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 Law of Universal Gravitation:

Where:

• \( F \) — Gravitational force (N)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
• \( m_1 \) — Mass of first object (kg)
• \( m_2 \) — Mass of second object (kg)
• \( r \) — Distance between centers of masses (m)

Explanation: The equation calculates the attractive force between two masses separated by a distance, using the universal gravitational constant.

3. Importance of Gravitational Force Calculation

Details: Understanding gravitational forces is fundamental to celestial mechanics, orbital dynamics, and many astrophysical phenomena. It helps in calculating planetary orbits, satellite trajectories, and understanding the structure of the universe.

4. Using the Calculator

Tips: Enter masses in kilograms and distance in meters. All values must be positive numbers. The gravitational constant is fixed at 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational constant?
A: The gravitational constant (G) is a fundamental physical constant that appears in Newton's law of universal gravitation. Its value is approximately 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².

Q2: Why is the force so small for everyday objects?
A: The gravitational constant is extremely small (6.67430 × 10⁻¹¹), which means gravitational forces between everyday objects are negligible compared to other forces like electromagnetic forces.

Q3: Does this work for any distance?
A: The equation works for point masses or spherical objects with the distance measured between their centers. For non-spherical objects, the calculation becomes more complex.

Q4: How accurate is this calculation?
A: For most practical purposes, Newton's law is sufficiently accurate. However, for extremely strong gravitational fields or high precision requirements, Einstein's general relativity provides more accurate results.

Q5: Can I calculate gravitational force between planets?
A: Yes, you can use this formula to calculate gravitational forces between celestial bodies, provided you use their masses and the distance between their centers.