1. What is the Gravitational Constant (G)?

Definition: The gravitational constant (G) is a fundamental physical constant that appears in Newton's law of universal gravitation.

Value: \( G = 6.67430 \times 10^{-11} \, \text{N} \, \text{m}^2/\text{kg}^2 \)

2. How Does the Gravitational Force Formula Work?

The calculator uses the formula:

Where:

• \( F \) — Gravitational force (Newtons)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ N m²/kg²)
• \( m_1, m_2 \) — Masses of the two objects (kg)
• \( r \) — Distance between centers of mass (meters)

Explanation: The force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

3. Importance of the Gravitational Constant

Details: G determines the strength of gravity in the universe. It's essential for calculating celestial mechanics, satellite orbits, and understanding fundamental forces.

4. Using the Calculator

Tips: Enter the masses of two objects in kilograms and their separation distance in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is G so small numerically?
A: Gravity is extremely weak compared to other fundamental forces, hence the small constant value.

Q2: How was G first measured?
A: Henry Cavendish first measured G in 1798 using a torsion balance experiment.

Q3: Is G constant everywhere?
A: Current physics assumes G is constant throughout the universe, though this is still being tested.

Q4: Why is G important in astrophysics?
A: It's crucial for calculating planetary orbits, galaxy dynamics, and understanding the universe's structure.

Q5: How precise is our knowledge of G?
A: G is the least precisely known fundamental constant, with a relative standard uncertainty of about 2.2×10⁻⁵.