1. What is the Gravitational Acceleration Formula?

The gravitational acceleration formula calculates the acceleration due to gravity at a specific distance from a mass. It is derived from Newton's law of universal gravitation and describes how gravitational force decreases with the square of the distance from the mass center.

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⁻¹ s⁻²)
• \( M \) — Mass of the object (kg)
• \( r \) — Distance from the center of mass (m)

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

3. Importance of Gravitational Acceleration Calculation

Details: Calculating gravitational acceleration is essential for understanding orbital mechanics, planetary science, satellite deployment, and various engineering applications. It helps determine the gravitational field strength around celestial bodies.

4. Using the Calculator

Tips: Enter mass in kilograms, distance in meters, and gravitational constant in m³ kg⁻¹ s⁻². All values must be positive numbers. The default gravitational constant is set to 6.67430×10⁻¹¹, but you can modify it if needed.

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational constant?
A: The gravitational constant (G) is a fundamental physical constant that determines the strength of the gravitational force between objects with mass.

Q2: Why does gravitational acceleration decrease with distance?
A: Gravitational acceleration follows an inverse-square law, meaning it decreases with the square of the distance from the mass center due to the spreading of gravitational field lines.

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

Q4: Can this formula be used for any mass?
A: Yes, the formula applies to any mass, from small objects to planets and stars, as long as the distance is measured from the center of mass.

Q5: How accurate is the gravitational constant?
A: The gravitational constant is known with relatively low precision compared to other fundamental constants, with current value 6.67430(15)×10⁻¹¹ m³ kg⁻¹ s⁻².