T TibCal

Gravity Calculator

Calculate gravity calculator calculate universal gravitational attraction force F between two masses m1 and m2 at distance r using Newton's law (F = G * m1 * m2 / r^2). Accurate physics formulas and unit conversions for engineers, students & technicians.

Calculate Universal Gravitational Force

Enter your physical parameters below to compute verified gravity metrics.

Mass of first body in kilograms (e.g. Earth = 5.972e24 kg).
Mass of second body in kilograms (e.g. human = 70.0 kg).
Distance between centers of mass in meters (e.g. Earth radius = 6371000 m).

Calculation Results

Primary Metric Output --
Metric Breakdown 1 --
Metric Breakdown 2 --
Metric Breakdown 3 --
Metric Breakdown 4 --
Metric Breakdown 5 --
Mathematical Standard --

Calculated using verified physical methodology: Universal Gravitation Law: F = G \m_1 m_2 / r^2
Gravitational Constant: G = 6.67430 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2

*Note: Results represent mutual attractive force acting along mass centers.

Quick Summary

The Gravity Calculator applies Newton's Law of Universal Gravitation ($F = G \m_1 m_2 / r^2$) to compute mutual gravitational attraction between any two masses across Newtons, kN, lbf, and dynes.

Formula Explanation

Universal Gravitation Law: F = G \m_1 m_2 / r^2
Gravitational Constant: G = 6.67430 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2

How It Works

The Gravity Calculator multiplies universal constant $G = 6.67430 \times 10^{-11}$ by masses $m_1$ and $m_2$, dividing by squared distance ($r^2$). It outputs mutual force ($F$) and surface gravity acceleration ($g = G \m_1 / r^2$).

Step-by-Step Worked Example

Practical Problem: Calculate gravitational force between Earth ($m_1 = 5.972\times 10^{24}\text{ kg}$) and a 70.0 kg person standing on Earth's surface ($r = 6.371\times 10^6\text{ meters}$).

  1. Step 1: Identify Input Parameters: $m_1 = 5.972\times 10^{24}\text{ kg}$, $m_2 = 70.0\text{ kg}$, $r = 6.371\times 10^6\text{ m}$, $G = 6.67430\times 10^{-11}$.
  2. Step 2: Square Distance ($r^2$): $r^2 = (6,371,000)^2 = 4.058964 \times 10^{13}\text{ m}^2$.
  3. Step 3: Multiply Mass Product ($m_1 m_2$): $m_1 m_2 = (5.972\times 10^{24}) \times 70 = 4.1804 \times 10^{26}\text{ kg}^2$.
  4. Step 4: Execute Universal Gravitation Law Formula: $F = (6.67430\times 10^{-11}) \times \frac{4.1804\times 10^{26}}{4.058964\times 10^{13}} = 687.35\text{ Newtons (N)}$.
  5. Step 5: Convert and Interpret Imperial & Acceleration Outputs: Force $F = 687.35\text{ N} = 154.52\text{ lbf}$. Surface Acceleration $g = \687.35 / 70 = 9.819\text{ m/s}^2$.

Real-World Calculation Examples

Scenario 1: Human Weight on Earth Surface

Parameters: $m_1 = 5.972\times 10^{24}\text{ kg}$, $m_2 = 70\text{ kg}$, $r = 6,371,000\text{ m}$

Result: $F = 687.35\text{ N}$ (154.52 lbf, 0.69 kN). Earth gravity weight.

Scenario 2: Earth-Moon Mutual Gravitational Pull

Parameters: $m_1 = 5.972\times 10^{24}\text{ kg}$, $m_2 = 7.348\times 10^{22}\text{ kg}$, $r = 384,400,000\text{ m}$

Result: $F = 1.982\times 10^{20}\text{ N}$ (198.2 Exanewtons). Tidal orbit attraction.

Scenario 3: Sun-Earth Gravitational Orbit Force

Parameters: $m_1 = 1.989\times 10^{30}\text{ kg}$ (Sun), $m_2 = 5.972\times 10^{24}\text{ kg}$, $r = 1.496\times 10^{11}\text{ m}$

Result: $F = 3.542\times 10^{22}\text{ N}$. Solar gravitational orbit force.

Scenario 4: International Space Station Orbit

Parameters: $m_1 = 5.972\times 10^{24}\text{ kg}$, $m_2 = 450,000\text{ kg}$ (ISS), $r = 6,771,000\text{ m}$ (400 km orbit)

Result: $F = 3,912,284\text{ N}$ (3.91 MN). Orbital gravitational pull.

Key Benefits of Using This Calculator

Inverse-Square Law Precision

Accurately demonstrates $F \propto 1/r^2$ distance sensitivity for astrophysics.

Local Acceleration Field Output

Computes local gravitational field acceleration $g = G m_1 / r^2$ in $\text{m/s}^2$.

Multi-Unit Readouts

Outputs force in Newtons, kilonewtons (kN), lbf, and dynes.

100% Free & Client-Side

Executes locally in your browser with zero latency or web server transmission.

Frequently Asked Questions (FAQ)

What is Newton's Law of Universal Gravitation?

Newton's Law states that every particle attracts every other particle with a force proportional to mass product and inversely proportional to square distance: F = G * m1 * m2 / r².

What is the Newtonian constant of gravitation G?

G = 6.67430 x 10^-11 N·m²/kg² (CODATA 2018 value).

What is the inverse-square law?

The inverse-square law means doubling distance r reduces gravitational attraction force to one-fourth (1/4th) of its original magnitude.

How calculates surface gravity g for any planet?

g = G * M_planet / R_planet², dividing universal constant by planet mass and squared radius.

How does General Relativity view gravity differently?

Einstein's General Relativity models gravity not as an attractive force, but as spacetime curvature caused by mass-energy density.

What is the SI unit of gravitational force?

The SI unit of force is the Newton (N).

How converts Newtons to lbf?

Multiply Newtons by 0.224809 to get pound-force (lbf) (e.g. 687 N = 154.5 lbf).

Why do astronauts in ISS feel weightless if gravity is 90% of Earth's?

Because both the ISS and astronauts are in continuous free fall around Earth at orbital speed (~7.6 km/s), eliminating contact normal force.

What is Cavendish's experiment?

Henry Cavendish measured G in 1798 using a torsion balance to measure lead sphere attraction, effectively "weighing the Earth".

Can gravitational force be repulsive?

In classical mechanics, gravity is purely attractive; cosmological dark energy causes cosmic acceleration expansion, acting as repulsive cosmic pressure.

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