mass has less energy than it would have at infinite separation, so its potential energy is negative.

Is gravity absent in an orbiting satellite?

No. Gravity provides the centripetal force that keeps the satellite in orbit.

Does escape speed depend on the object’s mass?

No. For a given planet and launch position, escape speed is independent of the mass of the escaping object.

Is Gravitation important for competitive examinations?

Yes. It combines force, circular motion and energy and appears frequently in CBSE, JEE and NEET questions.