COMPLETE FORMULA SHEET

PRERNA FOR IAS

COMPLETE FORMULA SHEET

1. Acceleration Due to Gravity (g)

Acceleration due to gravity, denoted by g, is the acceleration experienced by an object due to Earth's gravitational pull. It is given by the formula g = GM/R², where G is the gravitational constant, M is Earth’s mass, and R is Earth’s radius. Near Earth’s surface, its value is approximately 9.8 m/s². Gravity acts equally on all objects regardless of their mass in a vacuum. This is why a feather and an iron ball fall at the same rate when air resistance is absent. The concept of g is fundamental in understanding falling bodies and gravitational forces.

2. Variation of g

The value of gravitational acceleration g is not constant everywhere. It decreases with height above Earth because the distance from Earth’s center increases. It also decreases with depth below Earth’s surface and becomes zero at the center of Earth. Due to Earth’s rotation and slightly flattened shape, g is greater at the poles and smaller at the equator. The variation of g explains differences in weight at different locations. Understanding these changes is important in geophysics, satellite motion, and space science. It shows that gravity depends on distance from Earth’s center and local conditions.

3. Gravitational Field, Potential and Potential Energy

A gravitational field is the region around a mass where another mass experiences gravitational force. Gravitational potential is the work done per unit mass in bringing an object from infinity to a point in the field. Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is given by U = -GMm/r, which is always negative because gravity is an attractive force. As an object moves closer to Earth, its potential energy decreases and kinetic energy increases. These concepts are essential for understanding planetary motion and satellite dynamics.

4. Kepler’s Laws of Planetary Motion

Kepler’s Laws describe how planets move around the Sun. The First Law states that planets move in elliptical orbits with the Sun at one focus. The Second Law states that a line joining a planet and the Sun sweeps out equal areas in equal intervals of time, meaning planets move faster when closer to the Sun. The Third Law states that the square of a planet’s orbital period is proportional to the cube of its average distance from the Sun. These laws accurately explain planetary motion and formed the basis for Newton’s theory of gravitation and modern astronomy.

5. Escape Velocity