Universal Gravitational Constant Formula Calculator

Universal Gravitational Constant Formula:

\[ G = \frac{F r^2}{m_1 m_2} \]

Force (F):

Distance (r):

Mass 1 (m₁):

Mass 2 (m₂):

Gravitational Constant (G):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Universal Gravitational Constant Formula?

The Universal Gravitational Constant Formula calculates the gravitational constant (G) from Newton's law of universal gravitation. It represents the proportionality constant in the equation relating gravitational force between two objects to their masses and distance.

2. How Does the Calculator Work?

The calculator uses the gravitational constant formula:

\[ G = \frac{F r^2}{m_1 m_2} \]

Where:

\( G \) — Gravitational constant (m³/kg s²)
\( F \) — Gravitational force between objects (N)
\( r \) — Distance between centers of masses (m)
\( m_1 \) — Mass of first object (kg)
\( m_2 \) — Mass of second object (kg)

Explanation: This formula rearranges Newton's law of universal gravitation to solve for the gravitational constant G.

3. Importance of Gravitational Constant Calculation

Details: The gravitational constant is a fundamental physical constant that appears in Newton's law of universal gravitation and Einstein's theory of general relativity. Its precise measurement is crucial for understanding gravitational forces in astrophysics and cosmology.

4. Using the Calculator

Tips: Enter force in newtons, distance in meters, and masses in kilograms. All values must be positive numbers greater than zero.

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 m³/kg s², though precise measurements continue to be refined.

Q2: Why is the gravitational constant difficult to measure accurately?
A: Gravitational forces are extremely weak compared to other fundamental forces, making precise laboratory measurements challenging.

Q3: How was the gravitational constant first measured?
A: Henry Cavendish first measured G in 1798 using a torsion balance experiment.

Q4: Does the gravitational constant vary in different locations?
A: Current physical theories assume G is a universal constant that does not vary with location or time.

Q5: What are the practical applications of knowing G?
A: Accurate knowledge of G is essential for calculating planetary orbits, satellite trajectories, and understanding cosmological phenomena.