Gravitational Constant Given Radius Of Earth And Acceleration Of Gravity Calculator

Formula Used:

\[ G = \frac{g \times R_M^2}{M_{Earth}} \]

Gravitational Constant (G):

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1. What is the Gravitational Constant?

The gravitational constant (G) is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. It is a fundamental constant of nature that appears in Newton's law of universal gravitation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G = \frac{g \times R_M^2}{M_{Earth}} \]

Where:

\( G \) — Gravitational constant (N·m²/kg²)
\( g \) — Gravitational acceleration on Earth (m/s²)
\( R_M \) — Mean radius of the Earth (meters)
\( M_{Earth} \) — Earth mass (5.9722 × 10²⁴ kg)

Explanation: This formula derives the gravitational constant from Earth's gravitational acceleration, mean radius, and mass using Newton's law of universal gravitation.

3. Importance of Gravitational Constant

Details: The gravitational constant is fundamental to understanding gravitational forces in the universe. It is essential for calculating planetary orbits, satellite trajectories, and cosmological phenomena. Accurate determination of G is crucial for precision measurements in astrophysics and space exploration.

4. Using the Calculator

Tips: Enter the mean radius of Earth in meters and gravitational acceleration in m/s². Standard values are approximately 6,371,000 meters for radius and 9.80665 m/s² for gravitational acceleration.

5. Frequently Asked Questions (FAQ)

Q1: What is the accepted value of the gravitational constant?
A: The currently accepted value is approximately 6.67430 × 10⁻¹¹ N·m²/kg² as determined by precision laboratory measurements.

Q2: Why is the gravitational constant difficult to measure precisely?
A: Gravitational forces are extremely weak compared to other fundamental forces, making precise measurements challenging and susceptible to experimental errors.

Q3: How does this calculation compare to laboratory measurements?
A: This method provides a theoretical derivation based on Earth's parameters, while laboratory measurements use sensitive torsion balance experiments for direct measurement.

Q4: Can this formula be used for other celestial bodies?
A: Yes, the same principle applies to any celestial body when you know its mass, radius, and surface gravitational acceleration.

Q5: Why is Earth's mass used as a constant in this calculation?
A: Earth's mass (5.9722 × 10²⁴ kg) is a well-established value determined through various geophysical measurements and satellite observations.