Gravitational Force, Surface Gravity & Escape Velocity Calculator

Astrophysics & Orbital Mechanics: Newton's Law of Gravitation

• Inverse Square Law: Gravitational attraction is proportional to the product of both masses and inversely proportional to the square of the distance (doubling distance slashes gravitational pull by 75%).

• The √(2) Escape Velocity Rule: A spacecraft in a circular orbit at speed v_orbit only needs to accelerate by a factor of √(2) ≈ 1.414 (a 41.4% speed increase) to attain escape velocity and permanently break orbit.

How to Use This Calculator

Enter your Astronomical System Preset — choose from Earth & Moon (m1=5.972e24 kg, m2=7.348e22 kg, r=384,400 km), Sun & Earth (m1=1.989e30 kg, m2=5.972e24 kg, r=1.496e8 km), Earth Surface & 70 kg Human (m1=5.972e24 kg, m2=70 kg, r=6,371 km), Primary Mass (m₁ [kg]) (e.g. 5.972e24 (Earth mass = 5.972 × 10²⁴ kg)), Secondary Mass (m₂ [kg]) (e.g. 7.348e22 (Moon mass = 7.348 × 10²² kg)), and Center-to-Center Distance (r [Kilometers - km]) (e.g. 384,400 (384,400 km Earth-Moon orbit)). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Newton's Law of Universal Gravitation \& Orbital equations:

Gravitational Attraction: F = G (m_1 m_2) / (r^2) (G = 6.67430 × 10^-11 N·m^2/kg^2)

Gravitational Acceleration: g = (G m_1) / (r^2) (m/s^2)

Circular Orbital Velocity: v_orbit = √((G m_1) / (r)) (m/s)

Escape Velocity: v_escape = √((2 G m_1) / (r)) = v_orbit × √(2)

Worked Example

For example, calculating the gravitational force between Earth) and the Moon) at an orbital distance of \: Gravitational Attraction Force is 1.9820 × 10^20 Newtons (4.455 × 10^19 lbf). Lunar orbital velocity is \, with an escape velocity of \.

Understanding Your Result

Force in Newtons (N): 1 N = 1 kg·m/s². Reference values: 1 kg object at Earth's surface weighs 9.81 N, atmospheric pressure 101,325 Pa (N/m²). Pressure benchmarks: car tire 30–35 psi (207–241 kPa), blood pressure systolic 120 mmHg (16 kPa), deep sea at 3,000m depth ~300 atm (30 MPa). Torque = Force × moment arm length — doubling the wrench length doubles the torque for the same applied force. Always verify whether gauge or absolute pressure is required for the application.