Formula of Acceleration Due to Gravity

Gravitational Acceleration Formula:

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

Gravitational Acceleration (g):

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1. What is Gravitational Acceleration?

Gravitational acceleration (g) is the acceleration of an object caused by the force of gravity from a celestial body. It represents the rate at which an object's velocity changes due to gravitational pull near the surface of a planet or other massive body.

2. How Does the Calculator Work?

The calculator uses Newton's law of universal gravitation formula:

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

Where:

\( g \) — Gravitational acceleration (m/s²)
\( G \) — Gravitational constant (6.67430×10⁻¹¹ m³ kg⁻¹ s⁻²)
\( M \) — Mass of the celestial body (kg)
\( r \) — Radius from the center of mass (m)

Explanation: This formula calculates the acceleration due to gravity at the surface of a celestial body, derived from Newton's law of universal gravitation.

3. Importance of Gravitational Acceleration

Details: Gravitational acceleration is fundamental in physics and astronomy. It determines weight, affects orbital mechanics, influences atmospheric pressure, and is crucial for space missions and understanding planetary characteristics.

4. Using the Calculator

Tips: Enter the gravitational constant (typically 6.67430×10⁻¹¹), mass of the celestial body in kilograms, and radius in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Earth's gravitational acceleration?
A: Approximately 9.8 m/s² at sea level, though it varies slightly with latitude and altitude.

Q2: How does gravity change with altitude?
A: Gravity decreases with the square of the distance from the center of mass, so it weakens as altitude increases.

Q3: Why is the gravitational constant important?
A: It's a fundamental physical constant that determines the strength of gravitational force between objects with mass.

Q4: What factors affect gravitational acceleration?
A: Mass and radius of the celestial body, and to a lesser extent, rotation and density distribution.

Q5: How does gravity differ on other planets?
A: Different masses and radii result in different surface gravities (e.g., Moon: 1.6 m/s², Mars: 3.7 m/s², Jupiter: 24.8 m/s²).