Gravitational Force Calculator

Newton's Law of Universal Gravitation:

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

Gravitational Force (F):

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1. What is Gravitational Force?

Gravitational force is the attractive force between any two objects with mass. It's one of the four fundamental forces of nature and is described by Newton's Law of Universal Gravitation.

2. How Does the Calculator Work?

The calculator uses Newton's Law of Universal Gravitation:

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

Where:

\( F \) — Gravitational force (N)
\( G \) — Gravitational constant (6.674×10⁻¹¹ N·m²/kg²)
\( m_1 \) — Mass of first object (kg)
\( m_2 \) — Mass of second object (kg)
\( r \) — Distance between centers of the masses (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: Gravitational force governs the motion of planets, stars, and galaxies. It's essential for understanding orbital mechanics, tides, and the large-scale structure of the universe.

4. Using the Calculator

Tips: Enter masses in kilograms and distance in meters. All values must be positive (distance must be greater than zero).

5. Frequently Asked Questions (FAQ)

Q1: Why is the gravitational constant so small?
A: The gravitational force between everyday objects is extremely weak compared to other forces like electromagnetism. The small constant reflects this weakness.

Q2: Does this formula work for very large masses or distances?
A: For extremely strong gravitational fields (near black holes) or cosmic distances, Einstein's General Relativity provides more accurate results.

Q3: Why is the force inversely proportional to distance squared?
A: This "inverse square law" occurs because gravity's influence spreads out over the surface area of an expanding sphere (4πr²).

Q4: How does gravity compare between Earth and a person?
A: Using Earth's mass (5.97×10²⁴ kg), radius (6.371×10⁶ m), and a 70 kg person standing on the surface, the force is about 686 N (your weight).

Q5: Can gravitational force be negative?
A: The magnitude is always positive, but in physics we sometimes use negative signs to indicate direction (attraction toward another mass).