Gravitational Force Calculator

Newton's Law of Universal Gravitation:

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

Gravitational Force (F):

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

Newton's Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

2. How Does the Calculator Work?

The calculator uses Newton's gravitational formula:

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

Where:

\( F \) — Gravitational force (newtons)
\( G \) — 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 (meters)

Explanation: The force between two objects increases with their masses and decreases with the square of the distance between them.

3. Importance of Gravitational Force

Details: This fundamental force governs planetary motion, tides, and the structure of the universe. It's essential for understanding astrophysics, orbital mechanics, and many Earth-based phenomena.

4. Using the Calculator

Tips: Enter masses in kilograms and distance in meters. All values must be positive numbers. For astronomical calculations, use scientific notation (e.g., 5.972e24 for Earth's mass).

5. Frequently Asked Questions (FAQ)

Q1: Why is the gravitational constant so small?
A: The value reflects the relative weakness of gravity compared to other fundamental forces. It requires enormous masses (like planets) to produce noticeable effects.

Q2: Does this work for any two objects?
A: Yes, but the force becomes negligible for everyday objects. For example, two 100kg spheres 1m apart experience about 0.000000667 N of force.

Q3: How accurate is this calculation?
A: Extremely accurate for point masses or spherical objects. For irregular shapes, it gives an approximation of the center-to-center force.

Q4: What about Einstein's theory of relativity?
A: Newton's law works well for most practical applications. Relativity becomes important near extremely massive objects or at velocities approaching light speed.

Q5: Why does distance use squared in the formula?
A: This inverse-square law reflects how gravity spreads out in three-dimensional space, diminishing with the surface area of an expanding sphere.