Acceleration Due To Gravity Calculation Formula

Gravitational Formula:

\[ g = \frac{G \times M}{r^2} \]

Acceleration Due to Gravity (g):

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1. What is the Gravitational Formula?

The gravitational formula calculates the acceleration due to gravity (g) using Newton's law of universal gravitation. It determines the gravitational acceleration experienced by an object due to the gravitational pull of another mass.

2. How Does the Calculator Work?

The calculator uses the gravitational acceleration formula:

\[ g = \frac{G \times M}{r^2} \]

Where:

\( g \) — Acceleration due to gravity (m/s²)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
\( M \) — Mass of the celestial body (kg)
\( r \) — Distance from 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 Calculation

Details: Calculating gravitational acceleration is essential for space missions, satellite orbit calculations, understanding planetary motion, and various engineering applications involving gravity.

4. Using the Calculator

Tips: Enter the gravitational constant (pre-filled with standard value), mass in kilograms, and distance in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the standard value of gravitational constant?
A: The standard value is 6.67430 × 10⁻¹¹ m³/kg·s², which is pre-filled in the calculator for convenience.

Q2: How does distance affect gravitational acceleration?
A: Gravitational acceleration decreases with the square of the distance from the center of mass (inverse square law).

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 celestial body?
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: Why is the gravitational constant so small?
A: The gravitational constant is small because gravity is the weakest of the four fundamental forces, but it acts over infinite distance and is always attractive.