Acceleration Due To Gravity Value Calculator

Gravitational Acceleration Formula:

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

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 another massive object. It represents the rate at which an object's velocity changes due to gravitational attraction.

2. How Does the Calculator Work?

The calculator uses the gravitational acceleration formula:

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

Where:

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

Explanation: The formula calculates the acceleration due to gravity at a specific distance from a massive object, following Newton's law of universal gravitation.

3. Importance of Gravitational Acceleration Calculation

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

4. Using the Calculator

Tips: Enter the gravitational constant (default is 6.67430e-11), mass of the central body in kilograms, and distance from the center of mass in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is Earth's gravitational acceleration at surface?
A: Approximately 9.80665 m/s², calculated using Earth's mass (5.972 × 10²⁴ kg) and radius (6.371 × 10⁶ m).

Q2: How does gravitational acceleration change with altitude?
A: Gravitational acceleration decreases with the square of distance from the center of mass, so it decreases as altitude increases.

Q3: What is the gravitational constant value?
A: G = 6.67430 × 10⁻¹¹ m³/kg·s², which is a fundamental physical constant measured experimentally.

Q4: Can this formula be used for any celestial body?
A: Yes, the formula applies to any massive object - planets, stars, moons, or artificial satellites.

Q5: How accurate is this calculation?
A: The calculation is theoretically exact for point masses or spherical symmetric bodies. For non-spherical bodies, additional corrections may be needed.