7.2.2 Gravitational Field Strength

Gravitational Field:

A gravitational field is a region around a mass where another mass experiences a gravitational force. Gravitational fields can be classified as either:

1. Uniform Field
2. Radial Field

Types of Gravitational Fields

• Uniform Field: In a uniform gravitational field, the field strength is constant everywhere, meaning any object within this field will experience the same gravitational force regardless of its position. This is represented by parallel, equally spaced field lines pointing in the same direction. For example, near the Earth's surface, the gravitational field is approximately uniform over short distances.

• Radial Field: In a radial gravitational field, the strength of the gravitational force changes with distance from the centre of the mass creating the field. The field lines radiate outward from a central point (for instance, the centre of the Earth or any spherical mass) and become less dense as you move further from the centre, indicating a decrease in field strength. In a radial field, the gravitational force weakens with distance due to the inverse-square law.

Gravitational Field Strength $( g )$

The gravitational field strength $g$ at a point within a gravitational field represents the force exerted per unit mass at that point. It is measured in newtons per kilogram ($N/kg$).

• In a uniform field, $g$ is constant.
• In a radial field, $g$ varies with distance from the centre of mass. There are two formulas used to calculate $g$, depending on the nature of the field:

3. General Formula:

$$g = \frac{F}{m}$$

Where:

• $F$ is the gravitational force experienced by an object.
• $m$ is the mass of the object. This formula defines $g$ as the gravitational force per unit mass.

4. Formula for Radial Fields:

$$g = \frac{GM}{r^2}$$

Where:

• $G$ is the gravitational constant $(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2)$ .
• $M$ is the mass of the object creating the gravitational field.
• $r$ is the distance from the centre of the mass to the point where $g$ is being measured. This formula is specific to radial fields and indicates that $g$ decreases with the square of the distance $r$ from the mass $M$.