Universal Gravitation Calculator - Newton's Law & Orbital Mechanics

Calculate gravitational attraction force between any two masses, surface gravity acceleration (g), orbital velocity, and escape speed using Newton's Law of Universal Gravitation.

⚙️ Configuration & Inputs

Astronomical Preset

Mass 1 (kg) - Central Body Scientific notation accepted (e.g., 5.972e24 for Earth)

Mass 2 (kg) - Orbiting / Second Body e.g., 7.348e22 for Moon, 70 for human

Distance between centers r (km) Center-to-center distance in kilometers

📊 Results & Analysis

Gravitational Force (F) 1.982 × 10²⁰ N 4.456 × 10¹⁹ lbf

Orbital Velocity (v_orb) 1,018 m/s 3,665 km/h (2,277 mph)

Orbital Period (T) 27.32 days 655.7 hours

Escape Velocity (v_esc) 1.44 km/s 3,221 mph (from orbit)

Acceleration on Mass 2 (g) 0.00270 m/s² Acc on Mass 1: 3.32 × 10⁻⁵ m/s²

Gravitational Constant (G) 6.6743 × 10⁻¹¹ N·m²/kg² (CODATA 2018)

Newton's Law of Universal Gravitation & Orbital Mechanics

Sir Isaac Newton published the Law of Universal Gravitation in 1687, demonstrating that every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

1. Gravitational Force Formula

F = G × (m₁ × m₂) / r²

F: Gravitational attraction force (Newtons, N).
G: Universal Gravitational Constant = 6.67430 × 10⁻¹¹ N·m²/kg².
m₁, m₂: Masses of body 1 and body 2 (kilograms, kg).
r: Distance between the centers of mass (meters, m).

2. Orbital Velocity & Escape Speed

For a smaller mass orbiting a much larger central mass in a stable circular orbit:

Circular Orbital Speed: v_orb = √(G × M / r)
Orbital Period (Kepler's 3rd Law): T = 2π × √(r³ / (G × M))
Escape Velocity: v_esc = √(2 × G × M / r) = √2 × v_orb ≈ 1.414 × v_orb

Frequently Asked Questions

Gravitational force propagates outward in a three-dimensional sphere. Because the surface area of a sphere scales with 4πr², the energy and flux per unit area dilute by a factor of 1/r² as distance increases.

Orbital velocity is the precise horizontal speed required to keep a satellite in stable circular orbit where gravitational pull equals centripetal acceleration. Escape velocity is the minimum speed needed to break free entirely from the gravitational field without further propulsion, which is exactly √2 (41.4%) faster than circular orbital speed at that altitude.

By setting m₁ to Earth's mass (5.972 × 10²⁴ kg) and r to Earth's mean radius (6,371 km = 6.371 × 10⁶ m): g = (G × M) / R² = (6.6743 × 10⁻¹¹ × 5.972 × 10²⁴) / (6.371 × 10⁶)² ≈ 9.818 m/s².