Gravitational Acceleration Calculator

What is Gravitational Acceleration?

Gravitational acceleration is the acceleration of an object caused by the force of gravity. It is a fundamental concept in physics that describes how quickly an object's velocity changes due to gravitational attraction. On Earth's surface, this acceleration is approximately 9.8 m/s² (often rounded to 10 m/s²), but it can vary depending on factors such as altitude and the planet's local density.

Formula

The gravitational acceleration is given by Newton's law of universal gravitation:

\[ g = \frac{GM}{r^2} \]

Where:

• \( g \) is the gravitational acceleration (m/s²)
• \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2 \))
• \( M \) is the mass of the attracting body (kg)
• \( r \) is the distance from the center of the attracting body (m)

Calculation Steps

Let's calculate the gravitational acceleration on the surface of Earth:

1. Identify the known values:
   • \( G = 6.674 \times 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2 \)
   • \( M = 5.97 \times 10^{24} \text{ kg} \) (mass of Earth)
   • \( r = 6.37 \times 10^6 \text{ m} \) (radius of Earth)
2. Apply the gravitational acceleration formula: \[ g = \frac{GM}{r^2} \]
3. Substitute the known values: \[ g = \frac{(6.674 \times 10^{-11})(5.97 \times 10^{24})}{(6.37 \times 10^6)^2} \]
4. Perform the calculation: \[ g \approx 9.82 \text{ m/s}^2 \]

Example and Visual Representation

Let's visualize the gravitational acceleration on Earth:

This diagram illustrates:

• The Earth represented by the blue circle
• The radius (r) from the center of Earth to its surface
• The gravitational acceleration (g) acting on objects at Earth's surface

Understanding gravitational acceleration is crucial in various fields, including physics, astronomy, and engineering. It helps explain phenomena such as orbital mechanics, tides, and the behavior of objects in free fall.