1. What is Gravitational Acceleration?

Gravitational acceleration (g) is the acceleration of an object due to the force of gravity from another object. It represents the rate at which an object's velocity changes under gravitational influence and is calculated using Newton's law of universal gravitation.

2. How Does the Calculator Work?

The calculator uses the gravitational acceleration formula:

Where:

• \( g \) — Gravitational acceleration (m/s²)
• \( G \) — Gravitational constant (6.67430×10⁻¹¹ m³/kg·s²)
• \( M \) — Mass of the celestial body (kg)
• \( r \) — Distance from the center of mass (m)

Explanation: The formula shows that gravitational acceleration is directly proportional to the mass of the object and inversely proportional to the square of the distance from its center.

3. Importance of Gravitational Acceleration

Details: Understanding gravitational acceleration is crucial for space exploration, satellite orbit calculations, planetary science, and understanding fundamental physical phenomena. It helps determine orbital velocities, escape velocities, and the behavior of celestial bodies.

4. Using the Calculator

Tips: Enter mass in kilograms and distance in meters. Both values must be positive numbers. The distance should be measured from the center of the mass to the point where acceleration is being calculated.

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational constant G?
A: The gravitational constant (6.67430×10⁻¹¹ m³/kg·s²) is a fundamental physical constant that determines the strength of the gravitational force between two masses.

Q2: Why does gravitational acceleration decrease with distance?
A: Gravitational force follows an inverse-square law, meaning it decreases with the square of the distance from the mass center, resulting in reduced acceleration at greater distances.

Q3: What is Earth's surface gravitational acceleration?
A: Approximately 9.8 m/s² at Earth's surface, calculated using Earth's mass (5.972×10²⁴ kg) and radius (6.371×10⁶ m).

Q4: How does mass affect gravitational acceleration?
A: Greater mass produces stronger gravitational fields and higher acceleration values, as acceleration is directly proportional to mass.

Q5: Can this formula be used for any celestial body?
A: Yes, the formula applies universally to calculate gravitational acceleration for any mass, from small objects to planets and stars.