Tidal Force Calculator Formula

Understand the math behind the tidal force calculator. Each variable explained with a worked example.

Use the Tidal Force Calculator

Formulas Used

Tidal Acceleration

tidal_accel = 2 * 6.674e-11 * source_mass * object_size / pow(distance, 3)

Variables

VariableDescriptionDefault
source_massTidal Source Mass(kg)7.342e+22
distanceDistance to Source(m)384400000
object_sizeObject Size (dr)(m)12742000

How It Works

Tidal Force

Tidal forces arise because gravity varies with distance. The near side of an object feels a stronger pull than the far side.

Formula

a_tidal = 2 G M dr / d cubed

  • *M* = mass of the tidal source
  • *d* = distance from the source
  • *dr* = size of the object being tidally stretched

    • This is the leading term in a Taylor expansion of the gravitational field.

    Worked Example

    Moon's tidal pull across Earth (M = 7.342e22 kg, d = 3.844e8 m, dr = 1.274e7 m).

    source_mass = 7.342e+22distance = 384400000object_size = 12742000
    1. 01a = 2 G M dr / d cubed
    2. 02G M = 6.674e-11 * 7.342e22 = 4.899e12
    3. 03d cubed = (3.844e8)^3 = 5.68e25
    4. 04a = 2 * 4.899e12 * 1.274e7 / 5.68e25
    5. 05a = 2.20e-6 m/s2

    Ready to run the numbers?

    Open Tidal Force Calculator