Gravitational Force Calculator
Newton's Law of Universal Gravitation
Calculation Mode
Gravitational Parameters
Gravitational System Visualization
Gravitational Parameters
Force vs Distance
Force vs Mass
Real-World Gravitational Force Examples
Click on an example to use its values in the calculator
| System | Mass 1 | Mass 2 | Distance | Force |
|---|
Gravity on Different Celestial Bodies
Surface gravity (g) for a 70 kg person on different planets and moons
| Celestial Body | Mass (kg) | Radius (km) | Surface g (m/s²) | Weight of 70kg (N) |
|---|
Interesting Facts
Newton's Discovery
Newton formulated the law of universal gravitation in 1687, inspired by an apple falling from a tree
Earth-Moon Force
The gravitational force between Earth and Moon is about 1.98 × 10²⁰ N - enough to keep the Moon in orbit
Sun-Earth Force
The Sun exerts about 3.54 × 10²² N of force on Earth, keeping it in its 365-day orbit
Black Holes
Black holes have such strong gravity that not even light can escape their gravitational pull
Understanding Newton's Law of Universal Gravitation
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.
- Formula: F = G(m₁m₂)/r²
- Universal: Applies to all masses, from atoms to galaxies
- Inverse-square law: Force decreases with the square of distance
- Published: 1687 in Newton's "Principia Mathematica"
Key Formulas
The fundamental equations of gravitational physics:
- Gravitational Force: F = G(m₁m₂)/r²
- Gravitational Constant: G = 6.674 × 10⁻¹¹ N·m²/kg²
- Surface Gravity: g = GM/r²
- Weight: W = mg
- Orbital Velocity: v = √(GM/r)
- Orbital Period: T = 2π√(r³/GM)
- Escape Velocity: v_esc = √(2GM/r)
Gravitational Constant (G)
The gravitational constant is a fundamental physical constant:
- Value: G = 6.674 × 10⁻¹¹ N·m²/kg²
- Very small: Gravity is the weakest of the four fundamental forces
- Universal: Same value throughout the universe
- Measured: First measured by Henry Cavendish in 1798
Surface Gravity
Gravitational acceleration at the surface of a celestial body:
- Formula: g = GM/r²
- Earth: g = 9.81 m/s²
- Moon: g = 1.62 m/s² (1/6 of Earth)
- Mars: g = 3.72 m/s² (0.38 of Earth)
- Jupiter: g = 24.79 m/s² (2.53 of Earth)
Orbital Mechanics
Gravitational force governs the motion of celestial bodies:
- Orbital velocity: v = √(GM/r)
- Orbital period: T = 2π√(r³/GM) (Kepler's Third Law)
- Escape velocity: v_esc = √(2GM/r)
- Geostationary orbit: r = 42,164 km from Earth's center
Real-World Applications
- Space Exploration: Calculating trajectories and orbits
- Satellite Systems: GPS, communication, weather satellites
- Astronomy: Understanding planetary motion and galaxy formation
- Geophysics: Studying Earth's gravitational field
- Navigation: Determining position using gravity
Limitations & Extensions
Newton's law has important limitations:
- Strong gravity: Fails near black holes and neutron stars
- High speeds: Doesn't account for relativistic effects
- General Relativity: Einstein's theory extends Newton's law
- Gravitational waves: Predicted by Einstein, detected in 2015
Key Takeaways
F = Gm₁m₂/r²
Gravitational force is proportional to masses and inversely proportional to distance squared
Universal Law
Applies to all masses in the universe, from atoms to galaxies
Inverse-Square
Doubling distance reduces force to 1/4, tripling reduces to 1/9
Orbital Motion
Gravitational force provides centripetal force for orbits
Understanding Newton's Law of Universal Gravitation
Newton's Law of Universal Gravitation is one of the most fundamental laws in physics. It describes the gravitational attraction between any two masses in the universe. From the fall of an apple to the orbit of planets, this law governs the motion of celestial bodies and is essential for space exploration, satellite systems, and understanding the universe.
Gravitational Force Formulas
Key formulas for gravitational physics:
- Gravitational Force: F = G(m₁m₂)/r²
- Surface Gravity: g = GM/r²
- Weight: W = mg
- Orbital Velocity: v = √(GM/r)
- Orbital Period: T = 2π√(r³/GM)
- Escape Velocity: v_esc = √(2GM/r)
Key Relationships
Important relationships in gravitational physics:
- F ∝ m₁m₂: Force is directly proportional to the product of masses
- F ∝ 1/r²: Force is inversely proportional to the square of distance
- g ∝ M/r²: Surface gravity is proportional to mass and inversely to radius squared
- T² ∝ r³: Kepler's Third Law - orbital period squared proportional to radius cubed
Real-World Examples
Gravitational force in our universe:
- Earth-Moon: F ≈ 1.98 × 10²⁰ N, distance 384,400 km
- Earth-Sun: F ≈ 3.54 × 10²² N, distance 149.6 million km
- Two people: F ≈ 10⁻⁷ N at 1 meter distance (negligible)
- ISS: Orbits at 408 km altitude, experiencing 90% of Earth's gravity
Using This Calculator
Follow these steps:
- Step 1: Select calculation mode (Force, Mass 1, Mass 2, or Distance)
- Step 2: Enter the known values with appropriate units
- Step 3: Verify the gravitational constant (G = 6.674 × 10⁻¹¹ N·m²/kg²)
- Step 4: Click "Calculate" to see all gravitational parameters
- Step 5: View gravitational system visualization
- Step 6: See force vs distance and force vs mass charts
- Step 7: Check the Examples tab for real-world cases
- Step 8: Read the Guide tab to learn gravitational physics theory
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