1. What is Newton's Law of Universal Gravitation?

Definition: This fundamental physical law describes the gravitational attraction between two objects with mass.

Purpose: It explains and predicts the gravitational force between any two masses in the universe, from apples falling to planets orbiting.

2. How Does the Equation Work?

The equation is:

Where:

• \( F \) — Gravitational force (Newtons, N)
• \( G \) — Gravitational constant (6.67 × 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 mass (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 force governs celestial mechanics, determines weight, and is essential for understanding everything from tides to spacecraft trajectories.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the gravitational constant so small?
A: Gravity is the weakest fundamental force, and the small value reflects this weakness compared to other forces like electromagnetism.

Q2: Does this equation work for any distance?
A: It works for all distances where relativistic effects are negligible (not extremely massive objects or near light speeds).

Q3: Why is distance squared in the equation?
A: This inverse-square law reflects how gravity spreads out in three-dimensional space as distance increases.

Q4: How was the gravitational constant determined?
A: It was first measured by Henry Cavendish in 1798 using a torsion balance experiment.

Q5: Does this equation explain orbits?
A: Yes, combined with Newton's laws of motion, it explains elliptical orbits described by Kepler's laws.