Tidal Force Calculator Formula

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

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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

    Frequently Asked Questions

    Why does tidal force scale as 1/d cubed instead of 1/d squared?

    Tidal force is the difference in gravity across the object. Differentiating the inverse-square law gives an inverse-cube dependence, so the tidal effect falls off faster than gravity itself.

    Can tidal forces destroy objects?

    Yes. If a body ventures within the Roche limit, tidal forces exceed its self-gravity and can tear it apart (forming rings, for example).

    Is the Sun or Moon more important for Earth's tides?

    The Moon dominates Earth's tides because tidal force depends on the cube of distance. The Moon is much closer than the Sun, more than offsetting its lower mass.

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