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Calcimator

Gravitational Force Calculator

Newton's law of universal gravitation: F = Gm1m2/r².

Inputs

Results

Gravitational Force (N)

687.37

Acceleration of m₂ (m/s²)

9.82

Grav. Potential (J/kg)-62,560,200
Escape Velocity (m/s)11,185.7
Orbital Velocity (m/s)7,909.5
Orbital Period (s)5,061.02
Acceleration10%
How to Use This Calculator
  1. Enter mass 1 (kg) — e.g., Earth = 5.972e24 kg — and mass 2 (kg) — e.g., a person = 70 kg.
  2. Enter the center-to-center distance (m) between the two masses.
  3. Read gravitational force (N) and the acceleration of mass 2 (m/s2).
  4. Review gravitational potential (J/kg), escape velocity (m/s), and orbital velocity (m/s).
  5. Use orbital period (s) to understand the circular orbit at this distance.

What each input means

Mass 1 (kg)
Primary mass (e.g., Earth = 5.972e24 kg).
Mass 2 (kg)
Secondary mass (e.g., a person = 70 kg).
Distance (m)
Center-to-center distance (Earth radius = 6.371e6 m).

What each result means

Gravitational Force (N)
F = Gm₁m₂/r².
Acceleration of m₂ (m/s²)
g = F/m₂. Surface gravity if m₂ is a test mass.
Grav. Potential (J/kg)
Φ = -Gm₁/r. Potential energy per unit mass.
Escape Velocity (m/s)
vₑ = √(2Gm₁/r).
Orbital Velocity (m/s)
vₒ = √(Gm₁/r) for circular orbit.
Orbital Period (s)
T = 2πr/vₒ for circular orbit.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Mass 1 (kg) = 5.972e+24, Mass 2 (kg) = 70, Distance (m) = 6371000 = 3 input(s) provided
  2. Calculate Gravitational Force
    Gravitational Force = parseFloat(force.toPrecision(6))
    687.367 = 687.367
  3. Calculate Acceleration of m₂
    Acceleration of m₂ = parseFloat(acceleration2.toPrecision(6))
    9.81953 = 9.81953
  4. Calculate Grav. Potential
    Grav. Potential = parseFloat(gravPotential.toPrecision(6))
    -62560200 = -62560200
  5. Calculate Escape Velocity
    Escape Velocity = parseFloat(escapeVelocity.toPrecision(6))
    11185.7 = 11185.7

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