Net Gravitational Force Calculator

Net Gravitational Force Formula:

\[ F_{net} = \sum_{i=1}^{n} F_i = \sum_{i=1}^{n} \left( G \frac{m_1 m_i}{r_i^2} \right) \]

Mass of Object 1 (m₁):

Mass of Object 2 (m₂):

Distance Between Objects (r):

meters

Angle Between Forces (θ):

degrees

Net Gravitational Force (F_net):

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1. What is Net Gravitational Force?

The net gravitational force is the vector sum of all gravitational forces acting on an object. It determines the overall gravitational effect when multiple masses interact with a central object.

2. How Does the Calculator Work?

The calculator uses Newton's Law of Universal Gravitation and vector addition:

\[ F = G \frac{m_1 m_2}{r^2} \] \[ F_{net} = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos(\theta)} \]

Where:

\( F \) — Gravitational force (N)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
\( m_1, m_2 \) — Masses of the objects (kg)
\( r \) — Distance between centers of mass (m)
\( \theta \) — Angle between force vectors (degrees)

Explanation: The calculator first computes the gravitational force between two objects, then calculates the net force when considering the angle between multiple force vectors.

3. Importance of Net Gravitational Force

Details: Understanding net gravitational force is crucial in astrophysics, orbital mechanics, and any situation where multiple gravitational influences affect an object's motion.

4. Using the Calculator

Tips: Enter masses in kilograms, distance in meters, and angle in degrees (0° for same direction, 180° for opposite directions). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is gravitational force so weak compared to other forces?
A: Gravity is the weakest fundamental force but dominates at large scales because it's always attractive and has infinite range.

Q2: How does distance affect gravitational force?
A: Gravitational force follows an inverse-square law - doubling the distance reduces force to 1/4 of its original value.

Q3: What is the gravitational constant G?
A: G is a fundamental physical constant that determines the strength of gravity in Newton's law of gravitation.

Q4: Can gravitational force be negative?
A: The magnitude is always positive, but the direction can be considered negative in coordinate systems.

Q5: How accurate is this calculator for real-world applications?
A: It's accurate for classical mechanics problems, but general relativity must be considered for extreme precision or strong gravitational fields.