Tidal Force Calculator
Calculate gravitational tidal forces, differential acceleration, and equilibrium oceanic bulge heights for Earth, celestial moons, and exoplanetary systems.
Select Celestial System Preset:
Orbital & Physical Parameters
e.g. Earth = 5.972e24, Jupiter = 1.898e27
e.g. Moon = 7.342e22, Sun = 1.989e30
Earth radius = 6.371 × 10⁶ m (6,371 km)
Earth-Moon = 3.844 × 10⁸ m (384,400 km)
Tidal Accel
1.099µm/s²
1.099e-6 m/s²
Tidal Bulge
0.21m
21 cm theoretical
Tidal Force
6.56×10¹⁸ N
Bulk integrated force
Lunar Ratio
99.9%
vs Earth-Moon standard
Equilibrium Quadrupolar Bulge Geometry (Antipodal Symmetry)Bulge: 0.21 m
Inverse-Cube Distance Fall-Off Law (a ∝ 1/d³)µm/s² vs Distance
Moon vs. Sun Terrestrial Comparison
While the Sun's direct gravitational pull on Earth is ~178 times stronger than the Moon's, its tidal force is only 46.4% as large because the Sun is 389 times further away (1/389³ ≈ 1/58,900,000).
Lunar Tidal Force on Earth6.57 × 10¹⁸ N
Solar Tidal Force on Earth3.05 × 10¹⁸ N (46%)
Spring Tide Combined (Syzygy)9.62 × 10¹⁸ N (146%)
Neap Tide Net (Quadrature)3.52 × 10¹⁸ N (54%)
Step-by-Step Worked Mathematical Example: Earth-Moon System
Consider the Earth-Moon gravitational interaction at the terrestrial equator with standard astronomical parameters: Primary mass M1 = 5.972 × 1024 kg, Moon mass M2 = 7.342 × 1022 kg, Earth radius R1 = 6.371 × 106 m, and orbital separation d = 3.844 × 108 m.
1. Differential Accel:
a = (2 × G × M₂ × R₁) / d³
a = (2 × 6.6743e-11 × 7.342e22 × 6.371e6) / (3.844e8)³
a = 1.100 × 10⁻⁶ m/s²
2. Bulk Tidal Force:
F = M₁ × a_tidal
F = 5.972e24 kg × 1.100e-6 m/s²
F = 6.57 × 10¹⁸ N
3. Equilibrium Bulge:
h ≈ (a / g) × k₂ × R₁
h ≈ (1.10e-6 / 9.807) × 0.30 × 6.371e6
h ≈ 0.214 meters
Frequently Asked Questions (Scientific Guide)
Scientific References & Standards
NOAA Tides & Currents - Physical Oceanography & Tidal Theory
Official educational compendium of gravitational harmonic constituents and hydrodynamic tidal measurement.
NASA Jet Propulsion Laboratory - Planetary Satellite Physical Parameters
Precise astrodynamic masses, radii, and orbital semi-major axes for Solar System moons and planets.
Cambridge University Press - Geodynamics: Tidal Deformation and Rheology (Turcotte & Schubert)
Foundational planetary physics text covering Love numbers, elastic tidal deformation, and quadrupolar potentials.
International Astronomical Union (IAU) - Fundamental Astronomical Constants
Internationally standardized gravitational constant (G), planetary ephemerides, and celestial reference frames.
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Quick Tips
- 1Use consistent units throughout calculations
- 2Consider significant figures in results
- 3Document experimental conditions
- 4Verify results with control calculations