1. What is a Gravitational Force Vector Calculator?

Definition: This calculator computes the gravitational force vector between two masses using Newton's law of universal gravitation.

Purpose: It helps physics students and professionals calculate both the magnitude and direction of gravitational force between two objects.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \vec{F} \) — Gravitational force vector (N)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ N m²/kg²)
• \( m_1 \) — First mass (kg)
• \( m_2 \) — Second mass (kg)
• \( r \) — Distance between masses (m)
• \( \hat{e}_r \) — Unit vector in direction of force

Explanation: The negative sign indicates the force is attractive. The unit vector determines the force direction.

3. Importance of Gravitational Force Calculation

Details: Understanding gravitational forces is crucial for astrophysics, orbital mechanics, and fundamental physics research.

4. Using the Calculator

Tips: Enter both masses in kg, their separation distance in meters, and the unit vector components (automatically normalized). All mass and distance values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational constant G?
A: G = 6.67430 × 10⁻¹¹ N m²/kg², a fundamental physical constant governing gravitational attraction.

Q2: How do I determine the unit vector?
A: The unit vector points from one mass to the other. For simple cases along an axis, use (1,0,0), (0,1,0), or (0,0,1).

Q3: Why is the force negative?
A: The negative sign indicates the force is attractive, pulling masses together.

Q4: Can I use this for celestial bodies?
A: Yes, but for very large distances or masses, relativistic effects may become significant.

Q5: What if my unit vector isn't normalized?
A: The calculator automatically normalizes it by dividing each component by the vector magnitude.