1. What is the Gravitational Force Equation?

Definition: Newton's law of universal gravitation calculates the attractive force between two masses.

Purpose: It helps physicists, astronomers, and engineers understand and predict gravitational interactions between objects.

2. How Does the Equation Work?

The equation is:

Where:

• \( F \) — Gravitational force (Newtons, N)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ N m²/kg²)
• \( m_1 \) — Mass of first object (kilograms, kg)
• \( m_2 \) — Mass of second object (kilograms, kg)
• \( r \) — Distance between centers of masses (meters, m)

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 Gravitational Force

Details: This fundamental force governs celestial mechanics, orbital dynamics, and many everyday phenomena like weight and tides.

4. Using the Calculator

Tips: Enter the masses of both objects in kilograms and their separation distance in meters. Distance must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the gravitational constant so small?
A: The constant's small value reflects gravity's weakness compared to other fundamental forces at small scales.

Q2: Does this work for any distance?
A: Yes, but for very small distances (quantum scales) or very strong fields, general relativity is needed.

Q3: What's Earth's gravitational force on a person?
A: For a 70 kg person: F ≈ (6.67×10⁻¹¹ × 5.97×10²⁴ × 70)/(6.371×10⁶)² ≈ 686 N (your weight).

Q4: Why is it an inverse-square law?
A: Because gravity's influence spreads equally in all directions, decreasing with the surface area of a sphere (4πr²).

Q5: How was G first measured?
A: Henry Cavendish in 1798 used a torsion balance to measure the tiny attraction between lead spheres.