Newton's Law of Universal Gravitation
Newton's law states that every mass attracts every other mass with a force proportional to the product of masses and inversely proportional to the square of distance.
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Force follows inverse-square law: double distance = 1/4 force G = 6.67430×10⁻¹¹ N⋅m²/kg² (CODATA 2018) Surface gravity g depends only on planet mass and radius Escape velocity from Earth is ~11.2 km/s
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Why: Gravity governs planetary motion, satellite orbits, and everyday weight.
How: Enter masses and distance. The calculator computes force, surface gravity, escape velocity, and orbital parameters.
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🔧 Calculation Type
⚙️ Input Parameters
📊 Results
📈 Visualizations
Surface Gravity Comparison
Force vs Distance
📝 Step-by-Step Solution
Gravitational constant: G = 6.674e-11 N⋅m²/kg²
Mass 1: m₁ = 1.000e+3 kg
Mass 2: m₂ = 5.972e+24 kg
Distance: r = 6.371e+6 m
Newton's Law of Universal Gravitation: F = Gm₁m₂/r²
F = (6.674e-11 × 1.000e+3 × 5.972e+24) / 6.371e+6²
→ F = 9.820e+3 N
Gravitational acceleration on m₁: a = Gm₂/r²
→ a = 9.820e+0 m/s²
Gravitational potential energy: U = -Gm₁m₂/r
→ U = -6.256e+10 J
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Newton published the law in Principia (1687); G was first measured by Cavendish in 1798.
— Newton
G is the least precisely known fundamental constant (~1 part in 10⁵).
— NIST CODATA
Escape velocity is √2 times orbital velocity at the same radius.
— Orbital mechanics
ISS orbits at ~400 km; orbital period ~90 min.
— NASA
📋 Key Takeaways
- • Newton's Law of Universal Gravitation: F = Gm₁m₂/r²
- • Gravitational constant G = 6.67430×10⁻¹¹ N⋅m²/kg² (CODATA 2018)
- • Force follows an inverse-square law with distance
- • Surface gravity: g = GM/R² depends only on planet mass and radius
📖 What is Gravitational Force?
Gravitational force is the attractive force between any two objects with mass. It's one of the four fundamental forces of nature and is described by Newton's Law of Universal Gravitation (1687).
Always Attractive
Unlike electric/magnetic forces, gravity always attracts. There's no "negative mass" to create repulsion.
Inverse Square Law
Force decreases with distance squared. Double the distance = 1/4 the force. Triple = 1/9, etc.
Extremely Weak
Gravity is 10³⁶ times weaker than electromagnetism. We notice it only because Earth is so massive.
📐 Gravitational Formulas
Universal Gravitation
F = Gm₁m₂/r²
G = 6.674×10⁻¹¹ N⋅m²/kg²
F = gravitational force (N)
r = distance between centers (m)
Surface Gravity
g = GM/R²
M = mass of planet (kg)
R = radius of planet (m)
g = acceleration due to gravity (m/s²)
Escape Velocity
v_esc = √(2GM/r)
Minimum speed to escape gravity
Earth: ~11.2 km/s
Orbital Velocity
v_orbit = √(GM/r)
T = 2π√(r³/GM) (Kepler's 3rd)
For circular orbit
🌍 Solar System Data
| Body | Mass (kg) | Radius (km) | g (m/s²) | Escape (km/s) |
|---|---|---|---|---|
| Sun | 1.989×10³⁰ | 696,340 | 274 | 617.5 |
| Earth | 5.972×10²⁴ | 6,371 | 9.81 | 11.2 |
| Moon | 7.348×10²² | 1,737 | 1.62 | 2.38 |
| Mars | 6.417×10²³ | 3,390 | 3.72 | 5.03 |
| Jupiter | 1.898×10²⁷ | 69,911 | 24.79 | 59.5 |
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