Gravitational Force Calculator
Calculate gravitational attraction force between two masses.
Quadratic Equation Solver (ax² + bx + c = 0)
About Gravitational Force Calculator
The Universal Gravitation ($F = G \frac{m_1 m_2}{r^2}$) & Orbital Mechanics Calculator computes mutual attractive gravity between two masses, surface gravitational acceleration ($g = G M / R^2$), orbital velocity ($v = \sqrt{GM/r}$), and escape velocity ($v_{esc} = \sqrt{2GM/R}$).
How to Use Gravitational Force Calculator
Step 1
Pick a celestial preset (e.g. Earth + Satellite) or enter custom masses and separation distance.
Step 2
Review computed mutual gravitational force in Newtons, orbital speed, and escape velocity.
Step 3
Click "Copy Gravity Solution".
Practical Use Cases for Gravitational Force Calculator
Astrophysics & Planetary Surface Gravity Calculations
Compute surface gravity ($g$), weight on other planets (Moon, Mars, Jupiter), and atmospheric escape velocities for space missions.
Satellite Low Earth Orbit (LEO) & Geostationary Velocity Sizing
Calculate required orbital velocities and orbital periods ($T = 2\pi \sqrt{r^3/GM}$) for communication satellites.
Input & Output Examples
Calculating Earth-Moon Gravitational Attraction
Mass 1 (Earth): `5.972 × 10²⁴ kg`, Mass 2 (Moon): `7.342 × 10²² kg`, Distance: `3.844 × 10⁸ m`
Gravitational Force ($F$): `1.982 × 10²⁰ Newtons` | Moon Orbital Speed: `1,018 m/s (3,665 km/h)` | Orbital Period: `27.32 days`
Key Features & Performance
- ✓Solves: Newton's Law of Universal Gravitation ($G m_1 m_2 / r^2$), Planet Surface Acceleration ($g$), Orbital Speed, Escape Velocity.
- ✓Preloaded Celestial Presets: Sun, Earth, Moon, Mars, Jupiter, Venus, Saturn, ISS Orbit, Geostationary Orbit.
- ✓Unit support: Kilograms, Solar Masses, Earth Masses, Meters, Kilometers, Astronomical Units (AU), Light Years.
- ✓100% Client-Side astrophysics engine.
- ✓1-Click Copy gravitational report.
Key Terminology & Definitions
Gravitational Constant ($G$)
The fundamental physical constant of universal gravitation, equal to $6.67430 \times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$.
Escape Velocity ($v_{esc}$)
The minimum speed an unpropelled object must attain to break completely free from the gravitational pull of a massive celestial body ($v_{esc} = \sqrt{2GM/R}$).